diff --git a/.github/workflows/fitbot.yml b/.github/workflows/fitbot.yml
index 9f8e93a79b..b2282b200b 100644
--- a/.github/workflows/fitbot.yml
+++ b/.github/workflows/fitbot.yml
@@ -10,7 +10,7 @@ on:
 env:
   N3FIT_MAXNREP: 20 # total number of replicas to fit
   POSTFIT_NREP: 16 # requested replicas for postfit
-  REFERENCE_SET: NNBOT-03c99fd73-2024-07-26 # reference set for exact results
+  REFERENCE_SET: NNBOT-06f20cf6a-2024-07-26 # reference set for exact results
   STABLE_REFERENCE_SET: NNBOT-c0f99b7b3-2024-02-28 # reference set for last tag
   CONDA_PY: 312
   PYTHONHASHSEED: "0"
diff --git a/doc/sphinx/source/tutorials/polarized_fits.rst b/doc/sphinx/source/tutorials/polarized_fits.rst
index 4f1e698a87..37579a473b 100644
--- a/doc/sphinx/source/tutorials/polarized_fits.rst
+++ b/doc/sphinx/source/tutorials/polarized_fits.rst
@@ -33,6 +33,42 @@ as a boundary condition while ``n_std`` specifies the shift in terms of the stan
 deviation to be applied to the PDF central values. If ``n_std=0.0`` then the
 PDF central values will be used to constrain their polarized counterparts.
 
+.. note::
+
+   This will also be the PDF set to be used to compute observable predictions
+   during the fit.
+
+Instead, the unpolarized PDF set to be used to compute the `t0` covariance matrix need to be specified under the ``datacuts`` entry:
+
+.. code-block:: yaml
+
+  ...
+  datacuts:
+    t0pdfset: NNPDFpol11_100   # PDF set to generate t0 covmat
+    unpolarized_bc: NNPDF40_nnlo_pch_as_01180
+    q2min: 1.00                # Q2 minimum
+    w2min: 4.00                # W2 minimum
+  ...
+
+And if a theory covariance matrix is included in the fit
+(see :ref:`how to include a theory covariance matrix in a fit <_thcov_tutorial>`
+for more details), then the unpolarized PDF set also needs to be specified in the
+``theorycovmatconfig`` together with the polarized PDF to be used:
+
+.. code-block:: yaml
+
+  # Define the unpolarized PDF set to be used to compute predictions with validphys actions
+  ...
+  theorycovmatconfig:
+    point_prescription: '7 point'
+    theoryids:
+      from_: scale_variation_theories
+    pdf: NNPDFpol11_100
+    unpolarized_bc: NNPDF40_nnlo_pch_as_01180
+    use_thcovmat_in_fitting: true
+    use_thcovmat_in_sampling: true
+  ...
+
 Given that polarized fits require different fitting bases and different theory
 constraints, the fields under the ``fitting`` key require some adjustments.
 Specifically:
@@ -41,7 +77,7 @@ Specifically:
 
   ...
   fitting:
-    fitbasis: POLARIZED_EVOL
+    fitbasis: POLARIZED_EVOL_CMP
     sum_rules: TSR
     basis:
     - {fl: sng, trainable: false, smallx: [1.094, 1.118], largex: [1.46, 3.003]}
@@ -89,8 +125,8 @@ and then followed by the basis type (for example ``EVOL`` or ``FLAVOUR``).
 
    where the subscript :math:`r` indicates that the random seed per replica is always
    different. In practice, when imposing the positivity at the level of PDFs, we enforce
-   the constraints on the flavor combination :math:`\left( \Delta f_i + \Delta \bar{f}_i \right)`,
-   that is :math:`(\Delta) \mathcal{F}_k \equiv (\Delta) f_k + (\Delta) \bar{f}_k`.
+   the constraints on the individual flavor :math:`\Delta f_i` (or respectively :math:`\Delta \bar{f}_i`),
+   that is :math:`(\Delta) \mathcal{F}_k \equiv (\Delta) f_k` (or respectively :math:`(\Delta) \mathcal{F}_k \equiv (\Delta) \bar{f}_k`).
 
 Once the runcard is ready, the user can follow the guidelines :ref:`here <run-n3fit-fits>`
 to set up and run fits.
@@ -106,8 +142,6 @@ can simply be done by supplementing a flag to the ``evolven3fit``:
 
   evolven3fit evolve $runcard_folder --use_polarized
 
-Alternatively, the user can explicitly specify the path to the EKO using the flag ``--load``.
-
 
 Comparing polarized fits
 ------------------------
diff --git a/extra_tests/regression_fits/central_16.exportgrid b/extra_tests/regression_fits/central_16.exportgrid
index 8a1c7ad742..f2d14d0ed6 100644
--- a/extra_tests/regression_fits/central_16.exportgrid
+++ b/extra_tests/regression_fits/central_16.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, -2.312350034713745, 0.09160042554140091, 0.06509511172771454, 0.06514225900173187,
-  -16.440481185913086, 0.06529276072978973, 0.06524708867073059, 0.09136024117469788,
-  -2.3123505115509033, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.239459753036499, 0.09346988052129745, 0.06590303778648376, 0.06595669686794281,
-  -16.451295852661133, 0.06612314283847809, 0.06607125699520111, 0.09320636838674545,
-  -2.239459753036499, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.168872833251953, 0.09553579986095428, 0.06686369329690933, 0.06692465394735336,
-  -16.460674285888672, 0.06710875779390335, 0.06704993546009064, 0.09524670988321304,
-  -2.168872833251953, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1005163192749023, 0.09779838472604752, 0.06797530502080917, 0.06804462522268295,
-  -16.468524932861328, 0.06824829429388046, 0.06818155199289322, 0.09748125821352005,
-  -2.1005163192749023, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.0343191623687744, 0.10025887191295624, 0.06923703849315643, 0.06931591033935547,
-  -16.474733352661133, 0.06954126060009003, 0.0694655105471611, 0.09991100430488586,
-  -2.0343191623687744, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9702123403549194, 0.10291850566864014, 0.07064808905124664, 0.07073770463466644,
-  -16.47918701171875, 0.07098713517189026, 0.07090127468109131, 0.10253695398569107,
-  -1.9702123403549194, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9081295728683472, 0.10577918589115143, 0.0722079649567604, 0.07230991870164871,
-  -16.481761932373047, 0.07258602231740952, 0.07248858362436295, 0.10536067932844162,
-  -1.9081295728683472, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8480072021484375, 0.10884266346693039, 0.07391618937253952, 0.07403206080198288,
-  -16.482332229614258, 0.07433779537677765, 0.07422732561826706, 0.1083836778998375,
-  -1.8480072021484375, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7897816896438599, 0.1121116429567337, 0.07577284425497055, 0.07590459287166595,
-  -16.480745315551758, 0.07624316215515137, 0.07611792534589767, 0.11160825937986374,
-  -1.7897816896438599, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7333940267562866, 0.11558856070041656, 0.07777777314186096, 0.07792755216360092,
-  -16.476865768432617, 0.07830261439085007, 0.07816068828105927, 0.11503656208515167,
-  -1.7333940267562866, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6787846088409424, 0.11927653104066849, 0.07993127405643463, 0.08010155707597733,
-  -16.470521926879883, 0.08051712065935135, 0.08035627752542496, 0.11867120116949081,
-  -1.6787846088409424, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6258968114852905, 0.12317885458469391, 0.08223368227481842, 0.0824272632598877,
-  -16.461549758911133, 0.08288782089948654, 0.08270559459924698, 0.12251511216163635,
-  -1.6258968114852905, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5746759176254272, 0.1272994577884674, 0.08468583226203918, 0.08490587770938873,
-  -16.44975471496582, 0.08541641384363174, 0.08521004021167755, 0.12657169997692108,
-  -1.5746761560440063, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5250688791275024, 0.1316421777009964, 0.08728823065757751, 0.08753836154937744,
-  -16.434951782226562, 0.08810444921255112, 0.08787074685096741, 0.13084425032138824,
-  -1.5250688791275024, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.477023959159851, 0.13621161878108978, 0.09004191309213638, 0.09032627195119858,
-  -16.41691780090332, 0.09095407277345657, 0.09068949520587921, 0.13533678650856018,
-  -1.477023720741272, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4304908514022827, 0.141012504696846, 0.09294797480106354, 0.09327118843793869,
-  -16.39544105529785, 0.09396766126155853, 0.09366825222969055, 0.14005343616008759,
-  -1.4304908514022827, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.385421872138977, 0.14604991674423218, 0.09600746631622314, 0.09637483954429626,
-  -16.370275497436523, 0.09714765101671219, 0.09680891782045364, 0.1449984610080719,
-  -1.385421633720398, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.3417693376541138, 0.15132947266101837, 0.0992218405008316, 0.09963937848806381,
-  -16.341156005859375, 0.10049714148044586, 0.10011403262615204, 0.15017685294151306,
-  -1.3417695760726929, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.2994883060455322, 0.1568576842546463, 0.10259310156106949, 0.10306763648986816,
-  -16.30780792236328, 0.10401991009712219, 0.10358680039644241, 0.15559415519237518,
-  -1.2994885444641113, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.2585346698760986, 0.16263951361179352, 0.10612145811319351, 0.10666071623563766,
-  -16.26995086669922, 0.10771821439266205, 0.10722877085208893, 0.16125445067882538,
-  -1.2585349082946777, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.2188658714294434, 0.16868260502815247, 0.10980942845344543, 0.11042223125696182,
-  -16.227243423461914, 0.11159690469503403, 0.11104399710893631, 0.16716435551643372,
-  -1.2188658714294434, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.180439829826355, 0.17499376833438873, 0.11365848034620285, 0.11435475945472717,
-  -16.179363250732422, 0.11565990000963211, 0.11503565311431885, 0.17332960665225983,
-  -1.1804401874542236, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.1432173252105713, 0.18158017098903656, 0.11766988784074783, 0.11846096068620682,
-  -16.125946044921875, 0.11991144716739655, 0.1192069724202156, 0.17975609004497528,
-  -1.1432170867919922, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.1071584224700928, 0.1884496659040451, 0.1218452975153923, 0.12274394929409027,
-  -16.06659507751465, 0.1243564710021019, 0.12356189638376236, 0.18645022809505463,
-  -1.1071586608886719, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.072226643562317, 0.19561059772968292, 0.12618641555309296, 0.1272072196006775,
-  -16.000900268554688, 0.12900029122829437, 0.12810459733009338, 0.19341908395290375,
-  -1.072226643562317, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.0383846759796143, 0.2030712217092514, 0.13069431483745575, 0.13185366988182068,
-  -15.928424835205078, 0.13384810090065002, 0.13283905386924744, 0.2006690502166748,
-  -1.0383846759796143, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.0055973529815674, 0.21084041893482208, 0.13537031412124634, 0.13668684661388397,
-  -15.848674774169922, 0.1389058530330658, 0.1377698928117752, 0.2082073837518692,
-  -1.005597472190857, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.9738302826881409, 0.21892735362052917, 0.1402152180671692, 0.1417100429534912,
-  -15.761154174804688, 0.14417949318885803, 0.14290159940719604, 0.21604114770889282,
-  -0.9738302826881409, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.9430503845214844, 0.22734157741069794, 0.14522980153560638, 0.14692673087120056,
-  -15.66532039642334, 0.1496756672859192, 0.14823928475379944, 0.22417782247066498,
-  -0.9430503845214844, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.913224995136261, 0.23609232902526855, 0.15041379630565643, 0.15233977138996124,
-  -15.560587882995605, 0.15540069341659546, 0.1537875235080719, 0.23262420296669006,
-  -0.913224995136261, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.8843229413032532, 0.24519003927707672, 0.15576733648777008, 0.15795284509658813,
-  -15.44633960723877, 0.1613619476556778, 0.15955199301242828, 0.24138808250427246,
-  -0.8843229413032532, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.8563143014907837, 0.25464460253715515, 0.1612893044948578, 0.1637687385082245,
-  -15.321911811828613, 0.16756661236286163, 0.1655379682779312, 0.2504764795303345,
-  -0.8563141226768494, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.829169511795044, 0.26446613669395447, 0.16697794198989868, 0.16979002952575684,
-  -15.186601638793945, 0.1740221530199051, 0.17175093293190002, 0.2598963677883148,
-  -0.829169511795044, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.8028602600097656, 0.2746649980545044, 0.17283080518245697, 0.17601925134658813,
-  -15.03965950012207, 0.18073631823062897, 0.17819668352603912, 0.26965445280075073,
-  -0.8028601408004761, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.777358889579773, 0.28525131940841675, 0.178844153881073, 0.18245817720890045,
-  -14.880290031433105, 0.18771709501743317, 0.18488119542598724, 0.27975714206695557,
-  -0.7773590087890625, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.7526385188102722, 0.29623475670814514, 0.18501289188861847, 0.18910779058933258,
-  -14.707647323608398, 0.19497205317020416, 0.19181005656719208, 0.29020971059799194,
-  -0.7526385188102722, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.7286735773086548, 0.3076251447200775, 0.19133077561855316, 0.1959686279296875,
-  -14.52083969116211, 0.20250926911830902, 0.19898952543735504, 0.3010173738002777,
-  -0.7286735773086548, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.7054398655891418, 0.3194313645362854, 0.19778969883918762, 0.20304013788700104,
-  -14.318920135498047, 0.21033670008182526, 0.20642586052417755, 0.3121839463710785,
-  -0.7054398655891418, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.6829124689102173, 0.3316616117954254, 0.20437924563884735, 0.21032018959522247,
-  -14.100908279418945, 0.2184615433216095, 0.21412493288516998, 0.3237117826938629,
-  -0.6829124689102173, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.6610686182975769, 0.34432318806648254, 0.21108713746070862, 0.2178056538105011,
-  -13.865755081176758, 0.22689105570316315, 0.22209316492080688, 0.33560195565223694,
-  -0.6610686182975769, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.6398864388465881, 0.3574219048023224, 0.2178981900215149, 0.22549130022525787,
-  -13.612377166748047, 0.23563171923160553, 0.23033684492111206, 0.34785357117652893,
-  -0.6398864388465881, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.619344174861908, 0.37096157670021057, 0.2247939258813858, 0.23336954414844513,
-  -13.339654922485352, 0.24468879401683807, 0.2388620525598526, 0.3604629635810852,
-  -0.619344174861908, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.599422037601471, 0.38494396209716797, 0.23175272345542908, 0.24143047630786896,
-  -13.046436309814453, 0.25406667590141296, 0.2476751208305359, 0.37342363595962524,
-  -0.5994221568107605, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.5801003575325012, 0.399368017911911, 0.2387489229440689, 0.24966096878051758,
-  -12.731549263000488, 0.26376810669898987, 0.2567823827266693, 0.38672587275505066,
-  -0.5801003575325012, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.5613612532615662, 0.41422900557518005, 0.24575236439704895, 0.2580442428588867,
-  -12.393796920776367, 0.27379363775253296, 0.2661901116371155, 0.4003552794456482,
-  -0.5613612532615662, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.5431874990463257, 0.42951828241348267, 0.2527281641960144, 0.26655933260917664,
-  -12.032020568847656, 0.2841413617134094, 0.27590495347976685, 0.4142928123474121,
-  -0.54318767786026, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.5255635380744934, 0.4452211558818817, 0.2596357464790344, 0.27518007159233093,
-  -11.645085334777832, 0.29480600357055664, 0.28593316674232483, 0.4285130500793457,
-  -0.5255635380744934, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.5084746479988098, 0.4613174498081207, 0.2664291262626648, 0.28387513756752014,
-  -11.231925010681152, 0.30577850341796875, 0.29628193378448486, 0.44298407435417175,
-  -0.5084746479988098, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.4919084310531616, 0.4777781665325165, 0.27305543422698975, 0.29260575771331787,
-  -10.791593551635742, 0.3170444071292877, 0.30695798993110657, 0.45766517519950867,
-  -0.49190837144851685, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.47585329413414, 0.49456584453582764, 0.2794557213783264, 0.30132654309272766,
-  -10.323308944702148, 0.3285837471485138, 0.3179689645767212, 0.4725065231323242,
-  -0.47585323452949524, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.4603002965450287, 0.5116318464279175, 0.2855643928050995, 0.3099837303161621,
-  -9.826519012451172, 0.3403691351413727, 0.3293229639530182, 0.4874474108219147,
-  -0.4603002369403839, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.44524213671684265, 0.5289145708084106, 0.29130926728248596, 0.31851449608802795,
-  -9.300989151000977, 0.3523649275302887, 0.34102869033813477, 0.502414882183075,
-  -0.44524213671684265, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.4306739270687103, 0.5463374853134155, 0.29661235213279724, 0.32684651017189026,
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+  -0.0021524152252823114, -0.004586022347211838, 0.0011673090048134327, 0.010361621156334877,
+  0.015422183088958263, -0.0058931647799909115, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005183934234082699, -0.009973762556910515, 0.005345572717487812, -0.0018010830972343683,
+  -0.0035096912179142237, 0.0011186724295839667, 0.008781169541180134, 0.01346781849861145,
+  -0.0051839351654052734, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0045151486992836, -0.008572769351303577, 0.0044121453538537025, -0.001486372435465455,
+  -0.002625895431265235, 0.0010637390660122037, 0.007355561014264822, 0.011635364964604378,
+  -0.0045151482336223125, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0038871909491717815, -0.007271276321262121, 0.0035770724061876535,
+  -0.0012072896352037787, -0.0019132507732138038, 0.0010016304440796375, 0.006078796926885843,
+  0.009926299564540386, -0.003887190017849207, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.003300529671832919, -0.006070980802178383, 0.002838446293026209, -0.000962661171797663,
+  -0.0013507514959201217, 0.0009317119256593287, 0.004944704473018646, 0.008342210203409195,
+  -0.003300529671832919, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0027557574212551117, -0.00497346930205822, 0.0021940418519079685,
+  -0.0007511264411732554, -0.0009179562330245972, 0.0008536315290257335, 0.003946952987462282,
+  0.006884870119392872, -0.0027557569555938244, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0022536220494657755, -0.003980235196650028, 0.0016412694239988923,
+  -0.000571126292925328, -0.0005951528437435627, 0.000767354154959321, 0.003079039277508855,
+  0.005556274671107531, -0.002253622282296419, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0017950675683096051, -0.0030927134212106466, 0.0011771151330322027,
+  -0.00042088169720955193, -0.0003635372850112617, 0.0006732359761372209, 0.0023342932108789682,
+  0.00435870373621583, -0.001795067684724927, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0013813070254400373, -0.002312342170625925, 0.0007980743539519608,
+  -0.0002983788726851344, -0.00020540415425784886, 0.0005721009219996631, 0.0017058859812095761,
+  0.003294839058071375, -0.001381307258270681, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0010139105143025517, -0.0016406092327088118, 0.0005000279634259641,
+  -0.00020134136138949543, -0.00010433724673930556, 0.0004653777286875993, 0.001186824287287891,
+  0.0023678643628954887, -0.0010139105143025517, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0006949867238290608, -0.0010791923850774765, 0.00027809879975393414,
+  -0.0001272061199415475, -4.542783790384419e-05, 0.0003553187707439065, 0.0007700194255448878,
+  0.0015817435923963785, -0.0006949868402443826, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0004274641687516123, -0.0006301424582488835, 0.00012637233885470778,
+  -7.309745706152171e-05, -1.550297747598961e-05, 0.00024537942954339087, 0.00044837870518676937,
+  0.000941598555073142, -0.0004274642269592732, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0002156999398721382, -0.0002962893631774932, 3.740921602002345e-05,
+  -3.582395947887562e-05, -3.3923665796464775e-06, 0.00014098439714871347, 0.00021510539227165282,
+  0.0004545420815702528, -0.0002156999398721382, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.707255670335144e-05, -8.231757237808779e-05, 1.1180173942193505e-06,
+  -1.2026118383801077e-05, -2.5079435772568104e-07, 5.150139259058051e-05, 6.472939276136458e-05,
+  0.00013187038712203503, -6.707255670335144e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 16
diff --git a/extra_tests/regression_fits/central_16.json b/extra_tests/regression_fits/central_16.json
index d70a76c075..f3fa15cbbd 100644
--- a/extra_tests/regression_fits/central_16.json
+++ b/extra_tests/regression_fits/central_16.json
@@ -51,45 +51,45 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 2.6700103282928467,
-  "erf_vl": 2.596097469329834,
-  "chi2": 2.1046993732452393,
+  "erf_tr": 2.6700093746185303,
+  "erf_vl": 2.5960960388183594,
+  "chi2": 2.1047041416168213,
   "pos_state": "POS_VETO",
   "arc_lengths": [
-    1.3207828111870983,
-    1.4752518408583124,
-    1.1834879869850787,
-    1.001142499763364,
-    1.1960909456851319
+    1.3207826202191888,
+    1.4752515128602395,
+    1.1834880064420275,
+    1.0011424664941873,
+    1.1960902816154753
   ],
   "integrability": [
-    0.000920317608690574,
-    0.0009203176086889364,
-    4.833287800831698e-05,
-    0.46257802098989376,
-    0.0069634128594759925
+    0.000920316459089382,
+    0.0009203164590875224,
+    4.833296725237357e-05,
+    0.46257925033569225,
+    0.0069633987150139465
   ],
   "timing": {
     "walltime": {
-      "Total": 10.047237396240234,
+      "Total": 10.90460753440857,
       "start": 0.0,
-      "replica_set": 0.210205078125,
-      "replica_fitted": 10.047173023223877,
-      "replica_set_to_replica_fitted": 9.836967945098877
+      "replica_set": 0.22848939895629883,
+      "replica_fitted": 10.904474258422852,
+      "replica_set_to_replica_fitted": 10.675984859466553
     },
     "cputime": {
-      "Total": 11.469310126,
+      "Total": 12.365805662,
       "start": 0.0,
-      "replica_set": 0.2088275399999997,
-      "replica_fitted": 11.469243942000002,
-      "replica_set_to_replica_fitted": 11.260416402
+      "replica_set": 0.22668013299999945,
+      "replica_fitted": 12.365671202000001,
+      "replica_set_to_replica_fitted": 12.138991069000003
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
-    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
+    "nnpdf": "4.0.9.post1210.dev0+d36bcce78",
+    "validphys": "4.0.9.post1210.dev0+d36bcce78"
   }
 }
diff --git a/extra_tests/regression_fits/diagonal_45.exportgrid b/extra_tests/regression_fits/diagonal_45.exportgrid
index 2508b9ff32..c7fd6bea60 100644
--- a/extra_tests/regression_fits/diagonal_45.exportgrid
+++ b/extra_tests/regression_fits/diagonal_45.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, -2.3768630027770996, 0.12397096306085587, 0.09739158302545547, 0.09743872284889221,
-  -15.360092163085938, 0.09758953005075455, 0.09754385054111481, 0.12372853606939316,
-  -2.3768630027770996, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.3018882274627686, 0.12483403086662292, 0.09718990325927734, 0.09724350273609161,
-  -15.367839813232422, 0.09741021692752838, 0.09735839813947678, 0.12456803023815155,
-  -2.3018877506256104, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2292847633361816, 0.12592333555221558, 0.09717055410146713, 0.09723150730133057,
-  -15.374130249023438, 0.09741590172052383, 0.09735707193613052, 0.12563152611255646,
-  -2.2292847633361816, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1589787006378174, 0.12723934650421143, 0.09733206778764725, 0.09740131348371506,
-  -15.378862380981445, 0.09760524332523346, 0.09753856807947159, 0.12691918015480042,
-  -2.158978223800659, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.090895175933838, 0.12878109514713287, 0.09767135977745056, 0.09775014966726303,
-  -15.381932258605957, 0.09797576814889908, 0.09790006279945374, 0.1284298598766327,
-  -2.090894937515259, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.0249650478363037, 0.130548894405365, 0.09818673878908157, 0.09827627241611481,
-  -15.38322925567627, 0.09852596372365952, 0.09844014793634415, 0.13016362488269806,
-  -2.024965286254883, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9611202478408813, 0.1325443834066391, 0.0988774523139, 0.09897925704717636,
-  -15.382623672485352, 0.09925558418035507, 0.09915826469659805, 0.1321217566728592,
-  -1.9611202478408813, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.899293303489685, 0.13476763665676117, 0.09974124282598495, 0.09985700249671936,
-  -15.379993438720703, 0.10016290843486786, 0.10005252063274384, 0.13430412113666534,
-  -1.899293303489685, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.839421033859253, 0.1372210830450058, 0.10077797621488571, 0.10090958327054977,
-  -15.375197410583496, 0.10124829411506653, 0.10112317651510239, 0.13671264052391052,
-  -1.839421033859253, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7814404964447021, 0.13990594446659088, 0.10198629647493362, 0.10213591158390045,
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-  -1.7814407348632812, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7252919673919678, 0.1428242176771164, 0.10336537659168243, 0.10353545844554901,
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-  -1.7252919673919678, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6709166765213013, 0.1459788829088211, 0.10491522401571274, 0.1051085814833641,
-  -15.346274375915527, 0.1055690124630928, 0.10538694262504578, 0.1453082263469696,
-  -1.6709169149398804, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6182583570480347, 0.14937253296375275, 0.10663527995347977, 0.10685510188341141,
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-  -1.6182583570480347, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5672625303268433, 0.15300855040550232, 0.10852567851543427, 0.1087755635380745,
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-  -1.5672622919082642, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5178756713867188, 0.15689069032669067, 0.11058657616376877, 0.1108705997467041,
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-- [0.0, 0.0, -1.4700465202331543, 0.16102305054664612, 0.1128183901309967, 0.1131412610411644,
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-- [0.0, 0.0, -1.4237254858016968, 0.16540959477424622, 0.11522113531827927, 0.11558807641267776,
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-  -1.4237254858016968, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.3788641691207886, 0.17005573213100433, 0.1177959218621254, 0.11821299046278,
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-- [0.0, 0.0, -1.3354161977767944, 0.17496632039546967, 0.12054328620433807, 0.12101726233959198,
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-- [0.0, 0.0, -1.2933357954025269, 0.18014700710773468, 0.12346401810646057, 0.1240026205778122,
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-  -1.2933361530303955, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.2525794506072998, 0.18560358881950378, 0.12655878067016602, 0.12717081606388092,
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-  -1.2525794506072998, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.2131047248840332, 0.19134266674518585, 0.12982888519763947, 0.13052429258823395,
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-  -1.213104486465454, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.1748695373535156, 0.19737091660499573, 0.1332750916481018, 0.1340651512145996,
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-  -1.1748697757720947, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.137835144996643, 0.2036954015493393, 0.13689829409122467, 0.1377958208322525,
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-  -1.137835144996643, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.1019624471664429, 0.21032372117042542, 0.14069949090480804, 0.14171893894672394,
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-  -1.1019624471664429, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.0672136545181274, 0.217263862490654, 0.1446795016527176, 0.14583729207515717,
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-  -1.0672134160995483, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.0335524082183838, 0.22452367842197418, 0.14883854985237122, 0.15015335381031036,
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-  -1.0335524082183838, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.0009440183639526, 0.23211224377155304, 0.15317755937576294, 0.1546703428030014,
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-- [0.0, 0.0, -0.9693536162376404, 0.2400379180908203, 0.15769600868225098, 0.1593906283378601,
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-  -0.9693536162376404, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.9387486577033997, 0.2483101487159729, 0.1623939871788025, 0.1643172949552536,
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-  -0.9387486577033997, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.9090969562530518, 0.2569381892681122, 0.16727043688297272, 0.16945289075374603,
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-  -0.9090970754623413, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.8803674578666687, 0.26593196392059326, 0.1723243147134781, 0.17480024695396423,
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-  -0.8803674578666687, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.8525300621986389, 0.27530068159103394, 0.17755308747291565, 0.18036121129989624,
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-  -0.8525301814079285, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.8255555033683777, 0.28505438566207886, 0.18295401334762573, 0.18613797426223755,
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-  -0.8255555033683777, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.7994158864021301, 0.29520273208618164, 0.18852300941944122, 0.19213195145130157,
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-  -0.7994160056114197, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.77408367395401, 0.3057548701763153, 0.19425469636917114, 0.19834385812282562,
-  -13.53300666809082, 0.20417775213718414, 0.20101599395275116, 0.2996344566345215,
-  -0.77408367395401, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.7495325803756714, 0.31672045588493347, 0.20014254748821259, 0.20477394759655,
-  -13.346405982971191, 0.2112801969051361, 0.20776033401489258, 0.31000563502311707,
-  -0.7495326995849609, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.725737452507019, 0.328108012676239, 0.206178218126297, 0.21142145991325378,
-  -13.1452054977417, 0.21867911517620087, 0.21476764976978302, 0.3207402527332306,
-  -0.725737452507019, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.7026731967926025, 0.339925080537796, 0.21235093474388123, 0.21828389167785645,
-  -12.928470611572266, 0.22638145089149475, 0.22204354405403137, 0.33184000849723816,
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+  -0.06252816319465637, -0.0027793606277555227, 0.05017857998609543, 0.05741530656814575,
+  -0.021759605035185814, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.020441435277462006, -0.04398149996995926, 0.03251504525542259, -0.008575527928769588,
+  -0.05565444752573967, -0.0027125251945108175, 0.04597925767302513, 0.05380461364984512,
+  -0.020441435277462006, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.01916227675974369, -0.041245974600315094, 0.030009664595127106, -0.007864097133278847,
+  -0.049280885607004166, -0.0026187212206423283, 0.042002927511930466, 0.050298936665058136,
+  -0.019162273034453392, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.017922179773449898, -0.0385640449821949, 0.027602655813097954, -0.007183155510574579,
+  -0.04339683800935745, -0.0025018365122377872, 0.03824543580412865, 0.04689978063106537,
+  -0.017922179773449898, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.016721198335289955, -0.0359412282705307, 0.025295274332165718, -0.006533447187393904,
+  -0.037989843636751175, -0.0023655882105231285, 0.03470249101519585, 0.043608520179986954,
+  -0.016721194609999657, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.015559353865683079, -0.03338264301419258, 0.023088587448000908, -0.0059155626222491264,
+  -0.03304548189043999, -0.0022135304752737284, 0.03136957436800003, 0.040426433086395264,
+  -0.015559353865683079, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.014436678029596806, -0.030893146991729736, 0.02098357304930687, -0.005330007057636976,
+  -0.028547845780849457, -0.0020490738097578287, 0.028242068365216255, 0.03735480085015297,
+  -0.014436679892241955, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.013353205285966396, -0.02847723849117756, 0.018981019034981728, -0.004777155816555023,
+  -0.0244794599711895, -0.001875446061603725, 0.02531515806913376, 0.0343947559595108,
+  -0.013353207148611546, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.012308976612985134, -0.026139117777347565, 0.017081571742892265, -0.00425726268440485,
+  -0.020821556448936462, -0.001695731421932578, 0.02258387953042984, 0.0315474234521389,
+  -0.012308976612985134, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.011304018087685108, -0.023882677778601646, 0.01528574526309967, -0.0037704482674598694,
+  -0.017554158344864845, -0.001512848655693233, 0.020043116062879562, 0.02881387621164322,
+  -0.011304018087685108, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.010338392108678818, -0.021711550652980804, 0.013593859039247036, -0.0033167453948408365,
+  -0.014656305313110352, -0.0013295538956299424, 0.017687607556581497, 0.02619514986872673,
+  -0.010338393971323967, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.009412160143256187, -0.019629091024398804, 0.012006099335849285, -0.002896038582548499,
+  -0.012106155976653099, -0.0011484544957056642, 0.01551192719489336, 0.023692268878221512,
+  -0.009412162937223911, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.008525426499545574, -0.01763840764760971, 0.0105224484577775, -0.002508103149011731,
+  -0.009881188161671162, -0.0009719777735881507, 0.013510526157915592, 0.021306237205863,
+  -0.008525427430868149, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.007678310386836529, -0.015742385759949684, 0.00914272852241993, -0.0021525861229747534,
+  -0.007958343252539635, -0.0008023939444683492, 0.01167770940810442, 0.019038090482354164,
+  -0.007678310852497816, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006870964076370001, -0.013943633064627647, 0.007866546511650085, -0.0018289987929165363,
+  -0.006314156576991081, -0.0006417988915927708, 0.010007595643401146, 0.01688883639872074,
+  -0.006870963145047426, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006103599444031715, -0.012244612909853458, 0.006693313363939524, -0.0015367284649983048,
+  -0.004924992099404335, -0.0004921168438158929, 0.008494192734360695, 0.014859559014439583,
+  -0.006103598978370428, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005376474466174841, -0.010647553950548172, 0.005622218828648329, -0.001275020302273333,
+  -0.003767159068956971, -0.00035506687709130347, 0.00713135302066803, 0.012951383367180824,
+  -0.005376474466174841, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.004689916502684355, -0.009154507890343666, 0.004652209579944611, -0.0010429674293845892,
+  -0.002817087806761265, -0.0002322033396922052, 0.00591274444013834, 0.011165468953549862,
+  -0.00468991557136178, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00404434185475111, -0.007767391391098499, 0.0037819743156433105, -0.0008395242039114237,
+  -0.002051515271887183, -0.00012484155013225973, 0.004831911064684391, 0.009503127075731754,
+  -0.004044341389089823, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0034402606543153524, -0.006487944629043341, 0.003009910462424159,
+  -0.0006634688470512629, -0.0014476393116638064, -3.409227429074235e-05, 0.0038821918424218893,
+  0.007965725846588612, -0.0034402606543153524, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0028783169109374285, -0.005317813251167536, 0.0023340992629528046,
+  -0.0005134115344844759, -0.0009833109797909856, 3.920124436262995e-05, 0.0030567641369998455,
+  0.006554819643497467, -0.0028783173765987158, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0023593208752572536, -0.0042585511691868305, 0.0017522556008771062,
+  -0.0003877780691254884, -0.0006372117204591632, 9.44708299357444e-05, 0.002348611829802394,
+  0.0052721439860761166, -0.0023593208752572536, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0018842869903892279, -0.0033116494305431843, 0.0012616782914847136,
+  -0.0002847837167792022, -0.0003890385269187391, 0.000131482956930995, 0.0017505072755739093,
+  0.004119673278182745, -0.001884286873973906, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0014545228332281113, -0.002478621667250991, 0.0008591755176894367,
+  -0.00020242805476300418, -0.00021970692614559084, 0.00015040051948744804, 0.0012550147948786616,
+  0.0030997300054877996, -0.001454523066058755, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0010717145632952452, -0.0017610336653888226, 0.0005409495206549764,
+  -0.000138460032758303, -0.000111549292341806, 0.00015188561519607902, 0.0008544555748812854,
+  0.002215055050328374, -0.0010717145632952452, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.000738126749638468, -0.0011606704210862517, 0.00030244761728681624,
+  -9.036363917402923e-05, -4.854501457884908e-05, 0.0001372604165226221, 0.0005409239674918354,
+  0.0014690426178276539, -0.000738126749638468, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0004569087759591639, -0.000679725082591176, 0.00013808353105559945,
+  -5.533647345146164e-05, -1.6559040886932053e-05, 0.00010879647743422538, 0.00030629817047156394,
+  0.0008660401799716055, -0.0004569088341668248, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00023275722924154252, -0.00032124517019838095, 4.0743787394603714e-05,
+  -3.0305818654596806e-05, -3.621783207563567e-06, 7.028249819995835e-05, 0.00014236012066248804,
+  0.0004120208031963557, -0.0002327572146896273, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -7.367108628386632e-05, -9.031486843014136e-05, 6.180329137350782e-07,
+  -1.2141239494667388e-05, -2.676328847428522e-07, 2.8471613404690288e-05, 4.1328134102514014e-05,
+  0.00011631761299213395, -7.367107173195109e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 45
diff --git a/extra_tests/regression_fits/diagonal_45.json b/extra_tests/regression_fits/diagonal_45.json
index abbfa81d84..93d0845574 100644
--- a/extra_tests/regression_fits/diagonal_45.json
+++ b/extra_tests/regression_fits/diagonal_45.json
@@ -51,45 +51,45 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 3.7433669567108154,
-  "erf_vl": 3.0657339096069336,
-  "chi2": 2.176706075668335,
+  "erf_tr": 3.7433693408966064,
+  "erf_vl": 3.065732717514038,
+  "chi2": 2.1767027378082275,
   "pos_state": "POS_VETO",
   "arc_lengths": [
-    1.31744014798244,
-    1.5070503935489326,
-    1.1761950076336678,
-    1.0013647217831656,
-    1.2246978602489684
+    1.3174405034929306,
+    1.5070529634387448,
+    1.1761946839779471,
+    1.0013647273646804,
+    1.2246958247975697
   ],
   "integrability": [
-    0.0008957566533373817,
-    0.0008957566533358552,
-    4.806766594289691e-05,
-    0.463894024491309,
-    0.007004055194555159
+    0.0008957564787127614,
+    0.0008957564787128725,
+    4.80677109626626e-05,
+    0.46389447897672587,
+    0.007004046346990256
   ],
   "timing": {
     "walltime": {
-      "Total": 9.477155923843384,
+      "Total": 10.154094696044922,
       "start": 0.0,
-      "replica_set": 0.21604132652282715,
-      "replica_fitted": 9.477098941802979,
-      "replica_set_to_replica_fitted": 9.261057615280151
+      "replica_set": 0.22886013984680176,
+      "replica_fitted": 10.154032945632935,
+      "replica_set_to_replica_fitted": 9.925172805786133
     },
     "cputime": {
-      "Total": 10.790387835,
+      "Total": 11.552391722,
       "start": 0.0,
-      "replica_set": 0.21436629899999993,
-      "replica_fitted": 10.790329496999998,
-      "replica_set_to_replica_fitted": 10.575963198
+      "replica_set": 0.22704437600000027,
+      "replica_fitted": 11.552328112999998,
+      "replica_set_to_replica_fitted": 11.325283737
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
-    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
+    "nnpdf": "4.0.9.post1210.dev0+d36bcce78",
+    "validphys": "4.0.9.post1210.dev0+d36bcce78"
   }
 }
diff --git a/extra_tests/regression_fits/feature_scaling_81.json b/extra_tests/regression_fits/feature_scaling_81.json
index 00865ddf03..2959ecdc86 100644
--- a/extra_tests/regression_fits/feature_scaling_81.json
+++ b/extra_tests/regression_fits/feature_scaling_81.json
@@ -71,25 +71,25 @@
   ],
   "timing": {
     "walltime": {
-      "Total": 9.83653473854065,
+      "Total": 10.640647411346436,
       "start": 0.0,
-      "replica_set": 0.22139739990234375,
-      "replica_fitted": 9.836406946182251,
-      "replica_set_to_replica_fitted": 9.615009546279907
+      "replica_set": 0.2341294288635254,
+      "replica_fitted": 10.64057731628418,
+      "replica_set_to_replica_fitted": 10.406447887420654
     },
     "cputime": {
-      "Total": 11.082168318,
+      "Total": 11.966201521000002,
       "start": 0.0,
-      "replica_set": 0.2204650259999994,
-      "replica_fitted": 11.082038816,
-      "replica_set_to_replica_fitted": 10.861573790000001
+      "replica_set": 0.2321575600000001,
+      "replica_fitted": 11.966130038000003,
+      "replica_set_to_replica_fitted": 11.733972478000002
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
-    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
+    "nnpdf": "4.0.9.post1210.dev0+d36bcce78",
+    "validphys": "4.0.9.post1210.dev0+d36bcce78"
   }
 }
diff --git a/extra_tests/regression_fits/flavour_29.json b/extra_tests/regression_fits/flavour_29.json
index e67c032558..fb78f5b325 100644
--- a/extra_tests/regression_fits/flavour_29.json
+++ b/extra_tests/regression_fits/flavour_29.json
@@ -71,25 +71,25 @@
   ],
   "timing": {
     "walltime": {
-      "Total": 4.027747869491577,
+      "Total": 4.325552940368652,
       "start": 0.0,
-      "replica_set": 0.21877336502075195,
-      "replica_fitted": 4.027618646621704,
-      "replica_set_to_replica_fitted": 3.808845281600952
+      "replica_set": 0.22845125198364258,
+      "replica_fitted": 4.325416326522827,
+      "replica_set_to_replica_fitted": 4.096965074539185
     },
     "cputime": {
-      "Total": 4.170468237,
+      "Total": 4.471941011,
       "start": 0.0,
-      "replica_set": 0.2169810080000003,
-      "replica_fitted": 4.170337463000001,
-      "replica_set_to_replica_fitted": 3.9533564550000007
+      "replica_set": 0.226811251,
+      "replica_fitted": 4.471802753,
+      "replica_set_to_replica_fitted": 4.244991502
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
-    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
+    "nnpdf": "4.0.9.post1210.dev0+d36bcce78",
+    "validphys": "4.0.9.post1210.dev0+d36bcce78"
   }
 }
diff --git a/extra_tests/regression_fits/multi_dense_316.exportgrid b/extra_tests/regression_fits/multi_dense_316.exportgrid
index 268093483f..a161e60a73 100644
--- a/extra_tests/regression_fits/multi_dense_316.exportgrid
+++ b/extra_tests/regression_fits/multi_dense_316.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, -2.414682626724243, 0.032906413078308105, 0.00648618396371603, 0.006533617153763771,
-  -16.949392318725586, 0.006687344517558813, 0.006641445215791464, 0.03265798091888428,
-  -2.414682626724243, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.3386027812957764, 0.03612871840596199, 0.00865098461508751, 0.008704930543899536,
-  -16.960304260253906, 0.008874863386154175, 0.008822760544717312, 0.03585616126656532,
-  -2.338602304458618, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2649240493774414, 0.039499178528785706, 0.010920420289039612, 0.01098173949867487,
-  -16.96973991394043, 0.011169618926942348, 0.011110520921647549, 0.03920017182826996,
-  -2.2649240493774414, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1935720443725586, 0.04302005097270012, 0.013294789008796215, 0.013364536687731743,
-  -16.977588653564453, 0.013572296127676964, 0.013505223207175732, 0.04269205033779144,
-  -2.1935715675354004, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1244704723358154, 0.0466928705573082, 0.015773674473166466, 0.015852976590394974,
-  -16.983747482299805, 0.01608276180922985, 0.016006680205464363, 0.046333082020282745,
-  -2.1244702339172363, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.057549238204956, 0.05052153021097183, 0.018358789384365082, 0.018448911607265472,
-  -16.988086700439453, 0.01870310865342617, 0.01861686445772648, 0.05012689158320427,
-  -2.057549476623535, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.992738962173462, 0.054507434368133545, 0.021049322560429573, 0.021151790395379066,
-  -16.990489959716797, 0.021433057263493538, 0.02133525349199772, 0.05407460033893585,
-  -1.992738962173462, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9299731254577637, 0.05865481123328209, 0.02384714037179947, 0.023963691666722298,
-  -16.99082374572754, 0.024274958297610283, 0.024164026603102684, 0.058180104941129684,
-  -1.9299731254577637, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8691858053207397, 0.06296699494123459, 0.026753094047307968, 0.02688560262322426,
-  -16.988929748535156, 0.02723015286028385, 0.02710440754890442, 0.06244640424847603,
-  -1.8691858053207397, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8103145360946655, 0.0674474686384201, 0.029768045991659164, 0.029918726533651352,
-  -16.984663009643555, 0.030300196260213852, 0.030157653614878654, 0.06687658280134201,
-  -1.8103147745132446, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7532986402511597, 0.07210055738687515, 0.0328935906291008, 0.03306487202644348,
-  -16.97785758972168, 0.033487312495708466, 0.03332582488656044, 0.07147450745105743,
-  -1.7532986402511597, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6980786323547363, 0.07693096995353699, 0.03613148629665375, 0.03632623329758644,
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 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 316
diff --git a/extra_tests/regression_fits/multi_dense_316.json b/extra_tests/regression_fits/multi_dense_316.json
index 7ea0671429..5c6724cba6 100644
--- a/extra_tests/regression_fits/multi_dense_316.json
+++ b/extra_tests/regression_fits/multi_dense_316.json
@@ -51,45 +51,45 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 2.4744553565979004,
-  "erf_vl": 2.9059481620788574,
-  "chi2": 2.118800401687622,
+  "erf_tr": 2.4744620323181152,
+  "erf_vl": 2.905952215194702,
+  "chi2": 2.118803024291992,
   "pos_state": "POS_VETO",
   "arc_lengths": [
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-    1.488952866412567,
-    1.1794333655766738,
-    1.000696970195011,
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+    1.4889504508820537,
+    1.1794334718334645,
+    1.0006968075180218,
+    1.2461907760321072
   ],
   "integrability": [
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-    0.0008942512758955967,
-    5.0144157625053865e-05,
-    0.46068396419286617,
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+    5.014488272003792e-05,
+    0.46068788319826015,
+    0.007144232804419559
   ],
   "timing": {
     "walltime": {
-      "Total": 10.184973239898682,
+      "Total": 10.78720498085022,
       "start": 0.0,
-      "replica_set": 0.22072839736938477,
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   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
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-    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
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 }
diff --git a/extra_tests/regression_fits/no_csr_613.exportgrid b/extra_tests/regression_fits/no_csr_613.exportgrid
index 6a8cd6731b..85221ea69c 100644
--- a/extra_tests/regression_fits/no_csr_613.exportgrid
+++ b/extra_tests/regression_fits/no_csr_613.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
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+  -0.0009226638940162957, 0.0004542614915408194, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.000413824018323794, 0.0003197387559339404, -0.0009062697063200176,
+  0.000586597656365484, 5.97585276409518e-05, -0.00033620913745835423, 0.0011650810483843088,
+  -0.000660482095554471, 0.0003009402134921402, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00025635381462052464, 0.00019728824554476887, -0.0005706878728233278,
+  0.00041080257506109774, 2.5376328267157078e-05, -0.00023891842283774167, 0.0007471543503925204,
+  -0.00043818046106025577, 0.00018310113227926195, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00013954522728454322, 0.000104268423456233, -0.00031574396416544914,
+  0.00025504297809675336, 8.407731911574956e-06, -0.00014912514598108828, 0.0004237648390699178,
+  -0.00025785801699385047, 9.756220242707059e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.0132650105515495e-05, 4.094884207006544e-05, -0.0001379650057060644,
+  0.0001274040259886533, 1.7710898418954457e-06, -7.37805530661717e-05, 0.00019229622557759285,
+  -0.00012203769438201562, 4.0952912968350574e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.4724767424922902e-05, 7.088645816111239e-06, -3.383547664270736e-05,
+  3.758700404432602e-05, 1.2343663513547654e-07, -2.0759081962751225e-05, 5.077506648376584e-05,
+  -3.4071381378453225e-05, 9.690308615972754e-06, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 613
diff --git a/extra_tests/regression_fits/no_csr_613.json b/extra_tests/regression_fits/no_csr_613.json
index e3f52ddeba..062ee6aced 100644
--- a/extra_tests/regression_fits/no_csr_613.json
+++ b/extra_tests/regression_fits/no_csr_613.json
@@ -57,45 +57,45 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 50.92805480957031,
-  "erf_vl": 50.836299896240234,
-  "chi2": 29.386579513549805,
+  "erf_tr": 50.92805862426758,
+  "erf_vl": 50.8363151550293,
+  "chi2": 29.38657569885254,
   "pos_state": "POS_VETO",
   "arc_lengths": [
-    0.9916593111240226,
-    1.8120030443463793,
-    1.3579847509208942,
-    1.0247126070492014,
-    1.3362150500155137
+    0.9916593125415822,
+    1.8120025388759484,
+    1.3579847415972428,
+    1.0247126106802007,
+    1.3362166254852255
   ],
   "integrability": [
-    0.0005673126142922702,
-    0.0028061565826644486,
-    1.8679654999048667e-05,
-    0.002479236049112543,
-    0.017847452545539044
+    0.0005673122504940009,
+    0.0028061562043146526,
+    1.867965289595319e-05,
+    0.002479236427462339,
+    0.01784750772640159
   ],
   "timing": {
     "walltime": {
-      "Total": 8.546705961227417,
+      "Total": 9.047945737838745,
       "start": 0.0,
-      "replica_set": 0.22439932823181152,
-      "replica_fitted": 8.54661750793457,
-      "replica_set_to_replica_fitted": 8.322218179702759
+      "replica_set": 0.23447799682617188,
+      "replica_fitted": 9.04781460762024,
+      "replica_set_to_replica_fitted": 8.813336610794067
     },
     "cputime": {
-      "Total": 9.500806777000001,
+      "Total": 10.033265355,
       "start": 0.0,
-      "replica_set": 0.22265501399999987,
-      "replica_fitted": 9.500716870000002,
-      "replica_set_to_replica_fitted": 9.278061856
+      "replica_set": 0.2326763569999999,
+      "replica_fitted": 10.033132898,
+      "replica_set_to_replica_fitted": 9.800456540999999
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
-    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
+    "nnpdf": "4.0.9.post1210.dev0+d36bcce78",
+    "validphys": "4.0.9.post1210.dev0+d36bcce78"
   }
 }
diff --git a/extra_tests/regression_fits/no_lagrange_27.exportgrid b/extra_tests/regression_fits/no_lagrange_27.exportgrid
index ddaa672ee5..a6bcac45e9 100644
--- a/extra_tests/regression_fits/no_lagrange_27.exportgrid
+++ b/extra_tests/regression_fits/no_lagrange_27.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, -2.258500576019287, 0.03153587132692337, 0.004337960854172707, 0.004386408720165491,
-  -16.76667022705078, 0.00454088905826211, 0.004493969026952982, 0.031289223581552505,
-  -2.258500576019287, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.187333106994629, 0.03491134196519852, 0.006624337751418352, 0.006679425947368145,
-  -16.778554916381836, 0.006850240286439657, 0.00679699145257473, 0.034640777856111526,
-  -2.187333106994629, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.11841082572937, 0.03842877224087715, 0.009007791057229042, 0.009070442989468575,
-  -16.78903579711914, 0.009259352460503578, 0.00919891707599163, 0.03813199698925018,
-  -2.11841082572937, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.0516629219055176, 0.04209065064787865, 0.011488782241940498, 0.011560051701962948,
-  -16.798004150390625, 0.011769015341997147, 0.011700412258505821, 0.04176513850688934,
-  -2.0516629219055176, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9870189428329468, 0.045898694545030594, 0.014067047275602818, 0.014148061163723469,
-  -16.805368423461914, 0.01437925361096859, 0.014301449991762638, 0.04554168879985809,
-  -1.9870191812515259, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9244139194488525, 0.04985705763101578, 0.016744406893849373, 0.016836555674672127,
-  -16.811004638671875, 0.017092395573854446, 0.01700410805642605, 0.04946553334593773,
-  -1.9244141578674316, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.863782525062561, 0.05396819859743118, 0.019521106034517288, 0.019625859335064888,
-  -16.81478500366211, 0.019909020513296127, 0.019808923825621605, 0.053538862615823746,
-  -1.863782286643982, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8050611019134521, 0.058235473930835724, 0.022397983819246292, 0.022517133504152298,
-  -16.816593170166016, 0.02283061295747757, 0.02271706610918045, 0.0577646940946579,
-  -1.8050611019134521, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7481896877288818, 0.06266288459300995, 0.025376511737704277, 0.025511998683214188,
-  -16.816280364990234, 0.02585911564528942, 0.025730369612574577, 0.06214667856693268,
-  -1.748189926147461, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6931097507476807, 0.0672544464468956, 0.028458034619688988, 0.02861207351088524,
-  -16.813703536987305, 0.02899651601910591, 0.02885059081017971, 0.06668849289417267,
-  -1.6931097507476807, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6397637128829956, 0.07201482355594635, 0.03164428845047951, 0.03181943669915199,
-  -16.808696746826172, 0.03224531561136246, 0.03207993507385254, 0.07139436155557632,
-  -1.6397637128829956, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.588096261024475, 0.07694819569587708, 0.03493645042181015, 0.035135604441165924,
-  -16.801088333129883, 0.03560749813914299, 0.035420093685388565, 0.07626798748970032,
-  -1.5880964994430542, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.538054347038269, 0.0820600762963295, 0.03833683580160141, 0.03856325522065163,
-  -16.790700912475586, 0.039086248725652695, 0.038873977959156036, 0.08131444454193115,
-  -1.538054347038269, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4895859956741333, 0.0873555913567543, 0.041847117245197296, 0.0421045683324337,
-  -16.777332305908203, 0.04268435016274452, 0.04244391992688179, 0.08653824031352997,
-  -1.4895859956741333, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4426403045654297, 0.09284035116434097, 0.04546942934393883, 0.04576214402914047,
-  -16.760772705078125, 0.046405017375946045, 0.04613277688622475, 0.09194450080394745,
-  -1.4426400661468506, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.3971694707870483, 0.09852047264575958, 0.04920594394207001, 0.04953872784972191,
-  -16.740802764892578, 0.050251733511686325, 0.04994358494877815, 0.09753861278295517,
-  -1.3971697092056274, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.353126049041748, 0.10440217703580856, 0.05305889993906021, 0.0534372515976429,
-  -16.717180252075195, 0.05422823876142502, 0.0538795106112957, 0.10332609713077545,
-  -1.353126049041748, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.3104641437530518, 0.11049247533082962, 0.057030968368053436, 0.05746109038591385,
-  -16.689640045166016, 0.05833881348371506, 0.05794432386755943, 0.10931321233510971,
-  -1.3104641437530518, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.2691391706466675, 0.11679825931787491, 0.06112442538142204, 0.061613380908966064,
-  -16.657909393310547, 0.06258758902549744, 0.062141500413417816, 0.11550596356391907,
-  -1.2691391706466675, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.229109287261963, 0.12332701683044434, 0.06534195691347122, 0.06589775532484055,
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-  -1.229109287261963, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.1903316974639893, 0.13008663058280945, 0.0696861669421196, 0.07031790912151337,
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-  -1.1903316974639893, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.1527665853500366, 0.13708490133285522, 0.07415923476219177, 0.0748772993683815,
-  -16.53450584411621, 0.07621145993471146, 0.07556793838739395, 0.13538464903831482,
-  -1.1527665853500366, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.1163746118545532, 0.14433082938194275, 0.07876429706811905, 0.07958037406206131,
-  -16.482830047607422, 0.08106271177530289, 0.08033625036478043, 0.1424679309129715,
-  -1.1163746118545532, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.0811179876327515, 0.1518331915140152, 0.08350370079278946, 0.08443109691143036,
-  -16.425247192382812, 0.08607850968837738, 0.0852588415145874, 0.14979210495948792,
-  -1.0811179876327515, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.046960473060608, 0.1596013754606247, 0.08838006108999252, 0.08943387120962143,
-  -16.36134910583496, 0.0912652388215065, 0.09034090489149094, 0.1573651283979416,
-  -1.046960473060608, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.0138658285140991, 0.16764511168003082, 0.09339571744203568, 0.09459301084280014,
-  -16.290679931640625, 0.09662937372922897, 0.09558765590190887, 0.1651950478553772,
-  -1.0138658285140991, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.9817997217178345, 0.17597419023513794, 0.09855258464813232, 0.09991279244422913,
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-  -0.9817997217178345, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.9507285952568054, 0.18459926545619965, 0.10385289788246155, 0.10539796203374863,
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-  -0.9507285952568054, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.920620322227478, 0.19353097677230835, 0.1092982217669487, 0.1110529974102974,
-  -16.03307342529297, 0.11385706812143326, 0.112372025847435, 0.19030888378620148,
-  -0.920620322227478, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.8914430737495422, 0.20278044044971466, 0.11488988995552063, 0.11688251793384552,
-  -15.930168151855469, 0.12000371515750885, 0.11833499372005463, 0.1992502510547638,
-  -0.8914430737495422, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.8631665706634521, 0.21235886216163635, 0.12062855064868927, 0.12289082258939743,
-  -15.817729949951172, 0.12636590003967285, 0.12449247390031815, 0.20849107205867767,
-  -0.8631665706634521, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.835761308670044, 0.22227789461612701, 0.1265145242214203, 0.12908242642879486,
-  -15.695076942443848, 0.13295243680477142, 0.13085125386714935, 0.2180400788784027,
-  -0.835761308670044, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.8091986775398254, 0.232549250125885, 0.13254718482494354, 0.13546133041381836,
-  -15.561495780944824, 0.1397722214460373, 0.13741816580295563, 0.22790580987930298,
-  -0.8091985583305359, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.7834507822990417, 0.24318458139896393, 0.1387251764535904, 0.14203134179115295,
-  -15.416219711303711, 0.14683447778224945, 0.14420022070407867, 0.23809650540351868,
-  -0.7834506630897522, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.7584912180900574, 0.2541961073875427, 0.14504629373550415, 0.14879614114761353,
-  -15.258432388305664, 0.15414896607398987, 0.1512048989534378, 0.24862051010131836,
-  -0.7584912180900574, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.7342934012413025, 0.2655951678752899, 0.1515067219734192, 0.15575841069221497,
-  -15.087261199951172, 0.16172510385513306, 0.15843956172466278, 0.25948506593704224,
-  -0.7342932820320129, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.7108327746391296, 0.2773933708667755, 0.15810145437717438, 0.16292038559913635,
-  -14.901787757873535, 0.16957269608974457, 0.1659117192029953, 0.2706969976425171,
-  -0.7108327746391296, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.6880851984024048, 0.2896018922328949, 0.16482393443584442, 0.17028352618217468,
-  -14.701033592224121, 0.17770174145698547, 0.173629492521286, 0.2822624742984772,
-  -0.6880851984024048, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.6660269498825073, 0.302231103181839, 0.17166540026664734, 0.17784801125526428,
-  -14.483977317810059, 0.18612176179885864, 0.18160071969032288, 0.29418620467185974,
-  -0.6660270690917969, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.6446359157562256, 0.31529027223587036, 0.1786150187253952, 0.185612753033638,
-  -14.249531745910645, 0.19484218955039978, 0.18983356654644012, 0.30647164583206177,
-  -0.644635796546936, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.6238901019096375, 0.32878798246383667, 0.18565937876701355, 0.19357523322105408,
-  -13.996565818786621, 0.20387215912342072, 0.19833654165267944, 0.3191203474998474,
-  -0.623890221118927, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.6037694811820984, 0.342730849981308, 0.19278192520141602, 0.20173056423664093,
-  -13.723888397216797, 0.21321986615657806, 0.20711812376976013, 0.33213165402412415,
-  -0.6037696003913879, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.5842538475990295, 0.35712334513664246, 0.19996292889118195, 0.21007178723812103,
-  -13.430303573608398, 0.22289253771305084, 0.21618691086769104, 0.3455023169517517,
-  -0.5842536687850952, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.5653247237205505, 0.37196746468544006, 0.20717854797840118, 0.21858878433704376,
-  -13.114542961120605, 0.23289605975151062, 0.22555184364318848, 0.35922524333000183,
-  -0.565324604511261, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.5469644665718079, 0.3872617483139038, 0.2144010066986084, 0.22726842761039734,
-  -12.775341033935547, 0.24323473870754242, 0.23522216081619263, 0.37328997254371643,
-  -0.5469644665718079, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.5291567444801331, 0.40300068259239197, 0.22159737348556519, 0.23609314858913422,
-  -12.41144847869873, 0.25391024351119995, 0.24520720541477203, 0.3876807987689972,
-  -0.5291567444801331, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.511886715888977, 0.41917312145233154, 0.228729248046875, 0.24504069983959198,
-  -12.021617889404297, 0.26492106914520264, 0.2555164396762848, 0.402375727891922,
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-- [0.0, 0.0, -0.0014127468457445502, -0.0023880198132246733, 0.0009599741897545755,
-  -0.0001257154217455536, -0.0002120004064636305, 0.0002608768118079752, 0.0013863382628187537,
-  0.0032203984446823597, -0.0014127470785751939, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0010389721719548106, -0.00169211660977453, 0.0006164678488858044,
-  -7.815474964445457e-05, -0.00010769929212983698, 0.00023607166076544672, 0.000952104979660362,
-  0.0023059409577399492, -0.0010389720555394888, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0007138301734812558, -0.0011113400105386972, 0.00035565291182138026,
-  -4.5835968194296584e-05, -4.6896391722839326e-05, 0.00019755047105718404, 0.0006090688402764499,
-  0.0015333205228671432, -0.0007138301152735949, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0004403897619340569, -0.0006476583075709641, 0.00017209995712619275,
-  -2.5533792722853832e-05, -1.6005704310373403e-05, 0.00014793248556088656, 0.00034933743881992996,
-  0.0009072074899449944, -0.0004403897619340569, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0002232017577625811, -0.00030376625363714993, 5.896346192457713e-05,
-  -1.3611758731713053e-05, -3.502701247271034e-06, 9.151489939540625e-05, 0.0001650396443437785,
-  0.00043403220479376614, -0.0002232017577625811, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -6.996565934969112e-05, -8.412013266934082e-05, 6.955112439754885e-06,
-  -6.073974873288535e-06, -2.5897463729052106e-07, 3.590421692933887e-05, 4.902309592580423e-05,
-  0.00012390037591103464, -6.996568117756397e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005256849806755781, -0.010355005040764809, 0.005978408735245466, -0.0010892332065850496,
+  -0.0036192333791404963, -1.0282732546329498e-05, 0.007603105623275042, 0.013352123089134693,
+  -0.0052568488754332066, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0045829894952476025, -0.00889584794640541, 0.004963609389960766, -0.0008706536027602851,
+  -0.0027082364540547132, 7.470150740118697e-05, 0.006325484719127417, 0.011519694700837135,
+  -0.004582988563925028, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.003949566278606653, -0.0075409733690321445, 0.004051364492624998,
+  -0.0006816813256591558, -0.001973513513803482, 0.00014545828162226826, 0.005188902840018272,
+  0.00981274712830782, -0.003949565812945366, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.003357107052579522, -0.00629211962223053, 0.003240050980821252, -0.0005209403461776674,
+  -0.0013934783637523651, 0.00020099080575164407, 0.004186823032796383, 0.008232810534536839,
+  -0.003357107052579522, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0028062721248716116, -0.005150909535586834, 0.002527744509279728,
+  -0.0003868616186082363, -0.0009471108205616474, 0.00024055922403931618, 0.003312533488497138,
+  0.006781579460948706, -0.0028062716592103243, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0022978754714131355, -0.004118863493204117, 0.0019121657824143767,
+  -0.000277673767413944, -0.0006141284829936922, 0.0002637206926010549, 0.002559129847213626,
+  0.0054609463550150394, -0.0022978750057518482, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0018329351441934705, -0.003197423415258527, 0.001390628283843398,
+  -0.00019137485651299357, -0.0003751710755750537, 0.0002703833160921931, 0.0019195021595805883,
+  0.00427305418998003, -0.0018329351441934705, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.001412746380083263, -0.0023880205117166042, 0.0009599757613614202,
+  -0.00012571405386552215, -0.00021200079936534166, 0.00026087791775353253, 0.001386339426971972,
+  0.003220402402803302, -0.0014127467293292284, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0010389715898782015, -0.0016921174246817827, 0.0006164693622849882,
+  -7.815339631633833e-05, -0.0001076994594768621, 0.00023607249022461474, 0.0009521057363599539,
+  0.0023059439845383167, -0.0010389715898782015, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0007138299406506121, -0.0011113409418612719, 0.00035565378493629396,
+  -4.5835153287043795e-05, -4.6896479034330696e-05, 0.00019755036919377744, 0.0006090688402764499,
+  0.0015333222690969706, -0.0007138300570659339, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00044038958731107414, -0.0006476585404016078, 0.0001721005537547171,
+  -2.5533236112096347e-05, -1.6005731595214456e-05, 0.0001479329221183434, 0.00034933799179270864,
+  0.0009072087705135345, -0.00044038958731107414, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00022320164134725928, -0.00030376637005247176, 5.896376751479693e-05,
+  -1.361143404210452e-05, -3.50270693161292e-06, 9.151515405392274e-05, 0.0001650399062782526,
+  0.000434032961493358, -0.00022320167045108974, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.996562296990305e-05, -8.412015449721366e-05, 6.955207027203869e-06,
+  -6.07388028583955e-06, -2.589750351944531e-07, 3.590428605093621e-05, 4.902316868538037e-05,
+  0.0001239005650859326, -6.996562296990305e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 27
diff --git a/extra_tests/regression_fits/no_lagrange_27.json b/extra_tests/regression_fits/no_lagrange_27.json
index 7d5e64604d..a186c18807 100644
--- a/extra_tests/regression_fits/no_lagrange_27.json
+++ b/extra_tests/regression_fits/no_lagrange_27.json
@@ -51,45 +51,45 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 2.7999439239501953,
-  "erf_vl": 2.4885871410369873,
-  "chi2": 2.0643887519836426,
+  "erf_tr": 2.7999465465545654,
+  "erf_vl": 2.4885904788970947,
+  "chi2": 2.06439471244812,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.3221136759815355,
-    1.4870571225552478,
-    1.173534376130871,
-    1.000593715785606,
-    1.2220395497495782
+    1.322113606791354,
+    1.4870589137356718,
+    1.1735342433844764,
+    1.0005936802330058,
+    1.222040097491277
   ],
   "integrability": [
-    0.0009427238837846075,
-    0.0009427238837822483,
-    5.0013965618989076e-05,
-    0.474632330238818,
-    0.007130930665878887
+    0.0009427248514866093,
+    0.0009427248514843889,
+    5.001403087501188e-05,
+    0.47463181614875705,
+    0.007130894751751882
   ],
   "timing": {
     "walltime": {
-      "Total": 14.253797054290771,
+      "Total": 15.22148847579956,
       "start": 0.0,
-      "replica_set": 0.21603798866271973,
-      "replica_fitted": 14.253704071044922,
-      "replica_set_to_replica_fitted": 14.037666082382202
+      "replica_set": 0.23516511917114258,
+      "replica_fitted": 15.221322059631348,
+      "replica_set_to_replica_fitted": 14.986156940460205
     },
     "cputime": {
-      "Total": 15.377915377999999,
+      "Total": 16.402484346999998,
       "start": 0.0,
-      "replica_set": 0.21512377100000002,
-      "replica_fitted": 15.377821143,
-      "replica_set_to_replica_fitted": 15.162697372
+      "replica_set": 0.23330889300000024,
+      "replica_fitted": 16.402316713999998,
+      "replica_set_to_replica_fitted": 16.169007820999997
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
-    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
+    "nnpdf": "4.0.9.post1210.dev0+d36bcce78",
+    "validphys": "4.0.9.post1210.dev0+d36bcce78"
   }
 }
diff --git a/extra_tests/regression_fits/no_msr_92.exportgrid b/extra_tests/regression_fits/no_msr_92.exportgrid
index 9797499df9..7a5c697d99 100644
--- a/extra_tests/regression_fits/no_msr_92.exportgrid
+++ b/extra_tests/regression_fits/no_msr_92.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, -2.4362943172454834, 0.49421271681785583, 0.46692922711372375, 0.4669736623764038,
-  -0.534435510635376, 0.46713539958000183, 0.467092365026474, 0.4939541518688202,
+- [0.0, 0.0, -2.4362943172454834, 0.4942127764225006, 0.46692922711372375, 0.4669737219810486,
+  -0.5344355702400208, 0.4671354591846466, 0.467092365026474, 0.49395421147346497,
   -2.4362943172454834, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.3590054512023926, 0.48423776030540466, 0.4558604955673218, 0.4559110403060913,
-  -0.5343948006629944, 0.45608994364738464, 0.45604103803634644, 0.48395422101020813,
-  -2.3590054512023926, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.284184217453003, 0.47482988238334656, 0.4453137218952179, 0.44537118077278137,
-  -0.5342838764190674, 0.4455689787864685, 0.4455135464668274, 0.47451886534690857,
-  -2.284184217453003, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2117512226104736, 0.46597814559936523, 0.4352759122848511, 0.4353412389755249,
-  -0.5340980291366577, 0.43556007742881775, 0.4354971647262573, 0.46563705801963806,
-  -2.211751699447632, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1416308879852295, 0.4576728940010071, 0.42573535442352295, 0.4258095920085907,
-  -0.533832311630249, 0.42605164647102356, 0.4259802997112274, 0.45729878544807434,
-  -2.1416313648223877, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.0737497806549072, 0.4499039649963379, 0.41667959094047546, 0.4167640507221222,
-  -0.5334814786911011, 0.41703182458877563, 0.4169509708881378, 0.4494937062263489,
-  -2.0737497806549072, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.008035659790039, 0.4426635205745697, 0.40809857845306396, 0.40819454193115234,
-  -0.5330398678779602, 0.40849095582962036, 0.4083992838859558, 0.44221368432044983,
-  -2.008035659790039, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.944419503211975, 0.4359425902366638, 0.3999808132648468, 0.40008988976478577,
-  -0.5325012803077698, 0.4004179537296295, 0.400314062833786, 0.4354493319988251,
-  -1.944419503211975, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8828340768814087, 0.42973411083221436, 0.39231669902801514, 0.39244067668914795,
-  -0.5318593382835388, 0.39280396699905396, 0.39268621802330017, 0.429193377494812,
+- [0.0, 0.0, -2.3590052127838135, 0.4842379689216614, 0.4558607339859009, 0.4559112787246704,
+  -0.5343948006629944, 0.45609018206596375, 0.4560413062572479, 0.48395439982414246,
+  -2.3590052127838135, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.2841835021972656, 0.4748300015926361, 0.44531381130218506, 0.44537127017974854,
+  -0.5342838168144226, 0.44556906819343567, 0.44551363587379456, 0.47451895475387573,
+  -2.2841835021972656, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.2117507457733154, 0.4659779667854309, 0.43527573347091675, 0.4353410601615906,
+  -0.5340979695320129, 0.4355598986148834, 0.435496985912323, 0.46563684940338135,
+  -2.2117512226104736, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.1416311264038086, 0.45767298340797424, 0.4257354438304901, 0.42580971121788025,
+  -0.533832311630249, 0.4260517358779907, 0.42598041892051697, 0.4572988748550415,
+  -2.141631603240967, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.07374906539917, 0.44990402460098267, 0.416679710149765, 0.41676414012908936,
+  -0.5334813594818115, 0.4170319139957428, 0.416951060295105, 0.44949376583099365,
+  -2.07374906539917, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.008035898208618, 0.44266360998153687, 0.40809866786003113, 0.4081946611404419,
+  -0.5330398082733154, 0.4084910750389099, 0.40839940309524536, 0.4422138035297394,
+  -2.008035898208618, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.944419264793396, 0.4359426200389862, 0.3999808430671692, 0.40008991956710815,
+  -0.5325012803077698, 0.4004179835319519, 0.4003141224384308, 0.43544939160346985,
+  -1.944419264793396, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.8828340768814087, 0.4297340214252472, 0.3923165500164032, 0.392440527677536,
+  -0.5318594574928284, 0.392803817987442, 0.39268606901168823, 0.42919328808784485,
   -1.8828340768814087, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8232152462005615, 0.4240308701992035, 0.3850962221622467, 0.3852371573448181,
-  -0.5311073064804077, 0.38563939929008484, 0.3855060040950775, 0.42343807220458984,
+- [0.0, 0.0, -1.8232152462005615, 0.4240309000015259, 0.3850962817668915, 0.3852371871471405,
+  -0.5311073064804077, 0.3856394588947296, 0.3855060636997223, 0.42343810200691223,
   -1.8232152462005615, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7654993534088135, 0.41882678866386414, 0.37831056118011475, 0.3784707188606262,
+- [0.0, 0.0, -1.765499234199524, 0.41882678866386414, 0.37831056118011475, 0.3784707188606262,
   -0.53023761510849, 0.37891632318496704, 0.37876519560813904, 0.4181770384311676,
-  -1.7654993534088135, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7096259593963623, 0.41411617398262024, 0.37195077538490295, 0.3721327781677246,
-  -0.5292426943778992, 0.37262651324272156, 0.37245532870292664, 0.4134039580821991,
+  -1.765499234199524, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.7096259593963623, 0.4141162931919098, 0.3719509541988373, 0.37213289737701416,
+  -0.5292425751686096, 0.3726266622543335, 0.37245550751686096, 0.41340407729148865,
   -1.709626317024231, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.655536413192749, 0.40989387035369873, 0.3660087585449219, 0.3662155568599701,
-  -0.5281139612197876, 0.366762638092041, 0.36656883358955383, 0.4091132581233978,
-  -1.655536413192749, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6031728982925415, 0.40615537762641907, 0.36047643423080444, 0.3607114255428314,
-  -0.5268426537513733, 0.361317902803421, 0.3610985577106476, 0.40529993176460266,
-  -1.6031731367111206, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.552480697631836, 0.40289682149887085, 0.3553464114665985, 0.35561344027519226,
-  -0.5254191756248474, 0.3562857210636139, 0.35603752732276917, 0.40195930004119873,
-  -1.552480697631836, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5034065246582031, 0.4001143276691437, 0.3506108820438385, 0.3509142994880676,
-  -0.523833692073822, 0.3516599237918854, 0.3513791859149933, 0.399087131023407, -1.503406286239624,
-  0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.455897569656372, 0.39780548214912415, 0.3462636172771454, 0.3466082811355591,
-  -0.5220750570297241, 0.34743526577949524, 0.3471178114414215, 0.39667993783950806,
+- [0.0, 0.0, -1.6555362939834595, 0.40989381074905396, 0.3660086989402771, 0.3662154972553253,
+  -0.5281139612197876, 0.36676257848739624, 0.36656874418258667, 0.40911319851875305,
+  -1.6555362939834595, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.6031725406646729, 0.4061552584171295, 0.3604763448238373, 0.36071130633354187,
+  -0.5268426537513733, 0.36131778359413147, 0.36109843850135803, 0.4052998125553131,
+  -1.603172779083252, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.5524804592132568, 0.40289679169654846, 0.35534632205963135, 0.3556133508682251,
+  -0.5254191160202026, 0.35628563165664673, 0.356037437915802, 0.40195927023887634,
+  -1.5524804592132568, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.503406286239624, 0.4001142084598541, 0.3506108224391937, 0.35091421008110046,
+  -0.523833692073822, 0.3516598641872406, 0.3513790965080261, 0.3990870416164398,
+  -1.503406047821045, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.455897569656372, 0.3978056311607361, 0.3462637662887573, 0.3466084599494934,
+  -0.5220749974250793, 0.3474354147911072, 0.34711793065071106, 0.39668008685112,
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   -0.003996583633124828, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0033835365902632475, -0.00531254056841135, 0.0032773588318377733,
-  -0.0005952671635895967, -3.524964631651528e-05, 0.0019010920077562332, 0.0059926556423306465,
-  0.009075576439499855, -0.0033835365902632475, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0028157506603747606, -0.004338531754910946, 0.0025730363558977842,
-  -0.000427916063927114, -2.4102586394292302e-05, 0.0016736910911276937, 0.00482791056856513,
-  0.00751147698611021, -0.0028157508932054043, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.002293981611728668, -0.003458790248259902, 0.001962553011253476, -0.00029202864971011877,
-  -1.5719753719167784e-05, 0.0014475706266239285, 0.0038049917202442884, 0.006081510800868273,
-  -0.002293981844559312, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0018191717099398375, -0.0026747698429971933, 0.0014431963209062815,
-  -0.00018547680519986898, -9.657366717874538e-06, 0.0012235661270096898, 0.002917634090408683,
-  0.0047884490340948105, -0.0018191717099398375, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0013925295788794756, -0.001987866358831525, 0.001011812943033874,
-  -0.00010583185212453827, -5.486970621859655e-06, 0.0010030776029452682, 0.0021594837307929993,
-  0.003635534318163991, -0.0013925295788794756, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.001015606103464961, -0.0013994326582178473, 0.0006647128611803055,
-  -5.0305436161579564e-05, -2.8022113838233054e-06, 0.0007882180507294834, 0.0015241079963743687,
-  0.002626593690365553, -0.001015606103464961, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0006904749316163361, -0.0009108876693062484, 0.00039755553007125854,
-  -1.5692063243477605e-05, -1.2264500810488244e-06, 0.0005821041995659471, 0.0010051315184682608,
-  0.001766378409229219, -0.0006904748152010143, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0004199970280751586, -0.0005238226731307805, 0.00020513785420916975,
-  1.731293764350994e-06, -4.2066881178470794e-07, 0.0003893295652233064, 0.0005964144365862012,
-  0.0010610291501507163, -0.00041999705717898905, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.00020839522767346352, -0.0002402633981546387, 8.104409062070772e-05,
-  6.355017376336036e-06, -9.250381083347747e-08, 0.00021695575560443103, 0.00029257123242132366,
-  0.0005191177478991449, -0.00020839522767346352, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -6.273015605984256e-05, -6.332326302072033e-05, 1.6910595149965957e-05,
-  3.503181915220921e-06, -6.8713696954603165e-09, 7.708707562414929e-05, 9.058212890522555e-05,
-  0.00015440276183653623, -6.273014878388494e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00338353612460196, -0.005312539171427488, 0.003277356969192624, -0.0005952683859504759,
+  -3.524964631651528e-05, 0.0019010936375707388, 0.005992656107991934, 0.009075576439499855,
+  -0.0033835358917713165, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.002815751126036048, -0.004338532220572233, 0.0025730347260832787,
+  -0.0004279177519492805, -2.4102588213281706e-05, 0.0016736923716962337, 0.004827911499887705,
+  0.00751147698611021, -0.002815751126036048, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.002293981611728668, -0.0034587904810905457, 0.0019625516142696142,
+  -0.00029202972655184567, -1.5719753719167784e-05, 0.0014475715579465032, 0.003804992651566863,
+  0.006081509403884411, -0.002293981611728668, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0018191718263551593, -0.0026747703086584806, 0.0014431956224143505,
+  -0.00018547764921095222, -9.657365808379836e-06, 0.0012235664762556553, 0.00291763455606997,
+  0.0047884490340948105, -0.0018191721756011248, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0013925298117101192, -0.001987866358831525, 0.0010118124773725867,
+  -0.00010583215771475807, -5.486970621859655e-06, 0.0010030773701146245, 0.0021594834979623556,
+  0.0036355338525027037, -0.0013925298117101192, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0010156063362956047, -0.0013994331238791347, 0.0006647120462730527,
+  -5.030625834478997e-05, -2.802212293318007e-06, 0.000788218982052058, 0.001524109160527587,
+  0.00262659415602684, -0.0010156063362956047, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0006904748734086752, -0.0009108877275139093, 0.0003975551517214626,
+  -1.569237429066561e-05, -1.2264500810488244e-06, 0.0005821047234348953, 0.001005131984129548,
+  0.0017663787584751844, -0.0006904748734086752, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00041999705717898905, -0.0005238226731307805, 0.0002051375777227804,
+  1.7310376279056072e-06, -4.2066881178470794e-07, 0.0003893299144692719, 0.0005964147276245058,
+  0.0010610292665660381, -0.00041999705717898905, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00020839528588112444, -0.00024026347091421485, 8.104401786113158e-05,
+  6.354943707265193e-06, -9.250381793890483e-08, 0.00021695575560443103, 0.00029257123242132366,
+  0.000519117689691484, -0.00020839525677729398, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.27301778877154e-05, -6.332328484859318e-05, 1.6910544218262658e-05,
+  3.5031334846280515e-06, -6.871371027727946e-09, 7.708710472797975e-05, 9.058215073309839e-05,
+  0.00015440276183653623, -6.27301778877154e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 92
diff --git a/extra_tests/regression_fits/no_msr_92.json b/extra_tests/regression_fits/no_msr_92.json
index 7488ad2d41..ccaac80acf 100644
--- a/extra_tests/regression_fits/no_msr_92.json
+++ b/extra_tests/regression_fits/no_msr_92.json
@@ -51,45 +51,45 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 5.661355972290039,
-  "erf_vl": 5.671206951141357,
-  "chi2": 3.32541561126709,
+  "erf_tr": 5.661348342895508,
+  "erf_vl": 5.671204090118408,
+  "chi2": 3.3254077434539795,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.3377686642197593,
-    0.9939545210328817,
-    1.1826497742373074,
-    1.0015656778859183,
-    1.1694083050861181
+    1.3377685559283214,
+    0.9939545230594712,
+    1.182649842290376,
+    1.001565686943213,
+    1.1694082093346772
   ],
   "integrability": [
-    0.0009784703433980552,
-    0.0009784703433980135,
-    4.601749685653744e-05,
-    0.47618307173252106,
-    0.007452808495145062
+    0.0009784701542230809,
+    0.000978470154223074,
+    4.601749776607378e-05,
+    0.4761830791831016,
+    0.007452807330991865
   ],
   "timing": {
     "walltime": {
-      "Total": 19.36279797554016,
+      "Total": 20.706217765808105,
       "start": 0.0,
-      "replica_set": 0.22215056419372559,
-      "replica_fitted": 19.36264204978943,
-      "replica_set_to_replica_fitted": 19.140491485595703
+      "replica_set": 0.23932576179504395,
+      "replica_fitted": 20.70611071586609,
+      "replica_set_to_replica_fitted": 20.466784954071045
     },
     "cputime": {
-      "Total": 20.82930143,
+      "Total": 22.302579570000002,
       "start": 0.0,
-      "replica_set": 0.2209823669999995,
-      "replica_fitted": 20.829144176,
-      "replica_set_to_replica_fitted": 20.608161809
+      "replica_set": 0.23773320799999986,
+      "replica_fitted": 22.302470446,
+      "replica_set_to_replica_fitted": 22.064737238
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
-    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
+    "nnpdf": "4.0.9.post1210.dev0+d36bcce78",
+    "validphys": "4.0.9.post1210.dev0+d36bcce78"
   }
 }
diff --git a/extra_tests/regression_fits/no_sumrules_18.exportgrid b/extra_tests/regression_fits/no_sumrules_18.exportgrid
index 1152a1cb9c..a0e86f501a 100644
--- a/extra_tests/regression_fits/no_sumrules_18.exportgrid
+++ b/extra_tests/regression_fits/no_sumrules_18.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, -2.4376718997955322, 0.4963560998439789, 0.469154417514801, 0.46919873356819153,
-  -0.5368903875350952, 0.4692380130290985, 0.46919408440589905, 0.4962925910949707,
+- [0.0, 0.0, -2.4376718997955322, 0.49635592103004456, 0.4691542983055115, 0.4691985547542572,
+  -0.5368903875350952, 0.4692378342151642, 0.4691939651966095, 0.4962924122810364,
   -2.4376718997955322, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.3603436946868896, 0.4862646162509918, 0.4579818546772003, 0.45803213119506836,
-  -0.5368636846542358, 0.458075612783432, 0.458025723695755, 0.4861948788166046, -2.3603436946868896,
-  0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2854843139648438, 0.4767412543296814, 0.44733378291130066, 0.4473908841609955,
-  -0.5367674827575684, 0.44743892550468445, 0.4473823606967926, 0.4766647517681122,
+- [0.0, 0.0, -2.3603436946868896, 0.4862644076347351, 0.4579816460609436, 0.45803195238113403,
+  -0.5368636846542358, 0.4580754339694977, 0.4580255150794983, 0.4861946702003479,
+  -2.3603436946868896, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.2854843139648438, 0.47674113512039185, 0.4473336637020111, 0.44739073514938354,
+  -0.5367674827575684, 0.4474388062953949, 0.44738224148750305, 0.47666463255882263,
   -2.2854843139648438, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2130160331726074, 0.4677753746509552, 0.43719762563705444, 0.43726250529289246,
-  -0.5365970730781555, 0.43731558322906494, 0.43725135922431946, 0.4676913917064667,
+- [0.0, 0.0, -2.2130160331726074, 0.46777525544166565, 0.4371975362300873, 0.4372623860836029,
+  -0.5365970134735107, 0.4373154640197754, 0.4372512400150299, 0.4676912724971771,
   -2.213015556335449, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1428616046905518, 0.45935678482055664, 0.4275612533092499, 0.42763492465019226,
-  -0.5363475680351257, 0.42769381403923035, 0.42762088775634766, 0.4592647850513458,
+- [0.0, 0.0, -2.1428616046905518, 0.45935672521591187, 0.4275611937046051, 0.4276348650455475,
+  -0.536347508430481, 0.42769375443458557, 0.4276208281517029, 0.45926472544670105,
   -2.1428611278533936, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.0749471187591553, 0.4514754116535187, 0.4184126555919647, 0.418496310710907,
-  -0.5360134243965149, 0.4185614287853241, 0.4184786379337311, 0.45137444138526917,
-  -2.0749471187591553, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.0749473571777344, 0.45147526264190674, 0.41841253638267517, 0.41849619150161743,
+  -0.5360134243965149, 0.41856130957603455, 0.41847851872444153, 0.4513743221759796,
+  -2.0749473571777344, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -2.009202003479004, 0.44412246346473694, 0.4097408652305603, 0.4098358452320099,
   -0.5355893969535828, 0.4099079370498657, 0.4098139703273773, 0.4440116584300995,
   -2.009201765060425, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9455560445785522, 0.43728986382484436, 0.40153563022613525, 0.4016434848308563,
-  -0.5350694060325623, 0.40172329545021057, 0.4016166925430298, 0.43716830015182495,
+- [0.0, 0.0, -1.9455560445785522, 0.437289834022522, 0.4015355706214905, 0.40164345502853394,
+  -0.5350694060325623, 0.4017232656478882, 0.401616632938385, 0.43716827034950256,
   -1.9455560445785522, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8839428424835205, 0.4309695363044739, 0.3937865197658539, 0.3939090073108673,
-  -0.5344469547271729, 0.3939972519874573, 0.3938762843608856, 0.43083614110946655,
-  -1.8839428424835205, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.824297308921814, 0.42515450716018677, 0.38648417592048645, 0.38662323355674744,
-  -0.5337152481079102, 0.38672101497650146, 0.38658374547958374, 0.42500820755958557,
+- [0.0, 0.0, -1.88394296169281, 0.43096938729286194, 0.3937864303588867, 0.39390888810157776,
+  -0.5344468951225281, 0.3939971327781677, 0.39387619495391846, 0.430836021900177,
+  -1.88394296169281, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.824297308921814, 0.4251543879508972, 0.3864840865135193, 0.3866230845451355,
+  -0.5337153077125549, 0.3867208659648895, 0.3865836560726166, 0.4250081181526184,
   -1.8242970705032349, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7665562629699707, 0.4198381006717682, 0.379619300365448, 0.37977713346481323,
-  -0.5328671336174011, 0.37988555431365967, 0.37972986698150635, 0.4196777045726776,
+- [0.0, 0.0, -1.7665562629699707, 0.419838011264801, 0.3796192407608032, 0.37977707386016846,
+  -0.5328670740127563, 0.3798854947090149, 0.3797298073768616, 0.41967761516571045,
   -1.7665562629699707, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7106590270996094, 0.4150146245956421, 0.37318363785743713, 0.3733627200126648,
-  -0.5318947434425354, 0.37348276376724243, 0.3733062148094177, 0.414838582277298,
-  -1.7106590270996094, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.656546950340271, 0.41067832708358765, 0.36716851592063904, 0.3673717677593231,
-  -0.530789852142334, 0.36750492453575134, 0.3673047125339508, 0.4104853570461273,
-  -1.656546950340271, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.604162335395813, 0.4068247377872467, 0.3615665137767792, 0.3617972135543823,
-  -0.5295436978340149, 0.36194470524787903, 0.36171770095825195, 0.4066130220890045,
+- [0.0, 0.0, -1.7106589078903198, 0.4150144159793854, 0.37318339943885803, 0.37336254119873047,
+  -0.5318948030471802, 0.3734825849533081, 0.3733059763908386, 0.41483837366104126,
+  -1.7106589078903198, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.65654718875885, 0.41067829728126526, 0.36716845631599426, 0.36737173795700073,
+  -0.530789852142334, 0.36750489473342896, 0.36730465292930603, 0.41048532724380493,
+  -1.65654718875885, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.604162335395813, 0.40682464838027954, 0.361566424369812, 0.36179712414741516,
+  -0.5295436978340149, 0.36194461584091187, 0.3617176115512848, 0.40661293268203735,
   -1.604162573814392, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5534502267837524, 0.4034493565559387, 0.35637009143829346, 0.3566318452358246,
-  -0.528146505355835, 0.35679537057876587, 0.3565380871295929, 0.4032171666622162,
+- [0.0, 0.0, -1.5534502267837524, 0.40344926714897156, 0.3563700318336487, 0.3566317856311798,
+  -0.5281464457511902, 0.3567953109741211, 0.35653799772262573, 0.4032171070575714,
   -1.5534502267837524, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5043574571609497, 0.4005486071109772, 0.3515723943710327, 0.35186928510665894,
-  -0.5265888571739197, 0.3520507514476776, 0.3517591655254364, 0.4002940356731415,
-  -1.5043576955795288, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4568315744400024, 0.3981195092201233, 0.3471669852733612, 0.34750378131866455,
-  -0.524859607219696, 0.34770500659942627, 0.34737470746040344, 0.39784035086631775,
-  -1.4568315744400024, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4108232259750366, 0.39615902304649353, 0.34314724802970886, 0.3435291647911072,
-  -0.5229475498199463, 0.343752384185791, 0.3433782160282135, 0.39585283398628235,
+- [0.0, 0.0, -1.5043575763702393, 0.40054863691329956, 0.3515724241733551, 0.3518693149089813,
+  -0.5265889167785645, 0.35205078125, 0.3517592251300812, 0.40029409527778625, -1.5043578147888184,
+  0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.4568321704864502, 0.3981195390224457, 0.3471670150756836, 0.34750378131866455,
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+  0.0011667929356917739, -0.00100462615955621, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0006823049625381827, 9.376215166412294e-05, 0.0006811857456341386,
+  0.00026188232004642487, -1.2220259577588877e-06, 0.00033564033219590783, 0.0007571904570795596,
+  0.0007953373715281487, -0.0006823049625381827, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0004144445701967925, 7.290229405043647e-05, 0.0003858782001771033,
+  0.00017992981884162873, -4.1914452708624594e-07, 0.00023159924603533, 0.0004383928026072681,
+  0.0004859926411882043, -0.0004144445701967925, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00020519850659184158, 4.7100274969125167e-05, 0.00017738431051839143,
+  0.00010192589252255857, -9.216720542326584e-08, 0.0001326544734183699, 0.0002083257568301633,
   0.00024346751160919666, -0.00020519853569567204, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -6.150574336061254e-05, 1.9834607883240096e-05, 4.981512392987497e-05,
-  3.630002174759284e-05, -6.846264444249073e-09, 4.8308585974154994e-05, 6.184382073115557e-05,
-  7.534189353464171e-05, -6.150575063657016e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.150572880869731e-05, 1.9834602426271886e-05, 4.9815120291896164e-05,
+  3.6300025385571644e-05, -6.846265776516702e-09, 4.8308596888091415e-05, 6.18438352830708e-05,
+  7.534190081059933e-05, -6.150573608465493e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 18
diff --git a/extra_tests/regression_fits/no_sumrules_18.json b/extra_tests/regression_fits/no_sumrules_18.json
index dd936dea86..40cad4cce9 100644
--- a/extra_tests/regression_fits/no_sumrules_18.json
+++ b/extra_tests/regression_fits/no_sumrules_18.json
@@ -51,45 +51,45 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 5.234589576721191,
-  "erf_vl": 5.933957099914551,
-  "chi2": 3.2721152305603027,
+  "erf_tr": 5.234587669372559,
+  "erf_vl": 5.933964252471924,
+  "chi2": 3.272118330001831,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.3377848138904636,
-    0.9938499753341616,
-    1.0016840225668207,
-    0.990568630161653,
-    1.0071484433088025
+    1.3377848105472658,
+    0.9938499742310553,
+    1.0016840246357674,
+    0.9905686298978078,
+    1.007148454495649
   ],
   "integrability": [
-    0.0002282706336703827,
-    0.0002282706336700635,
-    1.0907395790099583e-05,
-    0.4776186943054198,
-    0.0018318516376890984
+    0.00022827063367029943,
+    0.00022827063367009126,
+    1.090739567638499e-05,
+    0.47761867940425856,
+    0.0018318514048583923
   ],
   "timing": {
     "walltime": {
-      "Total": 15.640143632888794,
+      "Total": 17.095475435256958,
       "start": 0.0,
-      "replica_set": 0.23237943649291992,
-      "replica_fitted": 15.640068531036377,
-      "replica_set_to_replica_fitted": 15.407689094543457
+      "replica_set": 0.24184823036193848,
+      "replica_fitted": 17.095387935638428,
+      "replica_set_to_replica_fitted": 16.85353970527649
     },
     "cputime": {
-      "Total": 16.991643305,
+      "Total": 18.510476551,
       "start": 0.0,
-      "replica_set": 0.22577083200000025,
-      "replica_fitted": 16.991566942000002,
-      "replica_set_to_replica_fitted": 16.76579611
+      "replica_set": 0.2397011959999995,
+      "replica_fitted": 18.510387164999997,
+      "replica_set_to_replica_fitted": 18.270685969
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
-    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
+    "nnpdf": "4.0.9.post1210.dev0+d36bcce78",
+    "validphys": "4.0.9.post1210.dev0+d36bcce78"
   }
 }
diff --git a/extra_tests/regression_fits/no_vsr_54.exportgrid b/extra_tests/regression_fits/no_vsr_54.exportgrid
index c643053359..fe10d2fca6 100644
--- a/extra_tests/regression_fits/no_vsr_54.exportgrid
+++ b/extra_tests/regression_fits/no_vsr_54.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, -2.350919485092163, 0.20183704793453217, 0.17518334090709686, 0.1752297282218933,
-  -16.511144638061523, 0.17526739835739136, 0.17522133886814117, 0.20177598297595978,
-  -2.350919485092163, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2766430377960205, 0.20059850811958313, 0.1728854924440384, 0.17293819785118103,
-  -16.519506454467773, 0.17297987639904022, 0.17292755842208862, 0.20053152740001678,
-  -2.2766430377960205, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.204718828201294, 0.1996545046567917, 0.17083929479122162, 0.1708991825580597,
-  -16.52630615234375, 0.17094524204730988, 0.1708858609199524, 0.19958096742630005,
-  -2.204718828201294, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.135073184967041, 0.19900250434875488, 0.1690405309200287, 0.1691085398197174,
-  -16.53144073486328, 0.16915948688983917, 0.1690920740365982, 0.1989217847585678,
-  -2.135073661804199, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.0676326751708984, 0.19864018261432648, 0.1674848198890686, 0.1675620973110199,
-  -16.534799575805664, 0.16761846840381622, 0.16754189133644104, 0.19855159521102905,
-  -2.0676326751708984, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.0023272037506104, 0.19856594502925873, 0.1661687046289444, 0.16625641286373138,
-  -16.5362606048584, 0.16631881892681122, 0.1662319302558899, 0.19846875965595245,
-  -2.0023269653320312, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9390889406204224, 0.19877871870994568, 0.165088951587677, 0.16518864035606384,
-  -16.535694122314453, 0.16525769233703613, 0.16515901684761047, 0.1986720710992813,
-  -1.9390891790390015, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.877852201461792, 0.1992773711681366, 0.16424229741096497, 0.16435550153255463,
-  -16.5329647064209, 0.16443191468715668, 0.1643199324607849, 0.19916032254695892,
-  -1.877852201461792, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8185523748397827, 0.20006154477596283, 0.16362614929676056, 0.1637546718120575,
-  -16.52791976928711, 0.16383932530879974, 0.1637122631072998, 0.19993311166763306,
-  -1.8185523748397827, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7611290216445923, 0.20113135874271393, 0.16323809325695038, 0.1633840650320053,
-  -16.520408630371094, 0.1634778529405594, 0.16333365440368652, 0.2009904682636261,
-  -1.7611290216445923, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7055213451385498, 0.20248694717884064, 0.16307587921619415, 0.16324159502983093,
-  -16.5102596282959, 0.16334551572799683, 0.16318188607692719, 0.20233234763145447,
-  -1.7055213451385498, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6516716480255127, 0.20412929356098175, 0.163137748837471, 0.16332592070102692,
-  -16.497297286987305, 0.1634409874677658, 0.16325537860393524, 0.2039596438407898,
-  -1.6516718864440918, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5995234251022339, 0.20605914294719696, 0.16342173516750336, 0.16363529860973358,
-  -16.4813289642334, 0.1637628972530365, 0.163552388548851, 0.2058730125427246, -1.599523663520813,
+- [0.0, 0.0, -2.3508875370025635, 0.2019854038953781, 0.17533138394355774, 0.1753777712583542,
+  -16.435802459716797, 0.17541544139385223, 0.17536936700344086, 0.20192433893680573,
+  -2.3508875370025635, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.276611804962158, 0.20074349641799927, 0.17303016781806946, 0.1730828732252121,
+  -16.444116592407227, 0.1731245517730713, 0.1730722337961197, 0.20067651569843292,
+  -2.276611804962158, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.204688549041748, 0.19979554414749146, 0.17098002135753632, 0.1710399091243744,
+  -16.450878143310547, 0.17108598351478577, 0.17102660238742828, 0.199722021818161,
+  -2.204688549041748, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.1350433826446533, 0.19913974404335022, 0.16917738318443298, 0.1692453920841217,
+  -16.455982208251953, 0.16929633915424347, 0.1692289263010025, 0.19905902445316315,
+  -2.1350438594818115, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.067603349685669, 0.19877371191978455, 0.16761799156665802, 0.16769523918628693,
+  -16.459320068359375, 0.16775156557559967, 0.16767501831054688, 0.19868512451648712,
+  -2.067603349685669, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.0022993087768555, 0.19869621098041534, 0.16629859805107117, 0.16638636589050293,
+  -16.460763931274414, 0.16644877195358276, 0.16636182367801666, 0.19859904050827026,
+  -2.0022990703582764, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.9390614032745361, 0.19890590012073517, 0.16521577537059784, 0.16531546413898468,
+  -16.460187911987305, 0.16538451611995697, 0.1652858406305313, 0.1987992376089096,
+  -1.9390616416931152, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.8778249025344849, 0.19940127432346344, 0.16436581313610077, 0.16447901725769043,
+  -16.457462310791016, 0.16455544531345367, 0.16444344818592072, 0.19928422570228577,
+  -1.8778249025344849, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.8185261487960815, 0.2001822590827942, 0.1637464165687561, 0.163875013589859,
+  -16.45243263244629, 0.16395966708660126, 0.16383253037929535, 0.2000538408756256,
+  -1.8185261487960815, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.7611032724380493, 0.20124921202659607, 0.1633555144071579, 0.16350148618221283,
+  -16.444944381713867, 0.1635952591896057, 0.16345106065273285, 0.20110832154750824,
+  -1.7611032724380493, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.7054961919784546, 0.20260180532932281, 0.16319027543067932, 0.1633559912443161,
+  -16.434831619262695, 0.1634598672389984, 0.16329625248908997, 0.20244720578193665,
+  -1.7054961919784546, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.6516468524932861, 0.20424120128154755, 0.1632491797208786, 0.16343733668327332,
+  -16.421916961669922, 0.1635524183511734, 0.16336679458618164, 0.2040715366601944,
+  -1.6516470909118652, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.5994993448257446, 0.20616845786571503, 0.16353055834770203, 0.16374412178993225,
+  -16.406007766723633, 0.16387172043323517, 0.16366121172904968, 0.20598234236240387,
+  -1.5994995832443237, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.548999547958374, 0.20838485658168793, 0.1640327423810959, 0.1642751693725586,
+  -16.386903762817383, 0.1644165962934494, 0.16417786478996277, 0.20818062126636505,
+  -1.548999547958374, 0.0, 0.0, 0.0]
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+  -16.364376068115234, 0.16518695652484894, 0.16491630673408508, 0.2106686681509018,
+  -1.5000938177108765, 0.0, 0.0, 0.0]
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+  -1.4527320861816406, 0.0, 0.0, 0.0]
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+  -16.30816650390625, 0.16740170121192932, 0.1670539528131485, 0.2165210247039795,
+  -1.4068644046783447, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.3624430894851685, 0.22018694877624512, 0.16823074221611023, 0.16863246262073517,
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+  -1.3624430894851685, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.3194211721420288, 0.223886176943779, 0.16982463002204895, 0.17028027772903442,
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+  -1.3194211721420288, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.277754306793213, 0.22789160907268524, 0.17163534462451935, 0.17215198278427124,
+  -16.191919326782227, 0.17241615056991577, 0.1719106286764145, 0.22753524780273438,
+  -1.277754306793213, 0.0, 0.0, 0.0]
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+  -1.2373992204666138, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.198312520980835, 0.2368389517068863, 0.17590802907943726, 0.17657193541526794,
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+  -1.198312520980835, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.1604543924331665, 0.24179032444953918, 0.17837032675743103, 0.1791227161884308,
+  -16.029977798461914, 0.179485023021698, 0.17875202000141144, 0.2413194626569748,
+  -1.1604543924331665, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.123783826828003, 0.24706697463989258, 0.18105028569698334, 0.18190263211727142,
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+  -1.123783826828003, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.088263988494873, 0.25267457962036133, 0.18394818902015686, 0.18491356074810028,
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+  -1.088263988494873, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.0538567304611206, 0.25861889123916626, 0.18706443905830383, 0.18815745413303375,
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+- [0.0, 0.0, -0.7886647582054138, 0.3283548057079315, 0.2249378114938736, 0.228219136595726,
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+- [0.0, 0.0, -0.011182966642081738, -0.0031807804480195045, 0.018199559301137924,
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+- [0.0, 0.0, -0.010221724398434162, -0.002880602376535535, 0.016161182895302773, -0.0019619367085397243,
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+- [0.0, 0.0, -0.009300286881625652, -0.0025899766478687525, 0.014259465970098972,
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+- [0.0, 0.0, -0.007577096577733755, -0.0020432493183761835, 0.010857575573027134,
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+- [0.0, 0.0, -0.006775570102035999, -0.001789720612578094, 0.009352716617286205, -0.0009338246891275048,
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+  -0.006775570102035999, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00601431168615818, -0.0015508841024711728, 0.007975165732204914, -0.0007346188649535179,
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+- [0.0, 0.0, -0.005293550435453653, -0.0013276588870212436, 0.006722124759107828,
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+- [0.0, 0.0, -0.0033776271156966686, -0.0007586854044348001, 0.0036788033321499825,
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+- [0.0, 0.0, -0.0004426957166288048, -5.4069620091468096e-05, 0.00024860285338945687,
+  4.9533791752764955e-05, -1.6237065210589208e-05, 6.522324838442728e-05, 0.00026512477779760957,
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+- [0.0, 0.0, -0.00022443788475356996, -2.192660940636415e-05, 0.00010368429502705112,
+  3.075346103287302e-05, -3.552537236828357e-06, 4.292274752515368e-05, 0.00011606306361500174,
+  0.0001479860657127574, -0.00022443788475356996, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -7.041347271297127e-05, -4.585976057569496e-06, 2.419800694042351e-05,
+  1.1136833563796245e-05, -2.6260138952238776e-07, 1.718239400361199e-05, 3.026336526090745e-05,
+  4.285756222088821e-05, -7.04134872648865e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 54
diff --git a/extra_tests/regression_fits/no_vsr_54.json b/extra_tests/regression_fits/no_vsr_54.json
index 89d97ee36d..5eed015101 100644
--- a/extra_tests/regression_fits/no_vsr_54.json
+++ b/extra_tests/regression_fits/no_vsr_54.json
@@ -51,45 +51,45 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 3.680145263671875,
-  "erf_vl": 3.991190195083618,
-  "chi2": 2.1375932693481445,
+  "erf_tr": 3.6802215576171875,
+  "erf_vl": 3.9897525310516357,
+  "chi2": 2.1351373195648193,
   "pos_state": "POS_VETO",
   "arc_lengths": [
-    1.323626790691144,
-    1.488321752436849,
-    1.001549686067655,
-    0.9905208725663955,
-    1.0077644418510328
+    1.3236605012539615,
+    1.4852389974226459,
+    1.0015495421617044,
+    0.990520937078149,
+    1.0077650988176345
   ],
   "integrability": [
-    0.00021608964471037106,
-    0.00021608964470987146,
-    1.0824777262330443e-05,
-    0.4680037945508948,
-    0.001764166401697409
+    0.00021608100633072058,
+    0.00021608100632941607,
+    1.0824776523365998e-05,
+    0.4680093601346005,
+    0.0017641116282882674
   ],
   "timing": {
     "walltime": {
-      "Total": 10.118329048156738,
+      "Total": 10.816762685775757,
       "start": 0.0,
-      "replica_set": 0.22046351432800293,
-      "replica_fitted": 10.118260622024536,
-      "replica_set_to_replica_fitted": 9.897797107696533
+      "replica_set": 0.2327578067779541,
+      "replica_fitted": 10.81659722328186,
+      "replica_set_to_replica_fitted": 10.583839416503906
     },
     "cputime": {
-      "Total": 11.564574429,
+      "Total": 12.319027604,
       "start": 0.0,
-      "replica_set": 0.2187228000000001,
-      "replica_fitted": 11.564504568,
-      "replica_set_to_replica_fitted": 11.345781768
+      "replica_set": 0.23111291699999992,
+      "replica_fitted": 12.318859921,
+      "replica_set_to_replica_fitted": 12.087747004
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
-    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
+    "nnpdf": "4.0.9.post1210.dev0+d36bcce78",
+    "validphys": "4.0.9.post1210.dev0+d36bcce78"
   }
 }
diff --git a/extra_tests/regression_fits/normal_fit_72.exportgrid b/extra_tests/regression_fits/normal_fit_72.exportgrid
index 7f2c76702e..972bfef394 100644
--- a/extra_tests/regression_fits/normal_fit_72.exportgrid
+++ b/extra_tests/regression_fits/normal_fit_72.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, 0.2142082005739212, 0.4887930154800415, 0.4688505530357361, 0.5080575346946716,
-  -18.204565048217773, 0.5084002614021301, 0.4691929817199707, 0.48891687393188477,
-  0.21420817077159882, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.20571914315223694, 0.4778967797756195, 0.45737579464912415, 0.49766814708709717,
-  -18.149396896362305, 0.4980601668357849, 0.4577675461769104, 0.4780433475971222,
-  0.20571917295455933, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.19740338623523712, 0.46743398904800415, 0.446321964263916, 0.48771703243255615,
-  -18.09271812438965, 0.4881654381752014, 0.4467701315879822, 0.4676070511341095,
-  0.1974034160375595, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.18925176560878754, 0.4573945105075836, 0.4356791079044342, 0.47819289565086365,
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-  0.18925176560878754, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.18125613033771515, 0.4477687180042267, 0.42543789744377136, 0.4690852165222168,
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   0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.17340795695781708, 0.43854695558547974, 0.4155888855457306, 0.4603828489780426,
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+  0.008589962497353554, -0.30318036675453186, -0.06135306507349014, -0.14627370238304138,
+  0.004863349720835686, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.004982469603419304, 0.16353434324264526, 0.19125506281852722, 0.21306540071964264,
+  0.007362863048911095, -0.28425368666648865, -0.0547778457403183, -0.13563551008701324,
+  0.004982473328709602, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.005070799496024847, 0.15184234082698822, 0.17647972702980042, 0.19973058998584747,
+  0.0062822033651173115, -0.2659073770046234, -0.048531509935855865, -0.1253964900970459,
+  0.005070811603218317, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0051297713071107864, 0.14060638844966888, 0.16234302520751953, 0.1867997646331787,
+  0.005334199871867895, -0.24815544486045837, -0.04262055456638336, -0.1155652105808258,
+  0.0051297773607075214, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0051608094945549965, 0.12983258068561554, 0.14884890615940094, 0.17428509891033173,
+  0.004506001714617014, -0.23101061582565308, -0.03705013915896416, -0.10614914447069168,
+  0.00516081927344203, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.005165337584912777, 0.11952541023492813, 0.1359996646642685, 0.1621972620487213,
+  0.0037856188137084246, -0.21448379755020142, -0.031824059784412384, -0.09715412557125092,
+  0.005165331531316042, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.005144751165062189, 0.10968822985887527, 0.12379620224237442, 0.15054573118686676,
+  0.003161927917972207, -0.19858461618423462, -0.026944836601614952, -0.08858482539653778,
+  0.005144743248820305, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.005100460723042488, 0.10032311826944351, 0.11223777383565903, 0.13933858275413513,
+  0.00262462068349123, -0.18332114815711975, -0.022413471713662148, -0.0804445892572403,
+  0.005100460723042488, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.005033889319747686, 0.09143096953630447, 0.10132220387458801, 0.12858282029628754,
+  0.0021641775965690613, -0.16870000958442688, -0.01822975091636181, -0.07273545116186142,
+  0.005033883266150951, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.004946424625813961, 0.0830112174153328, 0.09104570001363754, 0.11828391999006271,
+  0.0017718306044116616, -0.15472626686096191, -0.014392077922821045, -0.0654580369591713,
+  0.004946420434862375, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.004839463625103235, 0.07506219297647476, 0.08140302449464798, 0.10844617336988449,
+  0.0014395350590348244, -0.14140352606773376, -0.010897495783865452, -0.05861175060272217,
+  0.004839456640183926, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.004714402370154858, 0.06758090853691101, 0.07238734513521194, 0.09907259792089462,
+  0.0011599360732361674, -0.12873390316963196, -0.007741720415651798, -0.05219462886452675,
+  0.004714408423751593, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.004572643898427486, 0.06056314706802368, 0.06399038434028625, 0.0901648998260498,
+  0.000926329055801034, -0.11671798676252365, -0.004919207189232111, -0.04620344191789627,
+  0.004572647623717785, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.004415574949234724, 0.05400347337126732, 0.05620225891470909, 0.08172355592250824,
+  0.0007326349150389433, -0.10535494238138199, -0.002422965131700039, -0.040633685886859894,
+  0.004415572155267, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.004244584124535322, 0.04789525642991066, 0.0490117147564888, 0.07374779880046844,
+  0.0005733613506890833, -0.09464244544506073, -0.0002448146406095475, -0.0354795828461647,
+  0.004244586918503046, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.004061071667820215, 0.042230602353811264, 0.04240588843822479, 0.06623562425374985,
+  0.00044357054866850376, -0.08457665145397186, 0.0016248002648353577, -0.030734021216630936,
+  0.004061070736497641, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0038664271123707294, 0.03700043261051178, 0.03637046739459038, 0.05918377265334129,
+  0.00033884719596244395, -0.07515231519937515, 0.0031966965179890394, -0.02638867497444153,
+  0.003866428043693304, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0036620511673390865, 0.03219453617930412, 0.030889587476849556, 0.052587803453207016,
+  0.0002552639343775809, -0.06636263430118561, 0.00448301387950778, -0.02243398316204548,
+  0.0036620511673390865, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0034493468701839447, 0.027801472693681717, 0.025945954024791718, 0.046442076563835144,
+  0.00018935046682599932, -0.05819942429661751, 0.0054971398785710335, -0.018859097734093666,
+  0.0034493482671678066, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0032297270372509956, 0.023808706551790237, 0.02152075432240963, 0.040739756077528,
+  0.0001380603207508102, -0.050652969628572464, 0.006253741215914488, -0.0156520027667284,
+  0.0032297256402671337, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.003004607278853655, 0.020202545449137688, 0.01759370043873787, 0.035472892224788666,
+  9.874005627352744e-05, -0.043712157756090164, 0.0067687570117414, -0.012799427844583988,
+  0.0030046082101762295, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0027754248585551977, 0.016968142241239548, 0.014142950065433979, 0.030632292851805687,
+  6.909673538757488e-05, -0.037364277988672256, 0.007059367373585701, -0.010286876000463963,
+  0.0027754243928939104, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0025436265859752893, 0.014089634642004967, 0.011145203374326229, 0.02620776928961277,
+  4.716916737379506e-05, -0.03159525617957115, 0.00714402599260211, -0.008098716847598553,
+  0.0025436265859752893, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0023106823209673166, 0.01155003346502781, 0.00857567135244608, 0.0221879743039608,
+  3.129689866909757e-05, -0.026389528065919876, 0.007042392157018185, -0.006218097172677517,
+  0.002310681389644742, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0020780886989086866, 0.009331319481134415, 0.006408016663044691, 0.018560506403446198,
+  2.0091260012122802e-05, -0.02172997035086155, 0.006775373127311468, -0.004627016838639975,
+  0.0020780880004167557, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.001847380306571722, 0.007414488587528467, 0.004614420235157013, 0.015311982482671738,
+  1.240745132236043e-05, -0.017598042264580727, 0.0063651083037257195, -0.0033063292503356934,
+  0.001847380306571722, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0016201324760913849, 0.00577951967716217, 0.003165486501529813, 0.012427994050085545,
+  7.3167134360119235e-06, -0.013973621651530266, 0.00583494920283556, -0.0022357332054525614,
+  0.0016201327089220285, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0013979828217998147, 0.004405486397445202, 0.0020302787888795137, 0.009893236681818962,
+  4.080188773514237e-06, -0.010835062712430954, 0.005209474824368954, -0.0013938151532784104,
+  0.0013979830546304584, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0011826473055407405, 0.0032705713529139757, 0.0011762797366827726,
+  0.007691552396863699, 2.1234927771729417e-06, -0.008159139193594456, 0.004514481406658888,
+  -0.0007580389501526952, 0.0011826473055407405, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.000975947710685432, 0.002352136420086026, 0.0005693361163139343, 0.005806004628539085,
+  1.0125083917955635e-06, -0.005920968949794769, 0.003777002450078726, -0.0003047571808565408,
+  0.0009759478271007538, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.000779859023168683, 0.0016268392791971564, 0.0001736346894176677, 0.004219050519168377,
+  4.3049740838796424e-07, -0.004093992058187723, 0.0030253352597355843, -9.225626854458824e-06,
+  0.0007798589649610221, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0005965669406577945, 0.0010707250330597162, -4.838919994654134e-05,
+  0.002912656171247363, 1.5650749674023245e-07, -0.002649786416441202, 0.0022890614345669746,
+  0.0001544239348731935, 0.0005965668242424726, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.00042859240784309804, 0.0006594540318474174, -0.00013612421753350645,
+  0.0018686424009501934, 4.534832953595469e-08, -0.0015579538885504007, 0.0015991737600415945,
+  0.00021321416716091335, 0.00042859240784309804, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.00027899612905457616, 0.0003686140407808125, -0.00013091583969071507,
+  0.0010691193165257573, 9.179284887750327e-09, -0.0007857600576244295, 0.0009882382582873106,
+  0.00019542971858754754, 0.0002789961581584066, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.00015183669165708125, 0.0001743699103826657, -7.621219265274704e-05,
+  0.0004974220646545291, 9.655087840343413e-10, -0.0002975202223751694, 0.0004908391856588423,
+  0.00013090124411974102, 0.00015183669165708125, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 5.345364843378775e-05, 5.511318886419758e-05, -1.7613974705454893e-05,
+  0.00014045780699234456, 2.0528290872734445e-11, -5.308024992700666e-05, 0.00014492317859549075,
+  5.195315679884516e-05, 5.345364843378775e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 72
diff --git a/extra_tests/regression_fits/normal_fit_72.json b/extra_tests/regression_fits/normal_fit_72.json
index a274d6da13..e83ba97eb6 100644
--- a/extra_tests/regression_fits/normal_fit_72.json
+++ b/extra_tests/regression_fits/normal_fit_72.json
@@ -49,47 +49,47 @@
       "trainable": false
     }
   ],
-  "stop_epoch": 2087,
-  "best_epoch": 785,
-  "erf_tr": 5.284492015838623,
-  "erf_vl": 6.363158226013184,
-  "chi2": 3.2966108322143555,
+  "stop_epoch": 1884,
+  "best_epoch": 582,
+  "erf_tr": 5.436871528625488,
+  "erf_vl": 6.668923377990723,
+  "chi2": 3.4399309158325195,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.0569356998480046,
-    1.3363067530441,
-    4.207567946214925,
-    1.132385770803842,
-    1.0375105565332834
+    1.0540749014149013,
+    1.3084281896923846,
+    4.124475731961283,
+    1.1230317292106229,
+    1.1308339530748641
   ],
   "integrability": [
-    0.01315347442869294,
-    0.013153474428691247,
-    7.507757985691921e-06,
-    0.007867935462854136,
-    0.004969264555256259
+    0.013055968389383305,
+    0.013055968389380827,
+    7.936421781429281e-06,
+    0.006745368125848063,
+    0.0071892261039463445
   ],
   "timing": {
     "walltime": {
-      "Total": 15.853733539581299,
+      "Total": 16.169139862060547,
       "start": 0.0,
-      "replica_set": 0.23403573036193848,
-      "replica_fitted": 15.853573083877563,
-      "replica_set_to_replica_fitted": 15.619537353515625
+      "replica_set": 0.24132728576660156,
+      "replica_fitted": 16.168989896774292,
+      "replica_set_to_replica_fitted": 15.92766261100769
     },
     "cputime": {
-      "Total": 18.057106057,
+      "Total": 18.279248535,
       "start": 0.0,
-      "replica_set": 0.22598911499999907,
-      "replica_fitted": 18.056944325,
-      "replica_set_to_replica_fitted": 17.83095521
+      "replica_set": 0.2395706509999993,
+      "replica_fitted": 18.279097574,
+      "replica_set_to_replica_fitted": 18.039526923000004
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
-    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
+    "nnpdf": "4.0.9.post1210.dev0+d36bcce78",
+    "validphys": "4.0.9.post1210.dev0+d36bcce78"
   }
 }
diff --git a/extra_tests/regression_fits/polarized_evol.yml b/extra_tests/regression_fits/polarized_evol.yml
index cea9ccd333..d6b05d07dd 100644
--- a/extra_tests/regression_fits/polarized_evol.yml
+++ b/extra_tests/regression_fits/polarized_evol.yml
@@ -12,6 +12,7 @@ dataset_inputs:
 ############################################################
 datacuts:
   t0pdfset: NNPDFpol10_100   # PDF set to generate t0 covmat
+  unpolarized_bc: NNPDF40_nnlo_pch_as_01180
   q2min: 1.00                # Q2 minimum
   w2min: 4.00                # W2 minimum
 
@@ -23,7 +24,7 @@ positivity_bound:
 
 ############################################################
 theory:
-  theoryid: 822
+  theoryid: 41_100_010
 
 ############################################################
 trvlseed: 14613416
@@ -56,6 +57,7 @@ parameters:
   threshold_chi2: 3.5
 
 fitting:
+  savepseudodata: false
   fitbasis: POLARIZED_EVOL
   sum_rules: TSR
   basis:
@@ -69,7 +71,7 @@ positivity:
   posdatasets:
   - {dataset: NNPDF_POS_2P24GEV_XGL-POLARIZED, maxlambda: 1e8}
   - {dataset: NNPDF_POS_2P24GEV_XDQ-POLARIZED, maxlambda: 1e8}
-  - {dataset: NNPDF_POS_2P24GEV_XSQ-POLARIZED, maxlambda: 1e8}
+  - {dataset: NNPDF_POS_2P24GEV_XSQSUM-POLARIZED, maxlambda: 1e8}
   - {dataset: NNPDF_POS_2P24GEV_XUQ-POLARIZED, maxlambda: 1e8}
 
 ############################################################
diff --git a/extra_tests/regression_fits/polarized_evol_34.exportgrid b/extra_tests/regression_fits/polarized_evol_34.exportgrid
index 9a6961eb76..eaad199191 100644
--- a/extra_tests/regression_fits/polarized_evol_34.exportgrid
+++ b/extra_tests/regression_fits/polarized_evol_34.exportgrid
@@ -1,587 +1,588 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, 0.0, -0.18479739129543304, -0.18503735959529877, -0.18503735959529877,
-  -0.7364077568054199, -0.18503735959529877, -0.18503735959529877, -0.18479739129543304,
+- [0.0, 0.0, 0.0, -0.11227669566869736, -0.1128518283367157, -0.1128518283367157,
+  -0.9566451907157898, -0.1128518283367157, -0.1128518283367157, -0.11227669566869736,
   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, -0.1761014312505722, -0.17635415494441986, -0.17635415494441986,
-  -0.7018389701843262, -0.17635415494441986, -0.17635415494441986, -0.1761014312505722,
+- [0.0, 0.0, 0.0, -0.10646971315145493, -0.10707931965589523, -0.10707931965589523,
+  -0.9169837236404419, -0.10707931965589523, -0.10707931965589523, -0.10646971315145493,
   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, -0.16768233478069305, -0.16794832050800323, -0.16794832050800323,
-  -0.6682081818580627, -0.16794832050800323, -0.16794832050800323, -0.16768233478069305,
+- [0.0, 0.0, 0.0, -0.10085587203502655, -0.10150185972452164, -0.10150185972452164,
+  -0.8783043026924133, -0.10150185972452164, -0.10150185972452164, -0.10085587203502655,
   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, -0.15953262150287628, -0.15981245040893555, -0.15981245040893555,
-  -0.6354950070381165, -0.15981245040893555, -0.15981245040893555, -0.15953262150287628,
+- [0.0, 0.0, 0.0, -0.09542878717184067, -0.09611313790082932, -0.09611313790082932,
+  -0.8405823707580566, -0.09611313790082932, -0.09611313790082932, -0.09542878717184067,
   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, -0.1516437977552414, -0.15193797647953033, -0.15193797647953033,
-  -0.6036766171455383, -0.15193797647953033, -0.15193797647953033, -0.1516437977552414,
+- [0.0, 0.0, 0.0, -0.09018255770206451, -0.09090736508369446, -0.09090736508369446,
+  -0.8037809133529663, -0.09090736508369446, -0.09090736508369446, -0.09018255770206451,
   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, -0.14400820434093475, -0.14431728422641754, -0.14431728422641754,
-  -0.5727381706237793, -0.14431728422641754, -0.14431728422641754, -0.14400820434093475,
+- [0.0, 0.0, 0.0, -0.08511251956224442, -0.08587993681430817, -0.08587993681430817,
+  -0.7678810358047485, -0.08587993681430817, -0.08587993681430817, -0.08511251956224442,
   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, -0.1366180032491684, -0.13694249093532562, -0.13694249093532562,
-  -0.5426507592201233, -0.13694249093532562, -0.13694249093532562, -0.1366180032491684,
+- [0.0, 0.0, 0.0, -0.08021276444196701, -0.08102504163980484, -0.08102504163980484,
+  -0.7328478693962097, -0.08102504163980484, -0.08102504163980484, -0.08021276444196701,
   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, -0.12946650385856628, -0.12980693578720093, -0.12980693578720093,
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-- [0.0, 0.0, 0.0, -0.0010727494955062866, 0.012813172303140163, -0.0015449653146788478,
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-- [0.0, 0.0, 0.0, -0.0009585916996002197, 0.011366117745637894, -0.0013036385644227266,
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-- [0.0, 0.0, 0.0, -0.0008467287989333272, 0.010043314658105373, -0.001094904146157205,
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-- [0.0, 0.0, 0.0, -0.0007385323406197131, 0.00883670523762703, -0.0009146195370703936,
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-- [0.0, 0.0, 0.0, -0.0006352076889015734, 0.007738579995930195, -0.0007590281311422586,
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-- [0.0, 0.0, 0.0, -0.0005377781926654279, 0.006741677410900593, -0.0006248131976462901,
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-- [0.0, 0.0, 0.0, -0.00044709196663461626, 0.005839187186211348, -0.0005090857739560306,
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-- [0.0, 0.0, 0.0, -0.0003638165653683245, 0.005024733021855354, -0.0004093599854968488,
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-- [0.0, 0.0, 0.0, -0.0002884456771425903, 0.0042923856526613235, -0.0003235507174395025,
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   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, -0.0002212987601524219, 0.003636627923697233, -0.00024992681574076414,
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-- [0.0, 0.0, 0.0, -0.0001625319418963045, 0.0030523266177624464, -0.00018707876733969897,
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-- [0.0, 0.0, 0.0, -0.00011214185360586271, 0.0025346805341541767, -0.00013386945647653192,
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-- [0.0, 0.0, 0.0, -6.997808668529615e-05, 0.002079180907458067, -8.93738106242381e-05,
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-- [0.0, 0.0, 0.0, -3.5751054383581504e-05, 0.0016815672861412168, -5.2847190090687945e-05,
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-- [0.0, 0.0, 0.0, -9.042513738677371e-06, 0.001337762805633247, -2.3656890334677882e-05,
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-- [0.0, 0.0, 0.0, 1.0682300853659399e-05, 0.0010438387980684638, -1.2417168591127847e-06,
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-- [0.0, 0.0, 0.0, 2.4065420802799053e-05, 0.0007959528011269867, 1.4940546861907933e-05,
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-- [0.0, 0.0, 0.0, 3.1842464522924274e-05, 0.0005903124692849815, 2.545257484598551e-05,
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-- [0.0, 0.0, 0.0, 3.4832115488825366e-05, 0.0004231349448673427, 3.0915121897123754e-05,
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+- [0.0, 0.0, 0.0, 4.930340946884826e-05, 0.0007438079919666052, 4.8419475206173956e-05,
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-- [0.0, 0.0, 0.0, 3.392253347556107e-05, 0.00029060710221529007, 3.203889718861319e-05,
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+- [0.0, 0.0, 0.0, 4.96445682074409e-05, 0.0005306042730808258, 5.2319861424621195e-05,
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-- [0.0, 0.0, 0.0, 3.0058350603212602e-05, 0.00018886571342591196, 2.9644339520018548e-05,
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+- [0.0, 0.0, 0.0, 4.609272218658589e-05, 0.00036277930485084653, 5.044688077759929e-05,
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-- [0.0, 0.0, 0.0, 2.4225962988566607e-05, 0.00011397439084248617, 2.467361446178984e-05,
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+- [0.0, 0.0, 0.0, 3.962824848713353e-05, 0.00023481383686885238, 4.428288957569748e-05,
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-- [0.0, 0.0, 0.0, 1.743573375279084e-05, 6.192106229718775e-05, 1.818700366129633e-05,
-  -1.355306380901311e-06, 1.818700366129633e-05, 6.192106229718775e-05, 1.743573375279084e-05,
+- [0.0, 0.0, 0.0, 3.130271943518892e-05, 0.0001412135170539841, 3.533769995556213e-05,
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   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 1.0700179700506851e-05, 2.8622565878322348e-05, 1.13408777906443e-05,
-  -4.555448072096624e-07, 1.13408777906443e-05, 2.8622565878322348e-05, 1.0700179700506851e-05,
+- [0.0, 0.0, 0.0, 2.2218986487132497e-05, 7.651964551769197e-05, 2.5137704142252915e-05,
+  -1.617426391931076e-06, 2.5137704142252915e-05, 7.651964551769197e-05, 2.2218986487132497e-05,
   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 5.000708824809408e-06, 9.94933634501649e-06, 5.334441539162071e-06,
-  -9.803432732269357e-08, 5.334441539162071e-06, 9.94933634501649e-06, 5.000708824809408e-06,
+- [0.0, 0.0, 0.0, 1.350399361399468e-05, 3.53201394318603e-05, 1.519628676760476e-05,
+  -5.430982241705351e-07, 1.519628676760476e-05, 3.53201394318603e-05, 1.350399361399468e-05,
   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 1.2279158454475692e-06, 1.7719224842949188e-06, 1.2988150501769269e-06,
-  -7.095271481460941e-09, 1.2988150501769269e-06, 1.7719224842949188e-06, 1.2279158454475692e-06,
+- [0.0, 0.0, 0.0, 6.268316610658076e-06, 1.2280677765375003e-05, 6.953269803489093e-06,
+  -1.1676034006313785e-07, 6.953269803489093e-06, 1.2280677765375003e-05, 6.268316610658076e-06,
+  0.0, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0, 1.5320257489292999e-06, 2.19304320125957e-06, 1.6514823073521256e-06,
+  -8.442472498870757e-09, 1.6514823073521256e-06, 2.19304320125957e-06, 1.5320257489292999e-06,
   0.0, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 1.0
diff --git a/extra_tests/regression_fits/polarized_evol_34.json b/extra_tests/regression_fits/polarized_evol_34.json
index 937b10e891..e988f0c8a1 100644
--- a/extra_tests/regression_fits/polarized_evol_34.json
+++ b/extra_tests/regression_fits/polarized_evol_34.json
@@ -25,47 +25,47 @@
       "trainable": false
     }
   ],
-  "stop_epoch": 466,
-  "best_epoch": 354,
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 }
diff --git a/extra_tests/regression_fits/trainable_prepro_61.exportgrid b/extra_tests/regression_fits/trainable_prepro_61.exportgrid
index 19879d10a7..41f185b6d6 100644
--- a/extra_tests/regression_fits/trainable_prepro_61.exportgrid
+++ b/extra_tests/regression_fits/trainable_prepro_61.exportgrid
@@ -3,42 +3,42 @@ pdfgrid:
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+- [0.0, 0.0, -0.005986841861158609, -0.020732460543513298, 0.014006378129124641, 0.01300437655299902,
+  -0.01063520647585392, -0.0037378245033323765, -0.0024413266219198704, 0.01308903656899929,
+  -0.005986840929836035, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005186258815228939, -0.018198546022176743, 0.012194514274597168, 0.011420143768191338,
+  -0.008654516190290451, -0.0033361688256263733, -0.002338579623028636, 0.011588728986680508,
+  -0.0051862578839063644, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.004440126940608025, -0.01577857881784439, 0.010490724816918373, 0.009906022809445858,
+  -0.006904028356075287, -0.0029468671418726444, -0.0021970015950500965, 0.010146996937692165,
+  -0.004440126940608025, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -0.003748424118384719, -0.013481860980391502, 0.008897374384105206, 0.008467930369079113,
-  -0.00537921953946352, -0.002570769749581814, -0.002022574655711651, 0.00876769982278347,
+  -0.005379220005124807, -0.002570769749581814, -0.002022574655711651, 0.00876769982278347,
   -0.003748424118384719, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0031112441793084145, -0.011318108066916466, 0.0074171097949147224,
-  0.007112083025276661, -0.004073585383594036, -0.002208888763561845, -0.0018213923322036862,
-  0.007455191109329462, -0.0031112441793084145, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0025288208853453398, -0.009297501295804977, 0.006052890792489052,
-  0.005845013074576855, -0.0029785626102238894, -0.0018624237272888422, -0.0015996764414012432,
-  0.006214383523911238, -0.0025288208853453398, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.002001565182581544, -0.007430892903357744, 0.00480813579633832, 0.004673698451370001,
-  -0.0020834477618336678, -0.0015328613808378577, -0.0013638484524562955, 0.005050962325185537,
-  -0.002001565182581544, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0031112441793084145, -0.011318105272948742, 0.007417107932269573,
+  0.007112081162631512, -0.004073585849255323, -0.0022088875994086266, -0.0018213908188045025,
+  0.007455188315361738, -0.0031112441793084145, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0025288208853453398, -0.009297503158450127, 0.0060528917238116264,
+  0.005845014471560717, -0.002978562843054533, -0.0018624247750267386, -0.0015996773727238178,
+  0.006214385852217674, -0.0025288208853453398, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.002001565182581544, -0.0074308933690190315, 0.004808136261999607,
+  0.004673698917031288, -0.002083447529003024, -0.0015328616136685014, -0.0013638486852869391,
+  0.005050962790846825, -0.002001565182581544, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -0.0015301386592909694, -0.005730059929192066, 0.0036868900060653687,
-  0.0036057105753570795, -0.0013753321254625916, -0.0012220817152410746, -0.0011206099297851324,
+  0.0036057105753570795, -0.0013753322418779135, -0.0012220817152410746, -0.0011206099297851324,
   0.003971633967012167, -0.0015301386592909694, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0011155318934470415, -0.004208045080304146, 0.0026940442621707916,
-  0.0026494080666452646, -0.0008389419526793063, -0.0009325185674242675, -0.0008770746062509716,
-  0.002984505845233798, -0.0011155318934470415, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0007592430920340121, -0.002879832638427615, 0.001835785573348403,
-  0.001814357121475041, -0.00045648604282177985, -0.0006674375617876649, -0.0006410079658962786,
-  0.002099770586937666, -0.0007592432084493339, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0004635540535673499, -0.001763383042998612, 0.0011202656896784902,
-  0.0011119645787402987, -0.00020737346494570374, -0.00043138256296515465, -0.0004212286730762571,
-  0.0013308264315128326, -0.000463553995359689, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0002321321371709928, -0.0008818601490929723, 0.0005590428481809795,
-  0.0005568687920458615, -6.779083196306601e-05, -0.00023111065092962235, -0.00022847905347589403,
-  0.0006966663058847189, -0.0002321321371709928, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -7.164000271586701e-05, -0.00026940598036162555, 0.00017080882389564067,
-  0.00017058996309060603, -9.925638551067095e-06, -7.798225124133751e-05, -7.772142998874187e-05,
-  0.0002281411871081218, -7.164000271586701e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0011155317770317197, -0.0042080446146428585, 0.002694044029340148,
+  0.002649407833814621, -0.0008389417198486626, -0.0009325185092166066, -0.0008770745480433106,
+  0.0029845056124031544, -0.0011155317770317197, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0007592430338263512, -0.0028798324055969715, 0.0018357853405177593,
+  0.0018143568886443973, -0.00045648604282177985, -0.0006674373871646821, -0.0006410079076886177,
+  0.0020997703541070223, -0.000759243150241673, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0004635540535673499, -0.0017633828101679683, 0.0011202655732631683,
+  0.001111964462324977, -0.00020737347949761897, -0.0004313824465498328, -0.0004212285275571048,
+  0.001330826198682189, -0.000463553995359689, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00023213212261907756, -0.0008818600326776505, 0.0005590427899733186,
+  0.0005568687338382006, -6.77908246871084e-05, -0.00023111059272196144, -0.00022847900982014835,
+  0.0006966661894693971, -0.00023213212261907756, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -7.16399954399094e-05, -0.00026940598036162555, 0.00017080882389564067,
+  0.00017058996309060603, -9.925636732077692e-06, -7.798225124133751e-05, -7.772142998874187e-05,
+  0.0002281411871081218, -7.16399954399094e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 61
diff --git a/extra_tests/regression_fits/trainable_prepro_61.json b/extra_tests/regression_fits/trainable_prepro_61.json
index 249bf27b65..627cf8be93 100644
--- a/extra_tests/regression_fits/trainable_prepro_61.json
+++ b/extra_tests/regression_fits/trainable_prepro_61.json
@@ -51,45 +51,45 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 83.8855209350586,
-  "erf_vl": 88.8935317993164,
-  "chi2": 59.152374267578125,
+  "erf_tr": 83.88548278808594,
+  "erf_vl": 88.89351654052734,
+  "chi2": 59.1523551940918,
   "pos_state": "POS_VETO",
   "arc_lengths": [
-    1.0440971869251894,
-    1.5280262594614311,
-    1.003308424887163,
-    0.9979762366304027,
-    1.4192810768228845
+    1.0440971889703696,
+    1.5280262496667372,
+    1.0033084229348523,
+    0.9979762265909661,
+    1.419280914711661
   ],
   "integrability": [
-    0.11098539642989813,
-    0.11098539642989663,
-    0.00020276380928346827,
-    0.008434453862718572,
-    0.0018140714964820503
+    0.11098538897931776,
+    0.11098538897931609,
+    0.00020276379382200282,
+    0.008434453862718683,
+    0.0018140711472360849
   ],
   "timing": {
     "walltime": {
-      "Total": 11.157723665237427,
+      "Total": 11.894519090652466,
       "start": 0.0,
-      "replica_set": 0.23775172233581543,
-      "replica_fitted": 11.15766978263855,
-      "replica_set_to_replica_fitted": 10.919918060302734
+      "replica_set": 0.23260784149169922,
+      "replica_fitted": 11.894434690475464,
+      "replica_set_to_replica_fitted": 11.661826848983765
     },
     "cputime": {
-      "Total": 12.520099947000002,
+      "Total": 13.421419582999999,
       "start": 0.0,
-      "replica_set": 0.23561744399999984,
-      "replica_fitted": 12.520044984000002,
-      "replica_set_to_replica_fitted": 12.284427540000001
+      "replica_set": 0.23085444399999933,
+      "replica_fitted": 13.421333412,
+      "replica_set_to_replica_fitted": 13.190478968
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
-    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
+    "nnpdf": "4.0.9.post1210.dev0+d36bcce78",
+    "validphys": "4.0.9.post1210.dev0+d36bcce78"
   }
 }
diff --git a/n3fit/runcards/examples/nnpdfpol20_dis_nnlo.yaml b/n3fit/runcards/examples/nnpdfpol20_dis_nlo.yml
similarity index 52%
rename from n3fit/runcards/examples/nnpdfpol20_dis_nnlo.yaml
rename to n3fit/runcards/examples/nnpdfpol20_dis_nlo.yml
index 06169ddc66..4516ad47e2 100644
--- a/n3fit/runcards/examples/nnpdfpol20_dis_nnlo.yaml
+++ b/n3fit/runcards/examples/nnpdfpol20_dis_nlo.yml
@@ -1,37 +1,68 @@
 ############################################################
-# Configuration file for N3FIT
+# Configuration file for N3FIT Polarized Fits
 ############################################################
-description: NNPDFpol2.0 NNLO DIS fit with ID822 (W2min=4)
+description: NNPDFpol2.0 NLO Global fit (W2min=4)
 
 ############################################################
 dataset_inputs:
+# Polarized DIS datasets
 - {dataset: COMPASS15_NC_NOTFIXED_MUP_G1, frac: 0.60, cfac: [NRM]}
 - {dataset: COMPASS15_NC_NOTFIXED_MUD_G1, frac: 0.60, cfac: [NRM]}
 - {dataset: E142_NC_NOTFIXED_EN_G1, frac: 0.60, cfac: [NRM]}
 - {dataset: E143_NC_NOTFIXED_EP_G1, frac: 0.60, cfac: [NRM]}
 - {dataset: E143_NC_NOTFIXED_ED_G1, frac: 0.60, cfac: [NRM]}
 - {dataset: E154_NC_9GEV_EN_G1, frac: 0.60, cfac: [NRM]}
-- {dataset: E155_NC_9GEV_EN_G1F1RATIO, frac: 0.60, cfac: [NRM]}
-- {dataset: E155_NC_9GEV_EP_G1F1RATIO, frac: 0.60, cfac: [NRM]}
+- {dataset: E155_NC_9GEV_EN_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: E155_NC_9GEV_EP_G1F1RATIO, frac: 0.60, cfac: []}
 - {dataset: EMC_NC_NOTFIXED_MUP_G1, frac: 0.60, cfac: [NRM]}
 - {dataset: HERMES_NC_7GEV_ED_G1, frac: 0.60, cfac: [NRM]}
 - {dataset: HERMES_NC_7GEV_EP_G1, frac: 0.60, cfac: [NRM]}
 - {dataset: HERMES97_NC_7GEV_EN_G1, frac: 0.60, cfac: [NRM]}
-- {dataset: JLABE06_NC_3GEV_EN_G1F1RATIO, frac: 0.60, cfac: [NRM]}
-- {dataset: JLABEG1B_NC_NOTFIXED_EP_G1F1RATIO, frac: 0.60, cfac: [NRM]}
-- {dataset: JLABEG1B_NC_NOTFIXED_ED_G1F1RATIO, frac: 0.60, cfac: [NRM]}
+- {dataset: JLABE06_NC_3GEV_EN_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: JLABEG1B_NC_NOTFIXED_EP_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: JLABEG1B_NC_NOTFIXED_ED_G1F1RATIO, frac: 0.60, cfac: []}
 - {dataset: JLABE97_NC_NOTFIXED_EN_G1, frac: 0.60, cfac: [NRM]}
-- {dataset: JLABE99_NC_3GEV_EN_G1F1RATIO, frac: 0.60, cfac: [NRM]}
-- {dataset: JLABEG1DVCS_NC_5GEV_ED_G1F1RATIO, frac: 0.60, cfac: [NRM]}
-- {dataset: JLABEG1DVCS_NC_3GEV_EP_G1F1RATIO, frac: 0.60, cfac: [NRM]}
+- {dataset: JLABE99_NC_3GEV_EN_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: JLABEG1DVCS_NC_5GEV_ED_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: JLABEG1DVCS_NC_3GEV_EP_G1F1RATIO, frac: 0.60, cfac: []}
 - {dataset: SMC_NC_NOTFIXED_MUD_G1, frac: 0.60, cfac: [NRM]}
 - {dataset: SMC_NC_NOTFIXED_MUP_G1, frac: 0.60, cfac: [NRM]}
-- {dataset: SMCSX_NC_24GEV_MUD_G1F1RATIO, frac: 0.60, cfac: [NRM]}
-- {dataset: SMCSX_NC_17GEV_MUP_G1F1RATIO, frac: 0.60, cfac: [NRM]}
+- {dataset: SMCSX_NC_24GEV_MUD_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: SMCSX_NC_17GEV_MUP_G1F1RATIO, frac: 0.60, cfac: []}
+# Polarized DY datasets
+- {dataset: STAR_WMWP_510GEV_WM-AL, frac: 0.60, cfac: []}
+- {dataset: STAR_WMWP_510GEV_WP-AL, frac: 0.60, cfac: []}
+# Polarized Jet datasets
+- {dataset: STAR_2005_1JET_200GEV_ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2006_1JET_200GEV_ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2009_1JET_200GEV_CC-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2009_1JET_200GEV_CF-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2012_1JET_510GEV_ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2013_1JET_510GEV_ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2015_1JET_200GEV_CC-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2015_1JET_200GEV_CF-ALL, frac: 0.60, cfac: []}
+- {dataset: PHENIX_1JET_200GEV_ALL, frac: 0.60, cfac: []}
+# Poalrized Dijet datasets
+- {dataset: STAR_2009_2JET_200GEV_A-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2009_2JET_200GEV_B-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2009_2JET_200GEV_C-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2009_2JET_MIDRAP_200GEV_OS-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2009_2JET_MIDRAP_200GEV_SS-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2012_2JET_510GEV_A-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2012_2JET_510GEV_B-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2012_2JET_510GEV_C-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2012_2JET_510GEV_D-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2013_2JET_510GEV_A-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2013_2JET_510GEV_B-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2013_2JET_510GEV_C-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2013_2JET_510GEV_D-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2015_2JET_MIDRAP_200GEV_OS-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2015_2JET_MIDRAP_200GEV_SS-ALL, frac: 0.60, cfac: []}
 
 ############################################################
 datacuts:
-  t0pdfset: NNPDFpol10_100   # PDF set to generate t0 covmat
+  t0pdfset: NNPDFpol11_100   # PDF set to generate t0 covmat
+  unpolarized_bc: NNPDF40_nnlo_pch_as_01180
   q2min: 1.00                # Q2 minimum
   w2min: 4.00                # W2 minimum
 
@@ -43,7 +74,7 @@ positivity_bound:
 
 ############################################################
 theory:
-  theoryid: 822
+  theoryid: 41_100_010
 
 ############################################################
 trvlseed: 14613416
@@ -53,7 +84,7 @@ save: false
 genrep: true
 
 parameters:
-  nodes_per_layer: [25, 20, 4]
+  nodes_per_layer: [25, 20, 6]
   activation_per_layer: [tanh, tanh, linear]
   initializer: glorot_normal
   optimizer:
@@ -75,27 +106,34 @@ parameters:
   threshold_chi2: 3.5
 
 fitting:
-  fitbasis: POLARIZED_EVOL
+  fitbasis: POLARIZED_EVOL_CMP
   sum_rules: TSR
   basis:
   - {fl: sng, trainable: false, smallx: [1.094, 1.118], largex: [1.46, 3.003]}
   - {fl: g, trainable: false, smallx: [0.8189, 1.844], largex: [2.591, 5.697]}
   - {fl: t3, trainable: false, smallx: [-0.4401, 0.9163], largex: [1.773, 3.333]}
   - {fl: t8, trainable: false, smallx: [0.5852, 0.8537], largex: [1.533, 3.436]}
+  - {fl: v, trainable: false, smallx: [0.472, 0.9576], largex: [1.571, 3.559]}
+  - {fl: v3, trainable: false, smallx: [0.07483, 0.9501], largex: [1.514, 3.467]}
 
 ###########################################################
 positivity:
   posdatasets:
   - {dataset: NNPDF_POS_2P24GEV_XGL-POLARIZED, maxlambda: 1e8}
   - {dataset: NNPDF_POS_2P24GEV_XDQ-POLARIZED, maxlambda: 1e8}
-  - {dataset: NNPDF_POS_2P24GEV_XSQ-POLARIZED, maxlambda: 1e8}
+  - {dataset: NNPDF_POS_2P24GEV_XDB-POLARIZED, maxlambda: 1e8}
   - {dataset: NNPDF_POS_2P24GEV_XUQ-POLARIZED, maxlambda: 1e8}
+  - {dataset: NNPDF_POS_2P24GEV_XUB-POLARIZED, maxlambda: 1e8}
+  - {dataset: NNPDF_POS_2P24GEV_XSQSUM-POLARIZED, maxlambda: 1e8}
 
 ############################################################
+# TODO: Add integrability datasets for ΔV and ΔV3
 integrability:
   integdatasets:
   - {dataset: NNPDF_INTEG_1GEV_XGL-POLARIZED, maxlambda: 1e2}
   - {dataset: NNPDF_INTEG_1GEV_XSIGMA-POLARIZED, maxlambda: 1e2}
+  - {dataset: NNPDF_INTEG_1GEV_XV-POLARIZED, maxlambda: 1e2}
+  - {dataset: NNPDF_INTEG_1GEV_XV3-POLARIZED, maxlambda: 1e2}
 
 ############################################################
 debug: false
diff --git a/n3fit/runcards/examples/nnpdfpol20_dis_nlo_mhou.yml b/n3fit/runcards/examples/nnpdfpol20_dis_nlo_mhou.yml
new file mode 100644
index 0000000000..4755cd324a
--- /dev/null
+++ b/n3fit/runcards/examples/nnpdfpol20_dis_nlo_mhou.yml
@@ -0,0 +1,149 @@
+############################################################
+# Configuration file for N3FIT Polarized Fits
+############################################################
+description: NNPDFpol2.0 NLO Global fit with MHOU (W2min=4)
+
+############################################################
+dataset_inputs:
+# Polarized DIS datasets
+- {dataset: COMPASS15_NC_NOTFIXED_MUP_G1, frac: 0.60, cfac: [NRM]}
+- {dataset: COMPASS15_NC_NOTFIXED_MUD_G1, frac: 0.60, cfac: [NRM]}
+- {dataset: E142_NC_NOTFIXED_EN_G1, frac: 0.60, cfac: [NRM]}
+- {dataset: E143_NC_NOTFIXED_EP_G1, frac: 0.60, cfac: [NRM]}
+- {dataset: E143_NC_NOTFIXED_ED_G1, frac: 0.60, cfac: [NRM]}
+- {dataset: E154_NC_9GEV_EN_G1, frac: 0.60, cfac: [NRM]}
+- {dataset: E155_NC_9GEV_EN_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: E155_NC_9GEV_EP_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: EMC_NC_NOTFIXED_MUP_G1, frac: 0.60, cfac: [NRM]}
+- {dataset: HERMES_NC_7GEV_ED_G1, frac: 0.60, cfac: [NRM]}
+- {dataset: HERMES_NC_7GEV_EP_G1, frac: 0.60, cfac: [NRM]}
+- {dataset: HERMES97_NC_7GEV_EN_G1, frac: 0.60, cfac: [NRM]}
+- {dataset: JLABE06_NC_3GEV_EN_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: JLABEG1B_NC_NOTFIXED_EP_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: JLABEG1B_NC_NOTFIXED_ED_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: JLABE97_NC_NOTFIXED_EN_G1, frac: 0.60, cfac: [NRM]}
+- {dataset: JLABE99_NC_3GEV_EN_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: JLABEG1DVCS_NC_5GEV_ED_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: JLABEG1DVCS_NC_3GEV_EP_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: SMC_NC_NOTFIXED_MUD_G1, frac: 0.60, cfac: [NRM]}
+- {dataset: SMC_NC_NOTFIXED_MUP_G1, frac: 0.60, cfac: [NRM]}
+- {dataset: SMCSX_NC_24GEV_MUD_G1F1RATIO, frac: 0.60, cfac: []}
+- {dataset: SMCSX_NC_17GEV_MUP_G1F1RATIO, frac: 0.60, cfac: []}
+# Polarized DY datasets
+- {dataset: STAR_WMWP_510GEV_WM-AL, frac: 0.60, cfac: []}
+- {dataset: STAR_WMWP_510GEV_WP-AL, frac: 0.60, cfac: []}
+# Polarized Jet datasets
+- {dataset: STAR_2005_1JET_200GEV_ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2006_1JET_200GEV_ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2009_1JET_200GEV_CC-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2009_1JET_200GEV_CF-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2012_1JET_510GEV_ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2013_1JET_510GEV_ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2015_1JET_200GEV_CC-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2015_1JET_200GEV_CF-ALL, frac: 0.60, cfac: []}
+- {dataset: PHENIX_1JET_200GEV_ALL, frac: 0.60, cfac: []}
+# Poalrized Dijet datasets
+- {dataset: STAR_2009_2JET_200GEV_A-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2009_2JET_200GEV_B-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2009_2JET_200GEV_C-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2009_2JET_MIDRAP_200GEV_OS-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2009_2JET_MIDRAP_200GEV_SS-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2012_2JET_510GEV_A-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2012_2JET_510GEV_B-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2012_2JET_510GEV_C-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2012_2JET_510GEV_D-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2013_2JET_510GEV_A-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2013_2JET_510GEV_B-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2013_2JET_510GEV_C-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2013_2JET_510GEV_D-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2015_2JET_MIDRAP_200GEV_OS-ALL, frac: 0.60, cfac: []}
+- {dataset: STAR_2015_2JET_MIDRAP_200GEV_SS-ALL, frac: 0.60, cfac: []}
+
+############################################################
+datacuts:
+  t0pdfset: NNPDFpol11_100   # PDF set to generate t0 covmat
+  unpolarized_bc: NNPDF40_nnlo_pch_as_01180
+  q2min: 1.00                # Q2 minimum
+  w2min: 4.00                # W2 minimum
+
+############################################################
+# Define the unpolarized PDF set to be used as BC for POS
+positivity_bound:
+  unpolarized_bc: NNPDF40_nnlo_pch_as_01180
+  n_std: 1.00 # Standard Deviation to be added as Error
+
+############################################################
+theory:
+  theoryid: 41_100_010
+
+theorycovmatconfig:
+  point_prescription: '7 point'
+  theoryids:
+    from_: scale_variation_theories
+  pdf: NNPDFpol11_100
+  unpolarized_bc: NNPDF40_nnlo_pch_as_01180
+  use_thcovmat_in_fitting: true
+  use_thcovmat_in_sampling: true
+
+############################################################
+trvlseed: 14613416
+nnseed: 1865683875
+mcseed: 746898422
+save: false
+genrep: true
+
+parameters:
+  nodes_per_layer: [25, 20, 6]
+  activation_per_layer: [tanh, tanh, linear]
+  initializer: glorot_normal
+  optimizer:
+    clipnorm: 6.073e-6
+    learning_rate: 2.621e-3
+    optimizer_name: Nadam
+  epochs: 20000
+  positivity:
+    initial: 1
+    multiplier:
+    threshold: 1e-7
+  integrability:
+    initial: 1
+    multiplier:
+    threshold: 1e-2
+  stopping_patience: 0.1
+  layer_type: dense
+  dropout: 0.0
+  threshold_chi2: 3.5
+
+fitting:
+  fitbasis: POLARIZED_EVOL_CMP
+  sum_rules: TSR
+  basis:
+  - {fl: sng, trainable: false, smallx: [1.094, 1.118], largex: [1.46, 3.003]}
+  - {fl: g, trainable: false, smallx: [0.8189, 1.844], largex: [2.591, 5.697]}
+  - {fl: t3, trainable: false, smallx: [-0.4401, 0.9163], largex: [1.773, 3.333]}
+  - {fl: t8, trainable: false, smallx: [0.5852, 0.8537], largex: [1.533, 3.436]}
+  - {fl: v, trainable: false, smallx: [0.472, 0.9576], largex: [1.571, 3.559]}
+  - {fl: v3, trainable: false, smallx: [0.07483, 0.9501], largex: [1.514, 3.467]}
+
+###########################################################
+positivity:
+  posdatasets:
+  - {dataset: NNPDF_POS_2P24GEV_XGL-POLARIZED, maxlambda: 1e8}
+  - {dataset: NNPDF_POS_2P24GEV_XDQ-POLARIZED, maxlambda: 1e8}
+  - {dataset: NNPDF_POS_2P24GEV_XDB-POLARIZED, maxlambda: 1e8}
+  - {dataset: NNPDF_POS_2P24GEV_XUQ-POLARIZED, maxlambda: 1e8}
+  - {dataset: NNPDF_POS_2P24GEV_XUB-POLARIZED, maxlambda: 1e8}
+  - {dataset: NNPDF_POS_2P24GEV_XSQSUM-POLARIZED, maxlambda: 1e8}
+
+############################################################
+# TODO: Add integrability datasets for ΔV and ΔV3
+integrability:
+  integdatasets:
+  - {dataset: NNPDF_INTEG_1GEV_XGL-POLARIZED, maxlambda: 1e2}
+  - {dataset: NNPDF_INTEG_1GEV_XSIGMA-POLARIZED, maxlambda: 1e2}
+  - {dataset: NNPDF_INTEG_1GEV_XV-POLARIZED, maxlambda: 1e2}
+  - {dataset: NNPDF_INTEG_1GEV_XV3-POLARIZED, maxlambda: 1e2}
+
+############################################################
+debug: false
+maxcores: 4
diff --git a/n3fit/src/n3fit/checks.py b/n3fit/src/n3fit/checks.py
index 1b92cc4875..86f961c7e8 100644
--- a/n3fit/src/n3fit/checks.py
+++ b/n3fit/src/n3fit/checks.py
@@ -482,7 +482,7 @@ def check_polarized_configs(fitting, fitbasis, positivity_bound):
             )
         if positivity_bound.get("unpolarized_bc") is None:
             raise CheckError(
-                "For polarized fits, the name of the PDF has to be defined in positivity_bound::unpolarized_bc."
+                "For polarized fits, the unpolarized PDF has to be defined in positivity_bound::unpolarized_bc."
             )
         if fitting.get("sum_rules", True) and fitting.get("sum_rules") != "TSR":
             raise CheckError("The 'sum_rules' key needs to be 'TSR' for polarised PDF fits.")
diff --git a/n3fit/src/n3fit/layers/DIS.py b/n3fit/src/n3fit/layers/DIS.py
index 91dfc374ee..072d423e95 100644
--- a/n3fit/src/n3fit/layers/DIS.py
+++ b/n3fit/src/n3fit/layers/DIS.py
@@ -14,9 +14,9 @@
             | -- | -- | -- |
             | mask pdf | -  | 92 \ 65 |
             |mask fk | 330 \ 53 \  | 177 \ 53 |
-            
+
             These timings are all for one replica.
-            
+
             Crucially, `einsum` is a requirement of the multireplica case, while `tensordot` gives a benefit of a factor of 2x for the single replica case.
             Since this branching is required anyhow,
              by masking the PDF for 1 replica instead of padding the fktable we get an extra factor of x2
@@ -94,8 +94,8 @@ def compute_dis_observable_many_replica(pdf, padded_fk):
 
     Parameters
     ----------
-        pdf: tensor
-            pdf of shape (batch=1, replicas, xgrid, flavours)
+        pdf: list[tensor]
+            list of pdf of shape (batch=1, replicas, xgrid, flavours)
         padded_fk: tensor
             masked fk table of shape (ndata, xgrid, flavours)
 
@@ -104,7 +104,7 @@ def compute_dis_observable_many_replica(pdf, padded_fk):
         tensor
             observable of shape (batch=1, replicas, ndata)
     """
-    return op.einsum('brxf, nxf -> brn', pdf, padded_fk)
+    return op.einsum('brxf, nxf -> brn', pdf[0], padded_fk)
 
 
 def compute_dis_observable_one_replica(pdf, padded_fk):
@@ -112,4 +112,4 @@ def compute_dis_observable_one_replica(pdf, padded_fk):
     Same operations as above but a specialized implementation that is more efficient for 1 replica,
     masking the PDF rather than the fk table.
     """
-    return op.tensor_product(pdf, padded_fk, axes=[(2, 3), (1, 2)])
+    return op.tensor_product(pdf[0], padded_fk, axes=[(2, 3), (1, 2)])
diff --git a/n3fit/src/n3fit/layers/DY.py b/n3fit/src/n3fit/layers/DY.py
index 73cf4e66fc..f05416c5e4 100644
--- a/n3fit/src/n3fit/layers/DY.py
+++ b/n3fit/src/n3fit/layers/DY.py
@@ -74,8 +74,8 @@ def compute_dy_observable_many_replica(pdf, padded_fk):
 
     Parameters
     ----------
-        pdf: tensor
-            pdf of shape (batch=1, replicas, xgrid, flavours)
+        pdf: list[tensor]
+            list of pdf of shape (batch=1, replicas, xgrid, flavours)
         padded_fk: tensor
             masked fk table of shape (ndata, xgrid, flavours, xgrid, flavours)
 
@@ -84,8 +84,11 @@ def compute_dy_observable_many_replica(pdf, padded_fk):
         tensor
             observable of shape (batch=1, replicas, ndata)
     """
-    temp = op.einsum('nxfyg, bryg -> brnxf', padded_fk, pdf)
-    return op.einsum('brnxf, brxf -> brn', temp, pdf)
+    pdfa = pdf[1]
+    pdfb = pdf[0]
+    
+    temp = op.einsum('nxfyg, bryg -> brnxf', padded_fk, pdfa)
+    return op.einsum('brnxf, brxf -> brn', temp, pdfb)
 
 
 def compute_dy_observable_one_replica(pdf, mask_and_fk):
@@ -94,10 +97,14 @@ def compute_dy_observable_one_replica(pdf, mask_and_fk):
     masking the PDF rather than the fk table.
     """
     mask, fk = mask_and_fk
-    pdf = pdf[0][0]  # yg
-
-    mask_x_pdf = op.tensor_product(mask, pdf, axes=[(2,), (1,)])  # Ffg, yg -> Ffy
-    pdf_x_pdf = op.tensor_product(mask_x_pdf, pdf, axes=[(1,), (1,)])  # Ffy, xf -> Fyx
+    # Retrieve the two PDFs (which may potentially be coming from different initial states)
+    # Since this is the one-replica function, remove the batch and replica dimension
+    pdfb = pdf[0][0][0]  # xf
+    pdfa = pdf[1][0][0]  # yg
+
+    # TODO: check which PDF must go first in case of different initial states!!!
+    mask_x_pdf = op.tensor_product(mask, pdfa, axes=[(2,), (1,)])  # Ffg, yg -> Ffy
+    pdf_x_pdf = op.tensor_product(mask_x_pdf, pdfb, axes=[(1,), (1,)])  # Ffy, xf -> Fyx
     observable = op.tensor_product(fk, pdf_x_pdf, axes=[(1, 2, 3), (0, 1, 2)])  # nFyx, Fyx -> n
 
     return op.batchit(op.batchit(observable))  # brn
diff --git a/n3fit/src/n3fit/layers/observable.py b/n3fit/src/n3fit/layers/observable.py
index b6e2d30b09..48499529cc 100644
--- a/n3fit/src/n3fit/layers/observable.py
+++ b/n3fit/src/n3fit/layers/observable.py
@@ -93,30 +93,36 @@ def __init__(
     ):
         super(MetaLayer, self).__init__(**kwargs)
 
+        # A dataset can only involve DIS or DY convolutions, not both at the same time
         self.dataname = dataset_name
         self.nfl = nfl
-        self.boundary_pdf = [None] * len(fktable_data)
-        self.num_replicas = n_replicas  # TODO: Is there a reason this had to be in build?
+        self.boundary_pdf = []
+        self.num_replicas = n_replicas
         self.compute_observable = None  # A function (pdf, padded_fk) -> observable set in build
 
         all_bases = []
         xgrids = []
         fktables = []
-        for idx, (fkdata, fk) in enumerate(zip(fktable_data, fktable_arr)):
+        for fkdata, fk in zip(fktable_data, fktable_arr):
             xgrids.append(fkdata.xgrid.reshape(1, -1))
             all_bases.append(fkdata.luminosity_mapping)
             fktables.append(op.numpy_to_tensor(fk))
 
-            if self.is_pos_polarized() and not fkdata.is_polarized:
-                if boundary_condition is None:
-                    raise ValueError("Polarized FKTables require a boundary condition")
-                self.boundary_pdf[idx] = compute_pdf_boundary(
-                    pdf=boundary_condition["unpolarized_bc"],
-                    q0_value=fkdata.Q0,
-                    xgrid=fkdata.xgrid,
-                    n_std=boundary_condition.get("n_std", 0.0),
-                    n_replicas=n_replicas,
-                )
+            set_pdf_tmp = []
+            for conv_type in fkdata.convolution_types:
+                if boundary_condition is not None and conv_type == "UnpolPDF":
+                    nstd = boundary_condition.get("n_std", 1) if self.is_pos_polarized() else 0.0
+                    set_boundary = compute_pdf_boundary(
+                        pdf=boundary_condition["unpolarized_bc"],
+                        q0_value=fkdata.Q0,
+                        xgrid=fkdata.xgrid,
+                        n_std=nstd,
+                        n_replicas=n_replicas,
+                    )
+                    set_pdf_tmp.append(set_boundary)
+                else:
+                    set_pdf_tmp.append(None)
+            self.boundary_pdf.append(set_pdf_tmp)
         self.fktables = fktables
 
         # check how many xgrids this dataset needs
@@ -164,7 +170,7 @@ def call(self, pdf):
 
         observables = []
         for idx, (pdf, padded_fk) in enumerate(zip(pdfs, self.padded_fk_tables)):
-            pdf_to_convolute = pdf if self.boundary_pdf[idx] is None else self.boundary_pdf[idx]
+            pdf_to_convolute = [pdf if p is None else p for p in self.boundary_pdf[idx]]
             observable = self.compute_observable(pdf_to_convolute, padded_fk)
             observables.append(observable)
 
diff --git a/n3fit/src/n3fit/tests/regressions/quickcard_pol.yml b/n3fit/src/n3fit/tests/regressions/quickcard_pol.yml
index 84668efe13..8ab08c3333 100644
--- a/n3fit/src/n3fit/tests/regressions/quickcard_pol.yml
+++ b/n3fit/src/n3fit/tests/regressions/quickcard_pol.yml
@@ -12,6 +12,7 @@ dataset_inputs:
 ############################################################
 datacuts:
   t0pdfset: NNPDFpol10_100   # PDF set to generate t0 covmat
+  unpolarized_bc: NNPDF40_nnlo_pch_as_01180
   q2min: 1.00                # Q2 minimum
   w2min: 4.00                # W2 minimum
 
@@ -23,7 +24,7 @@ positivity_bound:
 
 ############################################################
 theory:
-  theoryid: 822
+  theoryid: 41_100_010
 
 ############################################################
 genrep: True    # on = generate MC replicas, False = use real data
diff --git a/n3fit/src/n3fit/tests/regressions/quickcard_pol_1.exportgrid b/n3fit/src/n3fit/tests/regressions/quickcard_pol_1.exportgrid
index 7f85331078..8095b715d8 100644
--- a/n3fit/src/n3fit/tests/regressions/quickcard_pol_1.exportgrid
+++ b/n3fit/src/n3fit/tests/regressions/quickcard_pol_1.exportgrid
@@ -1,528 +1,529 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, 0.0, 0.2471094090648995, 0.2480376168913184, 0.24629285689533906, 0.016336163686469538,
-  0.24629285689533906, 0.2480376168913184, 0.2471094090648995, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.24092324226225997, 0.24188513313047488, 0.24008352857731477, 0.016700575565345915,
-  0.24008352857731477, 0.24188513313047488, 0.24092324226225997, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.23489118518838242, 0.23588807252258706, 0.23402798624371685, 0.0170732764527806,
-  0.23402798624371685, 0.23588807252258706, 0.23489118518838242, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.22900923534841683, 0.23004249446540903, 0.22812225832680846, 0.0174543587870173,
-  0.22812225832680846, 0.23004249446540903, 0.22900923534841683, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.22327347177415854, 0.2243445440634657, 0.22236245927024753, 0.017843894844682167,
-  0.22236245927024753, 0.2243445440634657, 0.22327347177415854, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.21768005101641172, 0.21879044853955182, 0.2167447859054257, 0.018241932677370253,
-  0.2167447859054257, 0.21879044853955182, 0.21768005101641172, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.21222520304554887, 0.21337651360835397, 0.21126551375575092, 0.018648491442921824,
-  0.21126551375575092, 0.21337651360835397, 0.21222520304554887, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.20690522704479578, 0.2080991198045316, 0.20592099325227908, 0.01906355604926575,
-  0.20592099325227908, 0.2080991198045316, 0.20690522704479578, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.20171648707965836, 0.20295471875766616, 0.2007076458423903, 0.019487071018188532,
-  0.2007076458423903, 0.20295471875766616, 0.20171648707965836, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.19665540762571204, 0.1979398294066749, 0.1956219599712904, 0.01991893346461065,
-  0.1956219599712904, 0.1979398294066749, 0.19665540762571204, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.1917184689357342, 0.19305103414664115, 0.19066048691399848, 0.020358985073791344,
-  0.19066048691399848, 0.19305103414664115, 0.1917184689357342, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.18690220222584977, 0.18828497490154378, 0.18581983643311, 0.020807002944193048,
-  0.18581983643311, 0.18828497490154378, 0.18690220222584977, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.18220318465899166, 0.18363834911714078, 0.1810966722349854, 0.021262689147389147,
-  0.1810966722349854, 0.18363834911714078, 0.18220318465899166, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.17761803410260832, 0.17910790566935572, 0.176487707194116, 0.021725658838224596,
-  0.176487707194116, 0.17910790566935572, 0.17761803410260832, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.17314340363613417, 0.17469044068495682, 0.17198969831219174, 0.022195426728311273,
-  0.17198969831219174, 0.17469044068495682, 0.17314340363613417, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.1687759757823518, 0.1703827932732282, 0.1675994413748477, 0.022671391713691782,
-  0.1675994413748477, 0.1703827932732282, 0.1687759757823518, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.16451245643544704, 0.16618184116981718, 0.1633137652651925, 0.023152819423021942,
-  0.1633137652651925, 0.16618184116981718, 0.16451245643544704, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.1603495684573205, 0.16208449629710076, 0.15912952588897805, 0.023638822425762818,
-  0.15912952588897805, 0.16208449629710076, 0.1603495684573205, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.15628404491263648, 0.15808770024940977, 0.1550435996616562, 0.024128337810569753,
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-- [0.0, 0.0, 0.0, 0.0017819745798758606, 0.014984372252491948, 0.001702290408569475,
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-- [0.0, 0.0, 0.0, 0.001605803507006943, 0.013675163488263663, 0.00185257191721198,
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-- [0.0, 0.0, 0.0, 0.0012890353863491953, 0.011275704425841021, 0.0020579260477411434,
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-- [0.0, 0.0, 0.0, 0.001147586505492553, 0.010182059399879352, 0.0021157768163811586,
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-- [0.0, 0.0, 0.0, 0.0010168555926501988, 0.00915676733012908, 0.002145719784393471,
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-- [0.0, 0.0, 0.0, 0.0008964118378304798, 0.008197978289014364, 0.0021493307931217116,
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-- [0.0, 0.0, 0.0, 0.0007858240879347833, 0.007303790584938669, 0.002128261139651955,
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-- [0.0, 0.0, 0.0, 0.0006846615482215296, 0.006472255927362595, 0.0020842384902830754,
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-- [0.0, 0.0, 0.0, 0.0005924943700797348, 0.005701384734576198, 0.0020190682381318104,
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-- [0.0, 0.0, 0.0, 0.0005088941323416178, 0.004989151706423473, 0.0019346354297395932,
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-- [0.0, 0.0, 0.0, 0.0004334342227963241, 0.004333501821571049, 0.0018329074289457725,
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-- [0.0, 0.0, 0.0, 0.0003656901263610591, 0.0037323569744707355, 0.0017159375492991212,
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-- [0.0, 0.0, 0.0, 0.00030523962680324934, 0.0031836235513570447, 0.001585869979971299,
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-- [0.0, 0.0, 0.0, 0.0002516629305097431, 0.0026852013750038686, 0.0014449464732313913,
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-- [0.0, 0.0, 0.0, 0.00020454272463547586, 0.00223499465586195, 0.0012955154869523876,
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-- [0.0, 0.0, 0.0, 0.00016346419017440638, 0.001830925930005081, 0.0011400448436012908,
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-- [0.0, 0.0, 0.0, 0.00012801500765255945, 0.001470954553254338, 0.000981139593687231,
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-- [0.0, 0.0, 0.0, 9.778542947407864e-05, 0.0011531023838400804, 0.0008215678932752536,
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+- [0.0, 0.0, 0.0, 0.00022170896550096202, 0.0022500303911354076, 0.0013134547832921682,
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-- [0.0, 0.0, 0.0, 7.236857294675635e-05, 0.0008754913244336351, 0.0006642998398486648,
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+- [0.0, 0.0, 0.0, 0.00017792280516140753, 0.0018437378402436084, 0.0011549917930897622,
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-- [0.0, 0.0, 0.0, 5.136127549500203e-05, 0.0006364016120179343, 0.000512568596066279,
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+- [0.0, 0.0, 0.0, 0.0001399601541525961, 0.0014816583680000981, 0.0009933569516553747,
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-- [0.0, 0.0, 0.0, 3.4366334322406906e-05, 0.00043436937184363535, 0.0003699730737812722,
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+- [0.0, 0.0, 0.0, 0.00010741526617334973, 0.0011618246697667446, 0.0008313145408807829,
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-- [0.0, 0.0, 0.0, 2.0998355616304834e-05, 0.0002683670627534037, 0.00024066721607091107,
-  -6.225921261426889e-08, 0.00024066721607091107, 0.0002683670627534037, 2.0998355616304834e-05,
+- [0.0, 0.0, 0.0, 7.988676124829815e-05, 0.0008823710670796095, 0.0006718320585121392,
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   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 1.0900415162685148e-05, 0.00013818999540740233, 0.00012976203495853063,
-  -8.698341004839666e-09, 0.00012976203495853063, 0.00013818999540740233, 1.0900415162685148e-05,
+- [0.0, 0.0, 0.0, 5.697906090127557e-05, 0.0006415923532191712, 0.0005181418888198427,
+  -7.419374681931048e-07, 0.0005181418888198427, 0.0006415923532191712, 5.697906090127557e-05,
   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 3.8034629570953715e-06, 4.552129692939808e-05, 4.4420443585466934e-05,
-  -3.00320512793057e-10, 4.4420443585466934e-05, 4.552129692939808e-05, 3.8034629570953715e-06,
+- [0.0, 0.0, 0.0, 3.8305606556917445e-05, 0.00043804228654017416, 0.0003738449099704438,
+  -2.514039552008622e-07, 0.0003738449099704438, 0.00043804228654017416, 3.8305606556917445e-05,
+  0.0, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0, 2.3496524138640608e-05, 0.00027071577885791586, 0.0002431014915240132,
+  -6.225429503863743e-08, 0.0002431014915240132, 0.00027071577885791586, 2.3496524138640608e-05,
+  0.0, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0, 1.2219169987905467e-05, 0.00013943914260174938, 0.00013103721274063321,
+  -8.697666565550534e-09, 0.00013103721274063321, 0.00013943914260174938, 1.2219169987905467e-05,
+  0.0, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.0, 4.248210857580876e-06, 4.594529260045355e-05, 4.4847839143547894e-05,
+  -3.0029765622118575e-10, 4.4847839143547894e-05, 4.594529260045355e-05, 4.248210857580876e-06,
   0.0, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 1.0
diff --git a/n3fit/src/n3fit/tests/regressions/quickcard_pol_1.json b/n3fit/src/n3fit/tests/regressions/quickcard_pol_1.json
index f683eac8d8..95aa1d7a3d 100644
--- a/n3fit/src/n3fit/tests/regressions/quickcard_pol_1.json
+++ b/n3fit/src/n3fit/tests/regressions/quickcard_pol_1.json
@@ -25,46 +25,47 @@
       "trainable": false
     }
   ],
-  "stop_epoch": 600,
-  "best_epoch": 599,
-  "erf_tr": 2.5818292105708047,
-  "erf_vl": 1.9909996132247432,
-  "chi2": 1.319613746267476,
+  "stop_epoch": 62,
+  "best_epoch": 0,
+  "erf_tr": 3.7515686061190814,
+  "erf_vl": 2.8109852940898374,
+  "chi2": 2.2809830315372683,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.0207390340368907,
-    1.0307402955168719,
+    1.0211390079358347,
+    1.0307459282492994,
     0.9899487587939698,
     0.9899487587939698,
     0.9899487587939698
   ],
   "integrability": [
-    1.5265566588595902e-16,
-    4.163336342344337e-17,
-    4.163336342344337e-17,
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   "timing": {
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   "version": {
-    "tensorflow": "2.16.1, mkl=??",
-    "numpy": "1.24.0",
-    "nnpdf": "4.0.9.post574.dev0+412f8f857.dirty",
-    "validphys": "4.0.9.post574.dev0+412f8f857.dirty"
+    "keras": "3.4.1",
+    "tensorflow": "2.17.0, mkl=False",
+    "numpy": "1.26.4",
+    "nnpdf": "4.0.9.post1197.dev0+1247393cc.dirty",
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 }
diff --git a/n3fit/src/n3fit/tests/regressions/quickcard_pol_3.exportgrid b/n3fit/src/n3fit/tests/regressions/quickcard_pol_3.exportgrid
index 352eb46c75..1e83db63c6 100644
--- a/n3fit/src/n3fit/tests/regressions/quickcard_pol_3.exportgrid
+++ b/n3fit/src/n3fit/tests/regressions/quickcard_pol_3.exportgrid
@@ -1,570 +1,567 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
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-- [0.0, 0.0, 0.0, 0.062755804774023, 0.06401338232460589, 0.06391198364998928, 6.69377352801909,
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-- [0.0, 0.0, 0.0, 0.06044732050285676, 0.06175910311610148, 0.06164674656967025, 6.39840274917371,
-  0.06164674656967025, 0.06175910311610148, 0.06044732050285676, 0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.058220706120845275, 0.05958916512815283, 0.059464685264659166,
-  6.11575820112944, 0.059464685264659166, 0.05958916512815283, 0.058220706120845275,
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   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.000811481927046611, 0.0024143594765466767, -0.000661776631342615,
-  -5.107764012090297e-06, -0.000661776631342615, 0.0024143594765466767, 0.000811481927046611,
+- [0.0, 0.0, 0.0, 0.00033958290935261513, 0.0010004554264039507, -0.00028157760147802996,
+  -6.193918911491725e-07, -0.00028157760147802996, 0.0010004554264039507, 0.00033958290935261513,
   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.0006335793368705041, 0.0018782699775990155, -0.0005184787988944042,
-  -2.8046565393486045e-06, -0.0005184787988944042, 0.0018782699775990155, 0.0006335793368705041,
+- [0.0, 0.0, 0.0, 0.00022451982911507324, 0.0006599787489191248, -0.00018830090815560684,
+  -2.2753708388101794e-07, -0.00018830090815560684, 0.0006599787489191248, 0.00022451982911507324,
   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.00047612620344986633, 0.0014068111325110176, -0.00039171326078830753,
-  -1.4039794380477953e-06, -0.00039171326078830753, 0.0014068111325110176, 0.00047612620344986633,
+- [0.0, 0.0, 0.0, 0.00013166933750604617, 0.0003866110308935998, -0.00011230665498040263,
+  -6.257860965035967e-08, -0.00011230665498040263, 0.0003866110308935998, 0.00013166933750604617,
   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.0003395829838189614, 0.0010004554113491626, -0.00028157736160241086,
-  -6.19391733485424e-07, -0.00028157736160241086, 0.0010004554113491626, 0.0003395829838189614,
+- [0.0, 0.0, 0.0, 6.20283207956381e-05, 0.0001823368862387775, -5.4334354732377206e-05,
+  -1.014791085415506e-08, -5.4334354732377206e-05, 0.0001823368862387775, 6.20283207956381e-05,
   0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.00022451987134643176, 0.0006599787278624588, -0.0001883007591939652,
-  -2.2753702842657522e-07, -0.0001883007591939652, 0.0006599787278624588, 0.00022451987134643176,
-  0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 0.00013166935841117517, 0.0003866110119695284, -0.00011230657311610516,
-  -6.257859506393342e-08, -0.00011230657311610516, 0.0003866110119695284, 0.00013166935841117517,
-  0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 6.202832896855668e-05, 0.00018233687413472344, -5.433431864813517e-05,
-  -1.0147908594594603e-08, -5.433431864813517e-05, 0.00018233687413472344, 6.202832896855668e-05,
-  0.0, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.0, 1.7105492372389147e-05, 5.0648090511620985e-05, -1.5750128492374493e-05,
-  -4.528692991377619e-10, -1.5750128492374493e-05, 5.0648090511620985e-05, 1.7105492372389147e-05,
+- [0.0, 0.0, 0.0, 1.710549052240064e-05, 5.064809480720488e-05, -1.575013782239899e-05,
+  -4.5286939534122746e-10, -1.575013782239899e-05, 5.064809480720488e-05, 1.710549052240064e-05,
   0.0, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 1.0
diff --git a/n3fit/src/n3fit/tests/regressions/quickcard_pol_3.json b/n3fit/src/n3fit/tests/regressions/quickcard_pol_3.json
index 328e7f7cbf..d256f6cf3d 100644
--- a/n3fit/src/n3fit/tests/regressions/quickcard_pol_3.json
+++ b/n3fit/src/n3fit/tests/regressions/quickcard_pol_3.json
@@ -27,44 +27,44 @@
   ],
   "stop_epoch": 62,
   "best_epoch": 0,
-  "erf_tr": 2.236317604012866,
-  "erf_vl": 1.891036578607623,
-  "chi2": 1.5362983721971202,
+  "erf_tr": 1.7494748237680298,
+  "erf_vl": 2.569751168324924,
+  "chi2": 1.3848582707143415,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.0232185373829865,
-    0.9935004234019762,
+    1.0232184744756858,
+    0.9935004226127403,
     0.9899487587939698,
     0.9899487587939698,
     0.9899487587939698
   ],
   "integrability": [
-    5.342948306008566e-16,
-    1.1102230246251565e-16,
-    1.942890293094024e-16,
-    0.020493690636281092,
-    1.942890293094024e-16
+    3.712308238590367e-16,
+    1.6653345369377348e-16,
+    1.6653345369377348e-16,
+    0.020493688985168013,
+    3.3306690738754696e-16
   ],
   "timing": {
     "walltime": {
-      "Total": 8.025956392288208,
+      "Total": 9.35969853401184,
       "start": 0.0,
-      "replica_set": 0.2008500099182129,
-      "replica_fitted": 8.025688409805298,
-      "replica_set_to_replica_fitted": 7.824838399887085
+      "replica_set": 0.23132753372192383,
+      "replica_fitted": 9.359616994857788,
+      "replica_set_to_replica_fitted": 9.128289461135864
     },
     "cputime": {
-      "Total": 10.633196927999997,
+      "Total": 14.490381283000001,
       "start": 0.0,
-      "replica_set": 0.2002973319999981,
-      "replica_fitted": 10.632905010999998,
-      "replica_set_to_replica_fitted": 10.432607679
+      "replica_set": 5.183726517,
+      "replica_fitted": 14.490274503000002,
+      "replica_set_to_replica_fitted": 9.306547986000002
     }
   },
   "version": {
-    "tensorflow": "2.16.1, mkl=??",
-    "numpy": "1.24.0",
-    "nnpdf": "4.0.9.post574.dev0+412f8f857.dirty",
-    "validphys": "4.0.9.post574.dev0+412f8f857.dirty"
+    "tensorflow": "2.15.0, mkl=??",
+    "numpy": "1.26.4",
+    "nnpdf": "4.0.9.post993.dev0+a77ead0a5.dirty",
+    "validphys": "4.0.9.post993.dev0+a77ead0a5.dirty"
   }
 }
diff --git a/n3fit/src/n3fit/tests/test_layers.py b/n3fit/src/n3fit/tests/test_layers.py
index 340a99bf79..f5df35ddcc 100644
--- a/n3fit/src/n3fit/tests/test_layers.py
+++ b/n3fit/src/n3fit/tests/test_layers.py
@@ -32,7 +32,7 @@ class _fake_FKTableData:
     fktable: np.array
     luminosity_mapping: np.array
     xgrid: np.array
-    is_polarized: bool = False
+    convolution_types: tuple = ("UnpolPDF",)
 
 
 # Helper functions
@@ -114,7 +114,14 @@ def generate_had(nfk=1):
     fktables = []
     for _ in range(nfk):
         fk, comb = generate_input_had(flavs=FLAVS, xsize=XSIZE, ndata=NDATA, n_combinations=FLAVS)
-        fktables.append(_fake_FKTableData(fk, comb, np.ones((1, XSIZE))))
+        fktables.append(
+            _fake_FKTableData(
+                fk,
+                comb,
+                np.ones((1, XSIZE)),
+                convolution_types=("UnpolPDF", "UnpolPDF"),
+            )
+        )
     return fktables
 
 
diff --git a/nnpdf_data/nnpdf_data/new_commondata/NNPDF_POS_2P24GEV/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/NNPDF_POS_2P24GEV/metadata.yaml
index ef5971153c..e54c0ecce2 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/NNPDF_POS_2P24GEV/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/NNPDF_POS_2P24GEV/metadata.yaml
@@ -767,7 +767,7 @@ implemented_observables:
   data_uncertainties: []
 - observable_name: XDQ-POLARIZED
   observable:
-    description: DIS positivity Boundary Condition
+    description: Polarized DIS positivity Boundary Condition
     label: 'polarized positivity: $x \delta d$ PDF $Q^2=5$ GeV$^2$'
     units: ''
   process_type: POS_XDDQ
@@ -776,8 +776,8 @@ implemented_observables:
   ndata: 20
   plotting:
     kinematics_override: dis_sqrt_scale
-    theory_reference: Ball:2013lla
-    dataset_label: 'polarized positivity: $x \delta d$ PDF $Q^2=5$ GeV$^2$'
+    theory_reference: Altarelli:1998gn
+    dataset_label: 'polarized positivity for d: $x \delta d$ PDF $Q^2=5$ GeV$^2$'
     plot_x: x
   kinematic_coverage:
   - x
@@ -800,16 +800,54 @@ implemented_observables:
     file: kinematics_XDELTADQ.yaml
   theory:
     conversion_factor: 1.0
-    operation: SUBTRACT_ABSPAIR
+    operation: SUBTRACT_ABS
     FK_tables:
-    - - NNPDF_POS_ANTI_DOWN
     - - NNPDF_POS_DOWN
-    - - NNPDF_POS_ANTI_DDOWN
     - - NNPDF_POS_DDOWN
   data_uncertainties: []
-- observable_name: XSQ-POLARIZED
+- observable_name: XDB-POLARIZED
   observable:
-    description: DIS positivity Boundary Condition
+    description: Polarized DIS positivity Boundary Condition
+    label: 'polarized positivity: $x \delta \bar{d}$ PDF $Q^2=5$ GeV$^2$'
+    units: ''
+  process_type: POS_XDDB
+  tables: []
+  npoints: []
+  ndata: 20
+  plotting:
+    kinematics_override: dis_sqrt_scale
+    theory_reference: Altarelli:1998gn
+    dataset_label: 'polarized positivity: $x \delta \bar{d}$ PDF $Q^2=5$ GeV$^2$'
+    plot_x: x
+  kinematic_coverage:
+  - x
+  - Q2
+  - y
+  kinematics:
+    variables:
+      x:
+        description: "momentum fraction"
+        label: "$x$"
+        units: ""
+      Q2:
+        description: "virtuality"
+        label: "$Q^2$"
+        units: "$GeV^2$"
+      y:
+        description: "inelasticity"
+        label: "$y$"
+        units: ""
+    file: kinematics_XDELTADQ.yaml
+  theory:
+    conversion_factor: 1.0
+    operation: SUBTRACT_ABS
+    FK_tables:
+    - - NNPDF_POS_ANTI_DOWN
+    - - NNPDF_POS_ANTI_DDOWN
+  data_uncertainties: []
+- observable_name: XSQSUM-POLARIZED
+  observable:
+    description: Polarized DIS positivity Boundary Condition
     label: 'polarized positivity: $x \delta s$ PDF $Q^2=5$ GeV$^2$'
     units: ''
   process_type: POS_XDSQ
@@ -818,7 +856,7 @@ implemented_observables:
   ndata: 20
   plotting:
     kinematics_override: dis_sqrt_scale
-    theory_reference: Ball:2013lla
+    theory_reference: Altarelli:1998gn
     dataset_label: 'polarized positivity: $x \delta s$ PDF $Q^2=5$ GeV$^2$'
     plot_x: x
   kinematic_coverage:
@@ -851,7 +889,7 @@ implemented_observables:
   data_uncertainties: []
 - observable_name: XUQ-POLARIZED
   observable:
-    description: DIS positivity Boundary Condition
+    description: Polarized DIS positivity Boundary Condition
     label: 'polarized positivity: $x \delta u$ PDF $Q^2=5$ GeV$^2$'
     units: ''
   process_type: POS_XDUQ
@@ -860,7 +898,7 @@ implemented_observables:
   ndata: 20
   plotting:
     kinematics_override: dis_sqrt_scale
-    theory_reference: Ball:2013lla
+    theory_reference: Altarelli:1998gn
     dataset_label: 'polarized positivity: $x \delta u$ PDF $Q^2=5$ GeV$^2$'
     plot_x: x
   kinematic_coverage:
@@ -884,10 +922,48 @@ implemented_observables:
     file: kinematics_XDELTAUQ.yaml
   theory:
     conversion_factor: 1.0
-    operation: SUBTRACT_ABSPAIR
+    operation: SUBTRACT_ABS
     FK_tables:
-    - - NNPDF_POS_ANTI_UP
     - - NNPDF_POS_UP
-    - - NNPDF_POS_ANTI_DUP
     - - NNPDF_POS_DUP
   data_uncertainties: []
+- observable_name: XUB-POLARIZED
+  observable:
+    description: Polarized DIS positivity Boundary Condition
+    label: 'polarized positivity: $x \delta \bar{u}$ PDF $Q^2=5$ GeV$^2$'
+    units: ''
+  process_type: POS_XDUB
+  tables: []
+  npoints: []
+  ndata: 20
+  plotting:
+    kinematics_override: dis_sqrt_scale
+    theory_reference: Altarelli:1998gn
+    dataset_label: 'polarized positivity: $x \delta \bar{u}$ PDF $Q^2=5$ GeV$^2$'
+    plot_x: x
+  kinematic_coverage:
+  - x
+  - Q2
+  - y
+  kinematics:
+    variables:
+      x:
+        description: "momentum fraction"
+        label: "$x$"
+        units: ""
+      Q2:
+        description: "virtuality"
+        label: "$Q^2$"
+        units: "$GeV^2$"
+      y:
+        description: "inelasticity"
+        label: "$y$"
+        units: ""
+    file: kinematics_XDELTAUQ.yaml
+  theory:
+    conversion_factor: 1.0
+    operation: SUBTRACT_ABS
+    FK_tables:
+    - - NNPDF_POS_ANTI_UP
+    - - NNPDF_POS_ANTI_DUP
+  data_uncertainties: []
diff --git a/validphys2/src/validphys/comparefittemplates/comparecard_polarized.yaml b/validphys2/src/validphys/comparefittemplates/comparecard_polarized.yaml
index 351791e095..e304a3339a 100644
--- a/validphys2/src/validphys/comparefittemplates/comparecard_polarized.yaml
+++ b/validphys2/src/validphys/comparefittemplates/comparecard_polarized.yaml
@@ -73,11 +73,15 @@ PositivityBoundSpecs:
   ymin: -0.30
   ymax: 0.300
 
+PositivityFlavourSpecs:
+- basis: POLARIZED_FLAVOURPC
+  xmin: 0.001
+
 PDFnormalize:
   - Normtitle: Absolute
 
 Basespecs:
-  - basis: POLARIZED_EVOL
+  - basis: POLARIZED_EVOL_CMP
     Basistitle: Evolution basis
 
 PDFscalespecs:
@@ -137,6 +141,8 @@ dataspecs:
       from_: current
     speclabel:
       from_: current
+    unpolarized_bc:
+      from_: current
 
   - theoryid:
       from_: reference
@@ -146,14 +152,20 @@ dataspecs:
       from_: reference
     speclabel:
       from_: reference
-      
+    unpolarized_bc:
+      from_: reference
+
 t0_info:
   - use_t0: True
     datacuts:
       from_: fit
     t0pdfset:
-      from_: datacuts     
- 
+      from_: datacuts
+    positivity_bound:
+      from_: fit
+    unpolarized_bc:
+      from_: positivity_bound
+
 Normalize:
   normalize_to: 2
 
@@ -169,4 +181,3 @@ ProcessGroup:
 
 actions_:
   - report(main=true)
-
diff --git a/validphys2/src/validphys/comparefittemplates/pdf_positivity_bound.md b/validphys2/src/validphys/comparefittemplates/pdf_positivity_bound.md
index c1be865075..032e3bbdc2 100644
--- a/validphys2/src/validphys/comparefittemplates/pdf_positivity_bound.md
+++ b/validphys2/src/validphys/comparefittemplates/pdf_positivity_bound.md
@@ -1,5 +1,16 @@
 %NNPDF report comparing {@ current fit @} and {@ reference fit @}
 
+Bounds on individual fl
+-----------------------
+{@with PDFscalespecs@}
+##### {@Xscaletitle@} scale plots
+{@with PositivityFlavourSpecs@}
+{@plot_polarized_boundaries@}
+{@endwith@}
+{@endwith@}
+
+Bounds on Δq+Δqbar
+------------------
 {@with PDFscalespecs@}
 ##### {@Xscaletitle@} scale plots
 {@with PositivityBoundSpecs@}
diff --git a/validphys2/src/validphys/config.py b/validphys2/src/validphys/config.py
index bdd94e213c..a923542f1b 100644
--- a/validphys2/src/validphys/config.py
+++ b/validphys2/src/validphys/config.py
@@ -127,15 +127,14 @@ class CoreConfig(configparser.Config):
     def loader(self):
         return self.environment.loader
 
-    @element_of("pdfs")
-    @_id_with_label
-    def parse_pdf(self, name: str):
-        """A PDF set installed in LHAPDF."""
+    def _check_pdf_usable(self, pdf_name: str):
+        """Check that the given PDF can be loaded and the error type
+        is understood before continuing"""
         try:
-            pdf = self.loader.check_pdf(name)
+            pdf = self.loader.check_pdf(pdf_name)
         except PDFNotFound as e:
             raise ConfigError(
-                f"Bad PDF: {name} not installed", name, self.loader.available_pdfs
+                f"Bad PDF: {pdf_name} not installed", pdf_name, self.loader.available_pdfs
             ) from e
         except LoaderError as e:
             raise ConfigError(e) from e
@@ -147,6 +146,24 @@ def parse_pdf(self, name: str):
             raise ConfigError(str(e))
         return pdf
 
+    @element_of("pdfs")
+    @_id_with_label
+    def parse_pdf(self, name: str, unpolarized_bc=None):
+        """A PDF set installed in LHAPDF.
+        If an unpolarized boundary condition it defined, it will be registered as part of the PDF.
+        """
+        pdf = self._check_pdf_usable(name)
+        if unpolarized_bc is not None:
+            pdf.register_boundary(unpolarized_bc=unpolarized_bc)
+
+        return pdf
+
+    @element_of("unpolarized_bcs")
+    @_id_with_label
+    def parse_unpolarized_bc(self, name):
+        """Unpolarised PDF used as a Boundary Condition to impose positivity of pPDFs."""
+        return self.parse_pdf(name)
+
     @element_of("theoryids")
     @_id_with_label
     def parse_theoryid(self, theoryID: (str, int)):
@@ -269,7 +286,6 @@ def produce_fitenvironment(self, fit, fitinputcontext):
 
     def produce_fitcontext(self, fitinputcontext, fitpdf):
         """Set PDF, theory ID and data input from the fit config"""
-
         return dict(**fitinputcontext, **fitpdf)
 
     def produce_fitinputcontext(self, fit):
@@ -284,6 +300,14 @@ def produce_fitpdf(self, fit):
         """Like ``fitcontext`` only setting the PDF"""
         with self.set_context(ns=self._curr_ns.new_child({"fit": fit})):
             _, pdf = self.parse_from_("fit", "pdf", write=False)
+
+            # Register possible boundaries
+            try:
+                _, boundary = self.parse_from_("fit", "positivity_bound", write=False)
+                pdf.register_boundary(unpolarized_bc=boundary["unpolarized_bc"])
+            except ConfigError:
+                pass
+
         return {"pdf": pdf}
 
     def produce_fitunderlyinglaw(self, fit):
@@ -955,15 +979,9 @@ def parse_reweighting_experiments(self, experiments, *, theoryid, use_cuts, fit=
         """A list of experiments to be used for reweighting."""
         return self.parse_experiments(experiments, theoryid=theoryid, use_cuts=use_cuts, fit=fit)
 
-    def parse_t0pdfset(self, name):
+    def parse_t0pdfset(self, name, unpolarized_bc=None):
         """PDF set used to generate the t0 covmat."""
-        return self.parse_pdf(name)
-
-    @element_of("unpolarized_bcs")
-    @_id_with_label
-    def parse_unpolarized_bc(self, name):
-        """Unpolarised PDF used as a Boundary Condition to impose positivity of pPDFs."""
-        return self.parse_pdf(name)
+        return self.parse_pdf(name, unpolarized_bc=unpolarized_bc)
 
     def parse_use_t0(self, do_use_t0: bool):
         """Whether to use the t0 PDF set to generate covariance matrices."""
diff --git a/validphys2/src/validphys/convolution.py b/validphys2/src/validphys/convolution.py
index 753b4d9573..c95d686fba 100644
--- a/validphys2/src/validphys/convolution.py
+++ b/validphys2/src/validphys/convolution.py
@@ -402,17 +402,27 @@ def appl(df):
 
 def hadron_predictions(loaded_fk, pdf):
     """Implementation of :py:func:`fk_predictions` for hadronic observables."""
-    gv = functools.partial(evolution.grid_values, pdf=pdf)
-    res = _gv_hadron_predictions(loaded_fk, gv)
-    res.columns = range(pdf.get_members())
+    pdf_list = loaded_fk.determine_pdfs(pdf)
+    gv1 = functools.partial(evolution.grid_values, pdf=pdf_list[0])
+    if pdf_list[1] == pdf_list[0]:
+        gv2 = None
+    else:
+        gv2 = functools.partial(evolution.grid_values, pdf=pdf_list[1])
+    res = _gv_hadron_predictions(loaded_fk, gv1, gv2)
+    res.columns = range(pdf_list[0].get_members())
     return res
 
 
 def central_hadron_predictions(loaded_fk, pdf):
     """Implementation of :py:func:`central_fk_predictions` for hadronic
     observables."""
-    gv = functools.partial(evolution.central_grid_values, pdf=pdf)
-    return _gv_hadron_predictions(loaded_fk, gv)
+    pdf_list = loaded_fk.determine_pdfs(pdf)
+    gv1 = functools.partial(evolution.central_grid_values, pdf=pdf_list[0])
+    if pdf_list[1] == pdf_list[0]:
+        gv2 = None
+    else:
+        gv2 = functools.partial(evolution.central_grid_values, pdf=pdf_list[1])
+    return _gv_hadron_predictions(loaded_fk, gv1, gv2)
 
 
 def linear_hadron_predictions(loaded_fk, pdf):
@@ -425,20 +435,22 @@ def linear_hadron_predictions(loaded_fk, pdf):
     between each replica and the central value, ``replica_values -
     central_value``
     """
-    gv1 = functools.partial(evolution.central_grid_values, pdf=pdf)
+    pdf_list = loaded_fk.determine_pdfs(pdf)
+    gv1 = functools.partial(evolution.central_grid_values, pdf=pdf_list[0])
 
     def gv2(*args, **kwargs):
-        replica_values = evolution.grid_values(pdf, *args, **kwargs)
-        central_value = evolution.central_grid_values(pdf, *args, **kwargs)
+        replica_values = evolution.grid_values(pdf_list[1], *args, **kwargs)
+        central_value = evolution.central_grid_values(pdf_list[1], *args, **kwargs)
         return 2 * replica_values - central_value
 
     res = _gv_hadron_predictions(loaded_fk, gv1, gv2)
-    res.columns = range(pdf.get_members())
+    res.columns = range(pdf_list[0].get_members())
     return res
 
 
 def dis_predictions(loaded_fk, pdf):
     """Implementation of :py:func:`fk_predictions` for DIS observables."""
+    pdf = loaded_fk.determine_pdfs(pdf)[0]
     gv = functools.partial(evolution.grid_values, pdf=pdf)
     res = _gv_dis_predictions(loaded_fk, gv)
     res.columns = range(pdf.get_members())
@@ -448,5 +460,6 @@ def dis_predictions(loaded_fk, pdf):
 def central_dis_predictions(loaded_fk, pdf):
     """Implementation of :py:func:`central_fk_predictions` for DIS
     observables."""
+    pdf = loaded_fk.determine_pdfs(pdf)[0]
     gv = functools.partial(evolution.central_grid_values, pdf=pdf)
     return _gv_dis_predictions(loaded_fk, gv)
diff --git a/validphys2/src/validphys/core.py b/validphys2/src/validphys/core.py
index 97ea9d5260..a16227413e 100644
--- a/validphys2/src/validphys/core.py
+++ b/validphys2/src/validphys/core.py
@@ -70,6 +70,8 @@ def __dir__(self):
 PDFSETS = _PDFSETS()
 
 
+# TODO: make the PDF into a dataclass instead of a TupleComp
+# https://github.com/NNPDF/nnpdf/issues/408
 class PDF(TupleComp):
     """Base validphys PDF providing high level access to metadata.
 
@@ -90,17 +92,29 @@ class PDF(TupleComp):
     (3, 100)
     """
 
-    def __init__(self, name):
+    def __init__(self, name, boundary=None):
+        if boundary is not None:
+            raise ValueError(
+                "The keyword argument boundary is a transitional argument for tuplecomp"
+            )
         self.name = name
         self._plotname = name
         self._info = None
         self._stats_class = None
-        super().__init__(name)
+        # Boundary conditions:
+        self.unpolarized_bc = None
+        super().__init__(name, boundary)
 
     @property
     def label(self):
         return self._plotname
 
+    @property
+    def is_polarized(self):
+        """Returns ``True`` if the PDF has a boundary condition associated to it.
+        At the moment LHAPDF provides no mechanism to know whether a PDF is polarized."""
+        return self.unpolarized_bc is not None
+
     @label.setter
     def label(self, label):
         self._plotname = label
@@ -211,6 +225,27 @@ def get_members(self):
         """Return the number of members selected in ``pdf.load().grid_values``"""
         return len(self)
 
+    def register_boundary(self, unpolarized_bc=None):
+        """Register other PDFs as boundary conditions of this PDF"""
+        if unpolarized_bc is not None:
+            self.unpolarized_bc = unpolarized_bc
+
+            # Update `comp_tuple` so that the pseudo-dataclass still works
+            self.comp_tuple = (self.name, unpolarized_bc.name)
+
+    def make_only_cv(self):
+        return PDFcv(self.name)
+
+
+class PDFcv(PDF):
+    """An add-on for the PDF class that makes only the central value available"""
+
+    def load(self):
+        return self.load_t0()
+
+    def __len__(self):
+        return 1
+
 
 class CommonDataSpec(TupleComp):
     """Holds all the information necessary to load a commondata file and provides
diff --git a/validphys2/src/validphys/coredata.py b/validphys2/src/validphys/coredata.py
index d74f197a77..d016cc8ef3 100644
--- a/validphys2/src/validphys/coredata.py
+++ b/validphys2/src/validphys/coredata.py
@@ -63,7 +63,7 @@ class FKTableData:
     ndata: int
     xgrid: np.ndarray
     sigma: pd.DataFrame
-    is_polarized: bool = False
+    convolution_types: tuple[str] = None
     metadata: dict = dataclasses.field(default_factory=dict, repr=False)
     protected: bool = False
 
@@ -83,7 +83,7 @@ def with_cfactor(self, cfactor):
         return dataclasses.replace(self, sigma=new_sigma)
 
     def with_cuts(self, cuts):
-        """Return a copy of the FKTabe with the cuts applied.  The data index
+        """Return a copy of the FKTable with the cuts applied.  The data index
         of the sigma operator (the outermost level), contains the data point
         that have been kept. The ndata property is updated to reflect the new
         number of datapoints. If cuts is None, return the object unmodified.
@@ -189,6 +189,41 @@ def get_np_fktable(self):
 
         return fktable
 
+    def determine_pdfs(self, pdf):
+        """Determine the PDF (or PDFs) that should be used to be convoluted with this fktable.
+        Uses the `convolution_types` key to decide the PDFs.
+        If `convolution_types` is not defined, it returns the pdf object.
+        """
+        if self.convolution_types is None:
+            if self.hadronic:
+                return [pdf, pdf]
+            return [pdf]
+
+        conv_pdfs = []
+        for convolution_type in self.convolution_types:
+
+            # Check the type of convolutions that the fktable is asking for and match it to the PDF
+            if convolution_type == "UnpolPDF":
+                if pdf.is_polarized:
+                    if pdf.unpolarized_bc is None:
+                        raise ValueError(
+                            "The FKTable asked for an unpolarized PDF but received only polarized PDFs"
+                        )
+
+                    conv_pdfs.append(pdf.unpolarized_bc.make_only_cv())
+                else:
+                    conv_pdfs.append(pdf)
+
+            elif convolution_type == "PolPDF":
+                if not pdf.is_polarized:
+                    raise ValueError(
+                        """The FKTable asked for a polarized PDF, but the PDF received cannot be understood as polarized.
+                        When using a polarized PDF make sure to include a boundary condition `unpolarized_bc: <pdf name>` whenever needed (`t0`, `dataspecs`...)."""
+                    )
+                conv_pdfs.append(pdf)
+
+        return conv_pdfs
+
 
 @dataclasses.dataclass(eq=False)
 class CFactorData:
diff --git a/validphys2/src/validphys/fkparser.py b/validphys2/src/validphys/fkparser.py
index 3ac464a8a0..bc0f2e06e0 100644
--- a/validphys2/src/validphys/fkparser.py
+++ b/validphys2/src/validphys/fkparser.py
@@ -17,6 +17,7 @@
     fk = l.check_fktable(setname="ATLASTTBARTOT", theoryID=53, cfac=('QCD',))
     res = load_fktable(fk)
 """
+
 import dataclasses
 import functools
 import io
@@ -312,13 +313,9 @@ def parse_fktable(f):
             hadronic = res['GridInfo'].hadronic
             ndata = res['GridInfo'].ndata
             xgrid = res.pop('xGrid')
+
             return FKTableData(
-                sigma=sigma,
-                ndata=ndata,
-                Q0=Q0,
-                metadata=res,
-                hadronic=hadronic,
-                xgrid=xgrid,
+                sigma=sigma, ndata=ndata, Q0=Q0, metadata=res, hadronic=hadronic, xgrid=xgrid
             )
         elif header_name in _KNOWN_SEGMENTS:
             parser = _KNOWN_SEGMENTS[header_name]
diff --git a/validphys2/src/validphys/pdfbases.py b/validphys2/src/validphys/pdfbases.py
index 11272c2d23..8a0adf65b0 100644
--- a/validphys2/src/validphys/pdfbases.py
+++ b/validphys2/src/validphys/pdfbases.py
@@ -655,9 +655,28 @@ def f_(transform_func):
     default_elements=(r'sigma', 't3', 't8', 'gluon', 'sigma_t8', )
 )
 
+POLARIZED_EVOL_CMP = LinearBasis.from_mapping({
+    r'\Delta \Sigma'   : {'u': 1, 'ubar': 1, 'd': 1, 'dbar': 1, 's': 1, 'sbar': 1},
+    r'\Delta T3'       : {'u': 1, 'ubar': 1, 'd':-1, 'dbar':-1},
+    r'\Delta T8'       : {'u': 1, 'ubar': 1, 'd': 1, 'dbar': 1, 's':-2, 'sbar':-2},
+    r'\Delta g'        : {'g':1},
+    r'\Delta V'        : {'u': 1, 'ubar': -1, 'd': 1, 'dbar': -1},
+    r'\Delta V3'       : {'u': 1, 'ubar': -1, 'd': -1, 'dbar': 1},
+    r'(\Delta \Sigma + \Delta T8)/4' : {'u': 1/2, 'ubar': 1/2, 'd': 1/2, 'dbar': 1/2, 's':-1/4, 'sbar':-1/4},
+    },
+    aliases = {'g':r'\Delta g', 'gluon':r'\Delta g', r'singlet': r'\Delta \Sigma', 'sng': r'\Delta \Sigma',
+               'sigma': r'\Delta \Sigma', 't3': r'\Delta T3', 't8': r'\Delta T8', 'T3': r'\Delta T3',
+               'T8': r'\Delta T8','sigma_t8': r'(\Delta \Sigma + \Delta T8)/4', 'V3': r'\Delta V3',
+               'v3': r'\Delta V3', 'v': r'\Delta V', 'V': r'\Delta V', },
+    default_elements=(r'sigma', 't3', 't8', 'v', 'v3', 'gluon', 'sigma_t8', )
+)
+
 LUX_FLAVOURPC = copy.deepcopy(FLAVOURPC)
 LUX_FLAVOURPC.default_elements = ('u', 'ubar', 'd', 'dbar', 's', 'sbar', 'g', 'photon')
 
+POLARIZED_FLAVOURPC = copy.deepcopy(FLAVOURPC)
+POLARIZED_FLAVOURPC.default_elements = ('u', 'ubar', 'd', 'dbar', 'g')
+
 pdg = LinearBasis.from_mapping({
 'g/10': {'g':0.1},
 'u_{v}': {'u':1, 'ubar':-1},
@@ -878,7 +897,7 @@ def fitbasis_to_NN31IC(flav_info, fitbasis):
         v15 = {'u': 1, 'ubar': -1, 'd': 1, 'dbar': -1, 's': 1, 'sbar': -1, 'c': -3, 'cbar': 3, 'g': 0 }
 
 
-    elif fitbasis == 'POLARIZED_EVOL':  # With Perturbative Charm
+    elif fitbasis == 'POLARIZED_EVOL' or fitbasis == "POLARIZED_EVOL_CMP":  # With Perturbative Charm
         sng = {'sng': 1, 'v': 0, 'v3': 0, 'v8': 0, 't3': 0, 't8': 0, 't15': 0, 'g': 0 }
         v = {'sng': 0, 'v': 1, 'v3': 0, 'v8': 0, 't3': 0, 't8': 0, 't15': 0, 'g': 0 }
         v3 = {'sng': 0, 'v': 0, 'v3': 1, 'v8': 0, 't3': 0, 't8': 0, 't15': 0, 'g': 0 }
diff --git a/validphys2/src/validphys/pineparser.py b/validphys2/src/validphys/pineparser.py
index f61d9aa3ab..d7dd4488a8 100644
--- a/validphys2/src/validphys/pineparser.py
+++ b/validphys2/src/validphys/pineparser.py
@@ -155,23 +155,27 @@ def pineappl_reader(fkspec):
     # Extract metadata from the first grid
     pine_rep = pines[0]
 
-    # Check if it is Polarized FK table
-    is_polarized = pine_rep.key_values().get("polarized") == "True"
-
     # Is it hadronic? (at the moment only hadronic and DIS are considered)
     try:
         parton1 = pine_rep.key_values()["convolution_particle_1"]
         parton2 = pine_rep.key_values()["convolution_particle_2"]
     except KeyError:
+        # Old pineappl FKTables used  `initial_state` instead of `convolution_particle`
         parton1 = pine_rep.key_values()["initial_state_1"]
         parton2 = pine_rep.key_values()["initial_state_2"]
     hadronic = parton1 == parton2
 
-    # Sanity check (in case at some point we start fitting things that are not protons)
-    if hadronic and parton1 != "2212":
-        raise ValueError(
-            "pineappl_reader is not prepared to read a hadronic fktable with no protons!"
-        )
+    # NOTE: while the following can accept any number of convolutions, at the moment only
+    # 1 (DIS) or 2 (hadronic) are implemented.
+    # In the case of DIS grids, convolution 1 refers to the hadron
+    conv_types = [pine_rep.key_values().get("convolution_type_1", "UnpolPDF")]
+    if hadronic:
+        # Sanity check (in case at some point we start fitting things that are not protons)
+        if parton1 != "2212":
+            raise ValueError("vp can only read hadronic fktables with 2 protons!")
+
+        conv_types.append(pine_rep.key_values().get("convolution_type_2", "UnpolPDF"))
+
     Q0 = np.sqrt(pine_rep.muf2())
     xgrid = np.array([])
     for pine in pines:
@@ -268,7 +272,7 @@ def pineappl_reader(fkspec):
         sigma=sigma,
         ndata=ndata,
         Q0=Q0,
-        is_polarized=is_polarized,
+        convolution_types=tuple(conv_types),
         metadata=fkspec.metadata,
         hadronic=hadronic,
         xgrid=xgrid,
diff --git a/validphys2/src/validphys/theorycovariance/theorycovarianceutils.py b/validphys2/src/validphys/theorycovariance/theorycovarianceutils.py
index d71db0644e..7ff8628c23 100644
--- a/validphys2/src/validphys/theorycovariance/theorycovarianceutils.py
+++ b/validphys2/src/validphys/theorycovariance/theorycovarianceutils.py
@@ -33,7 +33,7 @@ def check_correct_theory_combination_internal(
         elif point_prescription == "3r point":
             correct_xifs = [1.0, 1.0, 1.0]
             correct_xirs = [1.0, 2.0, 0.5]
-        elif "n3lo" in point_prescription:
+        elif "n3lo" in point_prescription or "missing" in point_prescription:
             correct_xifs = [1.0, 1.0, 1.0]
             correct_xirs = [1.0, 0.5, 2.0]
         else: