From 74b791a16a01e121b8d3bddfb244221028b269db Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Fri, 26 May 2023 08:47:44 -0700
Subject: [PATCH 01/17] Stub of execution core slides

---
 .../Processor_Cores.jpeg                      | Bin 0 -> 61058 bytes
 .../validator-groups.png                      | Bin 0 -> 32098 bytes
 .../Deep_Dive_Availability_Cores_Slides.md    |  82 ++++++++++++++++++
 3 files changed, 82 insertions(+)
 create mode 100644 assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Processor_Cores.jpeg
 create mode 100644 assets/img/5-Polkadot/Availability_Cores_Deep_Dive/validator-groups.png
 create mode 100644 syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md

diff --git a/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Processor_Cores.jpeg b/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Processor_Cores.jpeg
new file mode 100644
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diff --git a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
new file mode 100644
index 000000000..0e7ba495f
--- /dev/null
+++ b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -0,0 +1,82 @@
+---
+title: Deep Dive, Availability Cores
+description: The Polkadot Abstraction for Flexible Blockspace Allocation
+duration: 1 hour
+---
+
+# Deep Dive, Availability Cores
+
+Notes:
+
+Hello!
+
+I'm Bradley Olson
+
+Was student at first Academy in Cambridge
+
+Currently on Parachains Core Team at Parity
+
+Will present 3 lectures providing a window into Polkadot core, a slice of where we're at and where we're headed.
+
+First a look at availability cores, the abstraction enabling flexible purchases of blockspace under the umbrella of Polkadot shared security.
+
+Lets get to it
+
+---
+
+## Availability Core Defined
+
+<pba-cols>
+<pba-col center>
+
+  - Availability cores are the abstraction that allocates Polkadot's validation of parachain block candidates.
+  - Cores divide validation into discrete units of capacity, ~1 core per 5 validators
+  - Why "availability"?
+  - Why "core"?
+
+</pba-col>
+<pba-col center>
+
+<img rounded style="width: 500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Processor_Cores.jpeg" alt="Processor cores image">
+
+</pba-col>
+</pba-cols>
+
+
+
+
+Notes:
+
+- "Availability", because a core is considered occupied by a parachain block candidate during the period when that candidate is being made available via erasure coding.
+- "Core", because many candidates can be made available in parallel, mimicking the parallel computation per core in a computer processor.
+
+---
+
+## Overview
+
+<pba-flex center>
+
+- What does an availability core represent?
+- How are availability cores scheduled?
+- How do cores gate each step of the parachains protocol?
+- What do cores give us now?
+- What roadmap items do cores accomodate?
+
+</pba-flex>
+
+---
+
+## Resources
+
+<pba-col center>
+
+1. [Implementers Guide: Scheduler Pallet](https://paritytech.github.io/polkadot/book/runtime/scheduler.html)
+1. 
+
+</pba-col>
+
+---
+
+<!-- .slide: data-background-color="#4A2439" -->
+
+# Questions
\ No newline at end of file

From 76f7e647cbc911d51e2a2d5127ba4a6c46acc217 Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Mon, 29 May 2023 11:20:55 -0700
Subject: [PATCH 02/17] Define blockspace and cores

---
 .../Availability_Cores_Deep_Dive/Train.jpeg   | Bin 0 -> 881404 bytes
 .../Deep_Dive_Availability_Cores_Slides.md    |  96 +++++++++++++++---
 2 files changed, 83 insertions(+), 13 deletions(-)
 create mode 100644 assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Train.jpeg

diff --git a/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Train.jpeg b/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Train.jpeg
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diff --git a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index 0e7ba495f..b8a48a529 100644
--- a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -24,13 +24,84 @@ Lets get to it
 
 ---
 
+## Overview
+
+<pba-flex center>
+
+- What do availability cores represent?
+- How is availability core use scheduled?
+- How do cores gate each step of the parachains protocol?
+- What advantages do cores give us now?
+- What roadmap items do cores accomodate?
+
+</pba-flex>
+
+---
+
+## Review, Blockspace
+
+> Blockspace is the capacity of a blockchain to finalize and commit operations
+
+Polkadot's primary product is _blockspace_.
+
+---
+
+## Disecting Polkadot Blockspace
+
+In a parachain block you get:
+
+<pba-flex center>
+
+- Proof of Validity
+    - max size: 5 * 1024 * 1024
+- Code upgrade 
+    - max size: 4 * 1024 * 1024
+    - cooldown: 14400 blocks
+- HRMP messages 
+    - Max message size: 102400
+    - Messages per block per channel: 10
+    - Max channels: 30
+- UMP messages
+    - Max message size: 65531
+    - Messages per block: 16
+
+</pba-flex>
+
+Notes:
+
+Max POV size implicitly limits the number of operations per block, since each on-chain operation and its impact on state are accounted for in the POV.
+
+Why not put everything in the POV?
+
+Short answer: Code upgrades and cross consensus messages have different data availability requirements than ordinary parachain operations.
+
+The relay chain needs to keep a copy of the current code for each parachain for PVF execution. 
+
+HRMP and UMP messages must be made available to their recipients, so they need to be cached on the relay chain for an indeterminate period.
+
+---
+
+## Blockspace, Use It or Lose It
+
+Polkadot blockspace is consumed in two ways:
+1. When the relay chain validates, includes, and finalizes a parachain block
+2. When the capacity to validate a parachain block is left unused and expires
+
+<img rounded style="width: 500px" src="../../../assets/img/5-Polkadot/OpenGov-PBA2/stopwatch.png" alt="Stopwatch">
+
+Notes:
+
+In this sense units of blockspace have very short lifespans, less than the relay block time of 6 seconds. To mitigate waste it is therefore critical to provide flexible markets for blockspace which maximize the proportion that is purchased and fully used.
+
+---
+
 ## Availability Core Defined
 
 <pba-cols>
 <pba-col center>
 
-  - Availability cores are the abstraction that allocates Polkadot's validation of parachain block candidates.
-  - Cores divide validation into discrete units of capacity, ~1 core per 5 validators
+  - Availability cores are the abstraction we use to allocate Polkadot's blockspace.
+  - Cores divide blockspace supply into discrete units, 1 parachain block per relay chain block per core
   - Why "availability"?
   - Why "core"?
 
@@ -42,9 +113,6 @@ Lets get to it
 </pba-col>
 </pba-cols>
 
-
-
-
 Notes:
 
 - "Availability", because a core is considered occupied by a parachain block candidate during the period when that candidate is being made available via erasure coding.
@@ -52,17 +120,19 @@ Notes:
 
 ---
 
-## Overview
+## Cores and Blockspace Over Time
 
-<pba-flex center>
+<img rounded style="width: 1100px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Train.jpeg" alt="Train">
+
+Notes:
+
+_analogy-freight-train_: A unit of blockspace is a reserved car in a train leaving the station at a specific time. Trains are scheduled to leave the station every six seconds. An availability core is a particular car index within all trains. If you have a lease on core 4, then you have the right to fill train car 4 on each train with whatever you want to ship.
+
+---
+
+## Assigning Cores to Parachains
 
-- What does an availability core represent?
-- How are availability cores scheduled?
-- How do cores gate each step of the parachains protocol?
-- What do cores give us now?
-- What roadmap items do cores accomodate?
 
-</pba-flex>
 
 ---
 

From 58969d83b29eb2d90360df229a3ecd5631cacfb5 Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Mon, 29 May 2023 13:49:58 -0700
Subject: [PATCH 03/17] Started cores and backing

---
 .../Deep_Dive_Availability_Cores_Slides.md    | 75 ++++++++++++++++++-
 1 file changed, 74 insertions(+), 1 deletion(-)

diff --git a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index b8a48a529..4ab80f5de 100644
--- a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -132,6 +132,80 @@ _analogy-freight-train_: A unit of blockspace is a reserved car in a train leavi
 
 ## Assigning Cores to Parachains
 
+Diagram for core assignments. Two cores paired to a single lease each. Two on-demand cores linked to the same on-demand claims queue. Show that every other claim in the queue goes to core 1. Show at least one free core. 
+
+---
+
+## Occupying Assigned Cores
+
+Diagram showing how backed candidates are supplied to occupy assigned cores. Show that a leasing chain with no backed candidates won't occupy a core. Show that an occupied core can't accept a second candidate. Show that each on-demand claim comes with a number of tries to submit a candidate that validators will back. Each relay block that passes with without a backed candidate produced to fill the availability core counts as a failed try.
+
+---
+
+## Mapping Backers to Cores
+
+<img rounded style="width: 1100px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/validator-groups.png" alt="Train">
+
+Notes:
+
+Validator groups rotate across availability cores in a round-robin fashion, with rotation occurring at fixed intervals. This is to prevent a byzantine backing group from interrupting the liveness of any one parachain for too long.
+
+---
+
+## Core States in the Runtime
+
+```rust
+
+    #[pallet::storage]
+    #[pallet::getter(fn availability_cores)]
+    pub(crate) type AvailabilityCores<T> = StorageValue<_, Vec<Option<CoreOccupied>>, ValueQuery>;
+
+    #[pallet::storage]
+    pub(crate) type ParathreadQueue<T> = StorageValue<_, ParathreadClaimQueue, ValueQuery>;
+
+    #[pallet::storage]
+    #[pallet::getter(fn scheduled)]
+    pub(crate) type Scheduled<T> = StorageValue<_, Vec<CoreAssignment>, ValueQuery>;
+
+    pub struct ParathreadClaimQueue {
+        queue: Vec<QueuedParathread>,
+        // this value is between 0 and config.parathread_cores
+        next_core_offset: u32,
+    }
+
+    pub struct CoreAssignment {
+        /// The core that is assigned.
+        pub core: CoreIndex,
+        /// The unique ID of the para that is assigned to the core.
+        pub para_id: ParaId,
+        /// The kind of the assignment.
+        pub kind: AssignmentKind,
+    }
+
+    pub enum CoreOccupied {
+        /// A parathread (on-demand parachain).
+        Parathread(ParathreadEntry),
+        /// A parachain.
+        Parachain,
+    }
+```
+
+---
+
+# How Cores Gate Each Step of the Parachains Protocol
+
+---
+
+## Cores and Backing
+
+- Backing groups are assigned to parachains by core
+- Backing groups will only back candidates from the chain assigned to their core
+- Backing groups for on-demand cores are made aware of on-demand claims ahead of time, so that they know to start the backing process early enough that availability retries aren't required.
+
+---
+
+## Cores and Backing Code
+
 
 
 ---
@@ -141,7 +215,6 @@ _analogy-freight-train_: A unit of blockspace is a reserved car in a train leavi
 <pba-col center>
 
 1. [Implementers Guide: Scheduler Pallet](https://paritytech.github.io/polkadot/book/runtime/scheduler.html)
-1. 
 
 </pba-col>
 

From 879d688e6d58ffbdeba0f4b5de0a433697f19698 Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Fri, 2 Jun 2023 15:52:00 -0700
Subject: [PATCH 04/17] Adding detail

---
 .../Execution_Cores_Visuals.svg               |   1 +
 .../Deep_Dive_Availability_Cores_Slides.md    | 285 +++++++++++++++---
 2 files changed, 243 insertions(+), 43 deletions(-)
 create mode 100644 assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Execution_Cores_Visuals.svg

diff --git a/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Execution_Cores_Visuals.svg b/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Execution_Cores_Visuals.svg
new file mode 100644
index 000000000..817f27dbf
--- /dev/null
+++ b/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Execution_Cores_Visuals.svg
@@ -0,0 +1 @@
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diff --git a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index 4ab80f5de..e51e7235f 100644
--- a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -29,7 +29,7 @@ Lets get to it
 <pba-flex center>
 
 - What do availability cores represent?
-- How is availability core use scheduled?
+- How do cores map parachain leases and claims to validator subsets?
 - How do cores gate each step of the parachains protocol?
 - What advantages do cores give us now?
 - What roadmap items do cores accomodate?
@@ -130,6 +130,35 @@ _analogy-freight-train_: A unit of blockspace is a reserved car in a train leavi
 
 ---
 
+# Mapping Leases and Claims to Validator Subsets
+
+---
+
+## Backing Group Formation
+
+<img rounded style="width: 1100px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/validator-groups.png" alt="Train">
+
+Notes:
+
+To understand how cores divide up parachains protocol work among validators, we first need to understand how those validators are grouped.
+Validators randomly assigned to groups at start of session.
+
+---
+
+## Assigning Backing Groups to Cores
+
+<img rounded style="width: 1500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Execution_Cores_Visuals.svg" alt="Train">
+
+Notes:
+
+Validator groups rotate across availability cores in a round-robin fashion, with rotation occurring at fixed intervals. This is to prevent a byzantine backing group from interrupting the liveness of any one parachain for too long.
+
+---
+
+## Assigning Approvers to Cores
+
+---
+
 ## Assigning Cores to Parachains
 
 Diagram for core assignments. Two cores paired to a single lease each. Two on-demand cores linked to the same on-demand claims queue. Show that every other claim in the queue goes to core 1. Show at least one free core. 
@@ -142,71 +171,240 @@ Diagram showing how backed candidates are supplied to occupy assigned cores. Sho
 
 ---
 
-## Mapping Backers to Cores
+## Core States in the Runtime
 
-<img rounded style="width: 1100px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/validator-groups.png" alt="Train">
+```rust
+
+#[pallet::storage]
+#[pallet::getter(fn availability_cores)]
+pub(crate) type AvailabilityCores<T> = StorageValue<_, Vec<Option<CoreOccupied>>, ValueQuery>;
+
+#[pallet::storage]
+pub(crate) type ParathreadQueue<T> = StorageValue<_, ParathreadClaimQueue, ValueQuery>;
+
+#[pallet::storage]
+#[pallet::getter(fn scheduled)]
+pub(crate) type Scheduled<T> = StorageValue<_, Vec<CoreAssignment>, ValueQuery>;
+
+pub struct ParathreadClaimQueue {
+    queue: Vec<QueuedParathread>,
+    // this value is between 0 and config.parathread_cores
+    next_core_offset: u32,
+}
+
+pub struct CoreAssignment {
+    /// The core that is assigned.
+    pub core: CoreIndex,
+    /// The unique ID of the para that is assigned to the core.
+    pub para_id: ParaId,
+    /// The kind of the assignment.
+    pub kind: AssignmentKind,
+}
+
+pub enum CoreOccupied {
+    /// A parathread (on-demand parachain).
+    Parathread(ParathreadEntry),
+    /// A parachain.
+    Parachain,
+}
+```
+
+---
+
+# How Cores Gate Each Step of the Parachains Protocol
+
+---
+
+## Cores and Backing Groups
+
+- Groups assigned by core
+- Groups only back candidates with appropriate assignment
+- Groups notified early of on-demand core assignments
 
 Notes:
 
-Validator groups rotate across availability cores in a round-robin fashion, with rotation occurring at fixed intervals. This is to prevent a byzantine backing group from interrupting the liveness of any one parachain for too long.
+- Backing groups are assigned to parachains by core
+- Backing groups will only back candidates for the chain assigned to their assigned core as of the candidate's relay parent
+- Backing groups for on-demand cores are made aware of on-demand claims ahead of time, so that they know to start the backing process early enough that inclusion retries aren't required.
 
 ---
 
-## Core States in the Runtime
+## Cores and Backing Groups, Code
+
+We limit seconding of candidates based on availability core assignments in the function `handle_second_message()` of the Backing Subsystem.
 
 ```rust
 
-    #[pallet::storage]
-    #[pallet::getter(fn availability_cores)]
-    pub(crate) type AvailabilityCores<T> = StorageValue<_, Vec<Option<CoreOccupied>>, ValueQuery>;
-
-    #[pallet::storage]
-    pub(crate) type ParathreadQueue<T> = StorageValue<_, ParathreadClaimQueue, ValueQuery>;
-
-    #[pallet::storage]
-    #[pallet::getter(fn scheduled)]
-    pub(crate) type Scheduled<T> = StorageValue<_, Vec<CoreAssignment>, ValueQuery>;
-
-    pub struct ParathreadClaimQueue {
-        queue: Vec<QueuedParathread>,
-        // this value is between 0 and config.parathread_cores
-        next_core_offset: u32,
-    }
-
-    pub struct CoreAssignment {
-        /// The core that is assigned.
-        pub core: CoreIndex,
-        /// The unique ID of the para that is assigned to the core.
-        pub para_id: ParaId,
-        /// The kind of the assignment.
-        pub kind: AssignmentKind,
-    }
-
-    pub enum CoreOccupied {
-        /// A parathread (on-demand parachain).
-        Parathread(ParathreadEntry),
-        /// A parachain.
-        Parachain,
-    }
+// Sanity check that candidate is from our assignment.
+if Some(candidate.descriptor().para_id) != rp_state.assignment {
+	gum::debug!(
+		target: LOG_TARGET,
+		our_assignment = ?rp_state.assignment,
+		collation = ?candidate.descriptor().para_id,
+		"Subsystem asked to second for para outside of our assignment",
+	);
+
+	return Ok(())
+}
+
 ```
 
+Notes:
+
+- rp_state is the state of the backing subsystem tracked per relay parent. 
+- The backing subsystem doesn't need to track assignments very far back. Without Asynchronous backing only the assignments at the heads of each active fork are needed. With Async backing we track up to AsyncBackingParams::allowed_ancestry_len
+- A single validator may end up simultaniously performing backing tasks relating to multiple cores even within the same fork of the chain. This happens if that validator's core assignment changed from one relay block to the next and allowed_ancestry_len > 0.
+
 ---
 
-# How Cores Gate Each Step of the Parachains Protocol
+## Cores and Backing On-Chain
+
+- Prior candidate must vacate core before next is backed on-chain
+- When backed on-chain the candidate immediately occupies the availability core
+- Candidates provided from backing subsystem (or prospective parachains) according to core assignment
+
+Notes:
+- Prior candidate leaves core by time out (1 block) or being made available
 
 ---
 
-## Cores and Backing
+## Cores and Backing On-Chain, Code
 
-- Backing groups are assigned to parachains by core
-- Backing groups will only back candidates from the chain assigned to their core
-- Backing groups for on-demand cores are made aware of on-demand claims ahead of time, so that they know to start the backing process early enough that availability retries aren't required.
+Function `request_backable_candidates` from the Provisioner subsystem
+
+```rust
+
+/// Requests backable candidates from Prospective Parachains subsystem
+/// based on core states.
+///
+/// Should be called when prospective parachains are enabled.
+async fn request_backable_candidates(
+	availability_cores: &[CoreState],
+	bitfields: &[SignedAvailabilityBitfield],
+	relay_parent: Hash,
+	sender: &mut impl overseer::ProvisionerSenderTrait,
+) -> Result<Vec<CandidateHash>, Error> {
+	let block_number = get_block_number_under_construction(relay_parent, sender).await?;
+
+	let mut selected_candidates = Vec::with_capacity(availability_cores.len());
+
+	for (core_idx, core) in availability_cores.iter().enumerate() {
+		let (para_id, required_path) = match core {
+			CoreState::Scheduled(scheduled_core) => {
+				// The core is free, pick the first eligible candidate from
+				// the fragment tree.
+				(scheduled_core.para_id, Vec::new())
+			},
+			CoreState::Occupied(occupied_core) => {
+				if bitfields_indicate_availability(core_idx, bitfields, &occupied_core.availability)
+				{
+					if let Some(ref scheduled_core) = occupied_core.next_up_on_available {
+						// The candidate occupying the core is available, choose its
+						// child in the fragment tree.
+						//
+						// TODO: doesn't work for on-demand parachains. We lean hard on the assumption
+						// that cores are fixed to specific parachains within a session.
+						// https://github.com/paritytech/polkadot/issues/5492
+						(scheduled_core.para_id, vec![occupied_core.candidate_hash])
+					} else {
+						continue
+					}
+				} else {
+					if occupied_core.time_out_at != block_number {
+						continue
+					}
+					if let Some(ref scheduled_core) = occupied_core.next_up_on_time_out {
+						// Candidate's availability timed out, practically same as scheduled.
+						(scheduled_core.para_id, Vec::new())
+					} else {
+						continue
+					}
+				}
+			},
+			CoreState::Free => continue,
+		};
+
+		let candidate_hash =
+			get_backable_candidate(relay_parent, para_id, required_path, sender).await?;
+
+		match candidate_hash {
+			Some(hash) => selected_candidates.push(hash),
+			None => {
+				gum::debug!(
+					target: LOG_TARGET,
+					leaf_hash = ?relay_parent,
+					core = core_idx,
+					"No backable candidate returned by prospective parachains",
+				);
+			},
+		}
+	}
+
+	Ok(selected_candidates)
+}
+
+```
+
+Notes:
+
+- Per core
+    - Discuss scheduled, free
+    - Discuss occupied
+        - `bitfields_indicate_availability`
+            - next_up_on_available
+        - availability time out
+            - next_up_on_timeout
+    - We get a backable candidate for the assigned para id of each core, if one exists. This backs the candidate on chain and fills the vacated core.
 
 ---
 
-## Cores and Backing Code
+## Cores and Availability
+
+- Core freed when bitfields indicate availability
+- 1/3 needed to reconstruct POV
+- Availability threshold 2/3 
+- But what do bits represent?
+
+---
+
+## Cores and Availability, Code
+
+Either graphic of taking the transverse of bitfields, or `bitfields_indicate_availability` code
+
+---
+
+## Cores and Approvals, Disputes, Finality
+
+- An included candidate already occupied an availability core
+- Approvals, Disputes, and Finality only provided to included candidates
+
+---
+
+## Advantages Cores Give us Now
+
+- Improved liveness through rotating backing groups
+- Flexible partitioning of resources (lease vs on-demand)
+- Intuitive unit of capacity over time
+
+---
+
+## Cores and Roadmap Items
+
+- Exotic core scheduling
+	- Multiple cores per parachain
+	- Lease
+
+---
 
+## Cores and Roadmap Items, Cont.
 
+- Strided blockspace regions
+	- EX: 2 chains each with 12 sec blocks
+- Cross timeframe cost comparisons
+- Custom bidding/purchasing logic
+	- Bid below given price
+	- Transaction pool larger than threshold
+	- Raise bid at peak usage
 
 ---
 
@@ -215,6 +413,7 @@ Validator groups rotate across availability cores in a round-robin fashion, with
 <pba-col center>
 
 1. [Implementers Guide: Scheduler Pallet](https://paritytech.github.io/polkadot/book/runtime/scheduler.html)
+1. [Forum Post: Strided Blockspace Regions](https://forum.polkadot.network/t/unifying-bulk-and-mid-term-blockspace-with-strided-regions/2228)
 
 </pba-col>
 

From 349fab12a3a182001626137067a3083873496066 Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Tue, 6 Jun 2023 12:37:30 -0700
Subject: [PATCH 05/17] Add graphics

---
 .../cores_big_picture.svg                     |  1 +
 ... => pairing_backing_groups_with_cores.svg} |  0
 .../pairing_leases_and_claims_with_cores.svg  |  1 +
 .../Deep_Dive_Availability_Cores_Slides.md    | 20 +++++++++++++++----
 4 files changed, 18 insertions(+), 4 deletions(-)
 create mode 100644 assets/img/5-Polkadot/Availability_Cores_Deep_Dive/cores_big_picture.svg
 rename assets/img/5-Polkadot/Availability_Cores_Deep_Dive/{Execution_Cores_Visuals.svg => pairing_backing_groups_with_cores.svg} (100%)
 create mode 100644 assets/img/5-Polkadot/Availability_Cores_Deep_Dive/pairing_leases_and_claims_with_cores.svg

diff --git a/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/cores_big_picture.svg b/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/cores_big_picture.svg
new file mode 100644
index 000000000..5c3ba734d
--- /dev/null
+++ b/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/cores_big_picture.svg
@@ -0,0 +1 @@
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diff --git a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index e51e7235f..219b0e1b1 100644
--- a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -147,7 +147,7 @@ Validators randomly assigned to groups at start of session.
 
 ## Assigning Backing Groups to Cores
 
-<img rounded style="width: 1500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Execution_Cores_Visuals.svg" alt="Train">
+<img rounded style="width: 1500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/pairing_backing_groups_with_cores.svg" alt="Train">
 
 Notes:
 
@@ -157,17 +157,29 @@ Validator groups rotate across availability cores in a round-robin fashion, with
 
 ## Assigning Approvers to Cores
 
+- Randomness via schnorrkel::vrf
+- Results in 30-40 assigned approvers per core
+- Different assignments each block to prevent DOS
+
 ---
 
-## Assigning Cores to Parachains
+## Assigning Leases and Claims to Cores
 
-Diagram for core assignments. Two cores paired to a single lease each. Two on-demand cores linked to the same on-demand claims queue. Show that every other claim in the queue goes to core 1. Show at least one free core. 
+<img rounded style="width: 1500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/pairing_leases_and_claims_with_cores.svg" alt="Train">
 
 ---
 
 ## Occupying Assigned Cores
 
-Diagram showing how backed candidates are supplied to occupy assigned cores. Show that a leasing chain with no backed candidates won't occupy a core. Show that an occupied core can't accept a second candidate. Show that each on-demand claim comes with a number of tries to submit a candidate that validators will back. Each relay block that passes with without a backed candidate produced to fill the availability core counts as a failed try.
+Notes:
+
+If a parachain has lease or on-demand claim to space in a relay block and that parachain's collators fail to supply a parablock candidate, what does that equate to in our freight train metaphor?
+
+---
+
+## Putting the Pieces Together
+
+<img rounded style="width: 1500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/cores_big_picture.svg" alt="Train">
 
 ---
 

From 17a7fc706e7c429afb172d5850e61a35441dcedf Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Thu, 8 Jun 2023 22:56:19 -0700
Subject: [PATCH 06/17] Pre Dry Run Commit

---
 .../advantage.png                             | Bin 0 -> 327005 bytes
 .../cores_big_picture.svg                     |   2 +-
 .../Availability_Cores_Deep_Dive/dice.jpeg    | Bin 0 -> 174777 bytes
 .../occupying_assigned_cores.svg              |   1 +
 .../Availability_Cores_Deep_Dive/road.jpeg    | Bin 0 -> 33992 bytes
 .../Deep_Dive_Availability_Cores_Slides.md    | 254 ++++++++++++------
 6 files changed, 177 insertions(+), 80 deletions(-)
 create mode 100644 assets/img/5-Polkadot/Availability_Cores_Deep_Dive/advantage.png
 create mode 100644 assets/img/5-Polkadot/Availability_Cores_Deep_Dive/dice.jpeg
 create mode 100644 assets/img/5-Polkadot/Availability_Cores_Deep_Dive/occupying_assigned_cores.svg
 create mode 100644 assets/img/5-Polkadot/Availability_Cores_Deep_Dive/road.jpeg

diff --git a/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/advantage.png b/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/advantage.png
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diff --git a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index 219b0e1b1..89b2d07d4 100644
--- a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -53,27 +53,29 @@ In a parachain block you get:
 <pba-flex center>
 
 - Proof of Validity
-    - max size: 5 * 1024 * 1024
+    - max size: 5 megabytes
 - Code upgrade 
-    - max size: 4 * 1024 * 1024
+    - max size: 4 megabytes
     - cooldown: 14400 blocks
 - HRMP messages 
-    - Max message size: 102400
+    - Max message size: 102400 bytes
     - Messages per block per channel: 10
     - Max channels: 30
 - UMP messages
-    - Max message size: 65531
+    - Max message size: 65531 bytes
     - Messages per block: 16
 
 </pba-flex>
 
 Notes:
 
-Max POV size implicitly limits the number of operations per block, since each on-chain operation and its impact on state are accounted for in the POV.
+- POV size limits operations by weight or benchmark
 
 Why not put everything in the POV?
 
-Short answer: Code upgrades and cross consensus messages have different data availability requirements than ordinary parachain operations.
+Short answer: Different data availability requirements
+
+Longer answer: Code upgrades and cross consensus messages have different data availability requirements than ordinary parachain operations.
 
 The relay chain needs to keep a copy of the current code for each parachain for PVF execution. 
 
@@ -89,10 +91,6 @@ Polkadot blockspace is consumed in two ways:
 
 <img rounded style="width: 500px" src="../../../assets/img/5-Polkadot/OpenGov-PBA2/stopwatch.png" alt="Stopwatch">
 
-Notes:
-
-In this sense units of blockspace have very short lifespans, less than the relay block time of 6 seconds. To mitigate waste it is therefore critical to provide flexible markets for blockspace which maximize the proportion that is purchased and fully used.
-
 ---
 
 ## Availability Core Defined
@@ -115,7 +113,7 @@ In this sense units of blockspace have very short lifespans, less than the relay
 
 Notes:
 
-- "Availability", because a core is considered occupied by a parachain block candidate during the period when that candidate is being made available via erasure coding.
+- "Availability", because a core is considered occupied by a parachain block candidate during the period when that candidate is being made available via erasure coding. But cores mediate access to the entire parablock validation pipeline, not just availability.
 - "Core", because many candidates can be made available in parallel, mimicking the parallel computation per core in a computer processor.
 
 ---
@@ -126,7 +124,12 @@ Notes:
 
 Notes:
 
-_analogy-freight-train_: A unit of blockspace is a reserved car in a train leaving the station at a specific time. Trains are scheduled to leave the station every six seconds. An availability core is a particular car index within all trains. If you have a lease on core 4, then you have the right to fill train car 4 on each train with whatever you want to ship.
+- Most apt metaphor: train
+- Relay block: Train leaving station every 6 seconds
+- Potential Parablock: Car space in scheduled train
+- Availability core: Car index within all trains
+
+If you have a lease on core 4, then you have the right to fill train car 4 on each train with whatever you want to ship.
 
 ---
 
@@ -141,7 +144,8 @@ _analogy-freight-train_: A unit of blockspace is a reserved car in a train leavi
 Notes:
 
 To understand how cores divide up parachains protocol work among validators, we first need to understand how those validators are grouped.
-Validators randomly assigned to groups at start of session.
+- Validators randomly assigned to groups at start of session.
+- Group count is active validator count / max group size rounded up
 
 ---
 
@@ -151,15 +155,28 @@ Validators randomly assigned to groups at start of session.
 
 Notes:
 
-Validator groups rotate across availability cores in a round-robin fashion, with rotation occurring at fixed intervals. This is to prevent a byzantine backing group from interrupting the liveness of any one parachain for too long.
+- Round robin, fixed intervals
+
+This prevents a byzantine backing group from interrupting the liveness of any one parachain for too long.
 
 ---
 
+<img rounded style="width: 300px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/dice.jpeg" alt="Train">
+
 ## Assigning Approvers to Cores
 
+<pba-flex center>
+
 - Randomness via schnorrkel::vrf
+- Delay tranches add approvers until threshold met
 - Results in 30-40 assigned approvers per core
-- Different assignments each block to prevent DOS
+- Different assignments each block prevent DOS
+
+</pba-flex>
+
+Notes:
+
+Q: Why don't we just have all active validators approve each candidate?
 
 ---
 
@@ -167,19 +184,33 @@ Validator groups rotate across availability cores in a round-robin fashion, with
 
 <img rounded style="width: 1500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/pairing_leases_and_claims_with_cores.svg" alt="Train">
 
+Notes:
+
+- Leases have indices and pair to cores with the same index
+- Cores for lease without a paired lease are left free, their blockspace wasted
+- When on-demand claims are queued, they are each assigned a designated core in ascending order bounded by the on-demand core count
+
 ---
 
-## Occupying Assigned Cores
+## Putting the Pieces Together
+
+<img rounded style="width: 1500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/cores_big_picture.svg" alt="Train">
 
 Notes:
 
-If a parachain has lease or on-demand claim to space in a relay block and that parachain's collators fail to supply a parablock candidate, what does that equate to in our freight train metaphor?
+- Depicts how leases are mapped to validator subsets
 
 ---
 
-## Putting the Pieces Together
+## Occupying Assigned Cores
 
-<img rounded style="width: 1500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/cores_big_picture.svg" alt="Train">
+<img rounded style="width: 1500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/occupying_assigned_cores.svg" alt="Train">
+
+Notes:
+
+If a parachain has a lease for space in a relay block and that parachain's collators fail to supply a parablock candidate, what does that equate to in our freight train metaphor?
+
+How about when the same happens for a parachain with an on-demand claim?
 
 ---
 
@@ -191,19 +222,40 @@ If a parachain has lease or on-demand claim to space in a relay block and that p
 #[pallet::getter(fn availability_cores)]
 pub(crate) type AvailabilityCores<T> = StorageValue<_, Vec<Option<CoreOccupied>>, ValueQuery>;
 
-#[pallet::storage]
-pub(crate) type ParathreadQueue<T> = StorageValue<_, ParathreadClaimQueue, ValueQuery>;
+
+pub enum CoreOccupied {
+    /// A parathread (on-demand parachain).
+    Parathread(ParathreadEntry),
+    /// A lease holding parachain.
+    Parachain,
+}
+
+/// Parathread = on-demand parachain
+pub struct ParathreadEntry {
+	/// The claim.
+	pub claim: ParathreadClaim,
+	/// Number of retries.
+	pub retries: u32,
+}
+
+```
+
+Notes:
+
+- Vector of possible core occupant types
+- None -> unoccupied
+- retries tracked for on-demand
+
+---
+
+## Core Assignments in The Runtime
+
+```rust
 
 #[pallet::storage]
 #[pallet::getter(fn scheduled)]
 pub(crate) type Scheduled<T> = StorageValue<_, Vec<CoreAssignment>, ValueQuery>;
 
-pub struct ParathreadClaimQueue {
-    queue: Vec<QueuedParathread>,
-    // this value is between 0 and config.parathread_cores
-    next_core_offset: u32,
-}
-
 pub struct CoreAssignment {
     /// The core that is assigned.
     pub core: CoreIndex,
@@ -213,37 +265,66 @@ pub struct CoreAssignment {
     pub kind: AssignmentKind,
 }
 
-pub enum CoreOccupied {
-    /// A parathread (on-demand parachain).
-    Parathread(ParathreadEntry),
-    /// A parachain.
-    Parachain,
+pub enum AssignmentKind {
+	/// A parachain.
+	Parachain,
+	/// A parathread (on-demand parachain).
+	Parathread(CollatorId, u32),
 }
+
 ```
 
----
+Notes:
 
-# How Cores Gate Each Step of the Parachains Protocol
+- Vec of all core assignments
+- Pairs ParaId with CoreIndex
+- AssignmentKind carries retry info for on-demand
 
 ---
 
-## Cores and Backing Groups
+## On-Demand Queue in The Runtime
+
+```rust
+
+#[pallet::storage]
+pub(crate) type ParathreadQueue<T> = StorageValue<_, ParathreadClaimQueue, ValueQuery>;
+
+pub struct ParathreadClaimQueue {
+    queue: Vec<QueuedParathread>,
+    // this value is between 0 and config.parathread_cores
+    next_core_offset: u32,
+}
+
+/// A queued parathread (on-demand parachain) entry, pre-assigned to a core.
+pub struct QueuedParathread {
+	claim: ParathreadEntry,
+	core_offset: u32,
+}
 
-- Groups assigned by core
-- Groups only back candidates with appropriate assignment
-- Groups notified early of on-demand core assignments
+```
 
 Notes:
 
-- Backing groups are assigned to parachains by core
-- Backing groups will only back candidates for the chain assigned to their assigned core as of the candidate's relay parent
-- Backing groups for on-demand cores are made aware of on-demand claims ahead of time, so that they know to start the backing process early enough that inclusion retries aren't required.
+- Vec of queued parathreads
+- `next_core_offset` determines the parathread core which will be pre-assigned the next claim to enter the queue
+
+---
+
+# How Cores Gate Each Step of the Parachains Protocol
 
 ---
 
-## Cores and Backing Groups, Code
+## How Core Assignments Mediate Backing
+
+Each collation contains a `relay_parent` field corresponding to the included relay block on which that collation is based
 
-We limit seconding of candidates based on availability core assignments in the function `handle_second_message()` of the Backing Subsystem.
+Validators query their core assignment as of `relay_parent` and refuse to second candidates not assiciated with their backing group
+
+---
+
+## How Core Assignments Mediate Backing (Cont.)
+
+`handle_second_message()` in the Backing Subsystem.
 
 ```rust
 
@@ -261,22 +342,20 @@ if Some(candidate.descriptor().para_id) != rp_state.assignment {
 
 ```
 
-Notes:
-
-- rp_state is the state of the backing subsystem tracked per relay parent. 
-- The backing subsystem doesn't need to track assignments very far back. Without Asynchronous backing only the assignments at the heads of each active fork are needed. With Async backing we track up to AsyncBackingParams::allowed_ancestry_len
-- A single validator may end up simultaniously performing backing tasks relating to multiple cores even within the same fork of the chain. This happens if that validator's core assignment changed from one relay block to the next and allowed_ancestry_len > 0.
-
 ---
 
 ## Cores and Backing On-Chain
 
-- Prior candidate must vacate core before next is backed on-chain
-- When backed on-chain the candidate immediately occupies the availability core
-- Candidates provided from backing subsystem (or prospective parachains) according to core assignment
+<pba-flex center>
+
+- Candidates provided to BABE according to core assignment
+- Backed on-chain -> immediately occupies core
+- Prior occupant must vacate first
+
+</pba-flex>
 
 Notes:
-- Prior candidate leaves core by time out (1 block) or being made available
+- Mention time-out vs made available
 
 ---
 
@@ -313,10 +392,6 @@ async fn request_backable_candidates(
 					if let Some(ref scheduled_core) = occupied_core.next_up_on_available {
 						// The candidate occupying the core is available, choose its
 						// child in the fragment tree.
-						//
-						// TODO: doesn't work for on-demand parachains. We lean hard on the assumption
-						// that cores are fixed to specific parachains within a session.
-						// https://github.com/paritytech/polkadot/issues/5492
 						(scheduled_core.para_id, vec![occupied_core.candidate_hash])
 					} else {
 						continue
@@ -360,63 +435,83 @@ async fn request_backable_candidates(
 Notes:
 
 - Per core
-    - Discuss scheduled, free
-    - Discuss occupied
+    - Discuss core states free, scheduled, occupied
+    - Discuss core freeing criteria
         - `bitfields_indicate_availability`
             - next_up_on_available
         - availability time out
             - next_up_on_timeout
-    - We get a backable candidate for the assigned para id of each core, if one exists. This backs the candidate on chain and fills the vacated core.
 
 ---
 
-## Cores and Availability
+## Cores and Erasure Coding (Availability)
+
+<pba-flex center>
 
 - Core freed when bitfields indicate availability
 - 1/3 needed to reconstruct POV
 - Availability threshold 2/3 
 - But what do bits represent?
 
----
+</pba-flex>
 
-## Cores and Availability, Code
+Notes:
 
-Either graphic of taking the transverse of bitfields, or `bitfields_indicate_availability` code
+- Available candidate considered included on the relay chain
 
 ---
 
 ## Cores and Approvals, Disputes, Finality
 
-- An included candidate already occupied an availability core
-- Approvals, Disputes, and Finality only provided to included candidates
+Each included candidate has already occupied an availability core
+
+Approvals, Disputes, and Finality are only provided to included candidates
 
 ---
 
+<img rounded style="width: 500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/advantage.png" alt="Processor cores image">
+
 ## Advantages Cores Give us Now
 
-- Improved liveness through rotating backing groups
-- Flexible partitioning of resources (lease vs on-demand)
-- Intuitive unit of capacity over time
+<pba-flex center>
 
----
+1. Improved liveness 
+1. Flexibility of market structure 
+1. Flexibility of allocation
+1. Intuitive unit of capacity over time
 
-## Cores and Roadmap Items
+</pba-flex>
 
-- Exotic core scheduling
-	- Multiple cores per parachain
-	- Lease
+Notes:
+
+1. Regularly rotating pairings between cores and backing groups
+1. Market structures: common good, lease, on-demand
+1. Cores accomodate huge changes in validation recipients from one block to the next
+1. Train metaphor 
 
 ---
 
-## Cores and Roadmap Items, Cont.
+## Cores and Roadmap Items
+
+<pba-cols>
+<pba-col center>
 
+- Exotic core scheduling
+	- Multiple cores per parachain
+	- Overlapping leases of many lengths
+	- Lease + On-demand
 - Strided blockspace regions
 	- EX: 2 chains each with 12 sec blocks
 - Cross timeframe cost comparisons
-- Custom bidding/purchasing logic
-	- Bid below given price
-	- Transaction pool larger than threshold
-	- Raise bid at peak usage
+- Secondary markets for blockspace regions
+
+</pba-col>
+<pba-col center>
+
+<img rounded style="width: 600px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/road.jpeg" alt="Processor cores image">
+
+</pba-col>
+</pba-cols>
 
 ---
 
@@ -426,6 +521,7 @@ Either graphic of taking the transverse of bitfields, or `bitfields_indicate_ava
 
 1. [Implementers Guide: Scheduler Pallet](https://paritytech.github.io/polkadot/book/runtime/scheduler.html)
 1. [Forum Post: Strided Blockspace Regions](https://forum.polkadot.network/t/unifying-bulk-and-mid-term-blockspace-with-strided-regions/2228)
+1. [Rob Habermeier's Blog: Polkadot Blockspace Over Blockchains](https://www.rob.tech/polkadot-blockspace-over-blockchains/)
 
 </pba-col>
 

From 2545fef54a573cf7195c396ce45c1910274281b3 Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Fri, 9 Jun 2023 20:08:26 -0700
Subject: [PATCH 07/17] tweak note

---
 .../Availability_Cores/Deep_Dive_Availability_Cores_Slides.md   | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index 89b2d07d4..931d4cb7d 100644
--- a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -69,7 +69,7 @@ In a parachain block you get:
 
 Notes:
 
-- POV size limits operations by weight or benchmark
+- POV size implicitly limits operations per block
 
 Why not put everything in the POV?
 

From 99d3d9f80ff34b0dde2df8cf4ef698479d77cb11 Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Fri, 28 Jul 2023 20:48:22 -0700
Subject: [PATCH 08/17] Nearly there

---
 .../exotic_core_scheduling.svg                |   1 +
 .../occupying_assigned_cores.svg              |   1 -
 .../occupying_assigned_cores_on_demand.svg    |   1 +
 .../occupying_assigned_cores_with_lease.svg   |   1 +
 .../Deep_Dive_Availability_Cores_Slides.md    | 207 +++++++++---------
 5 files changed, 108 insertions(+), 103 deletions(-)
 create mode 100644 assets/img/5-Polkadot/Availability_Cores_Deep_Dive/exotic_core_scheduling.svg
 delete mode 100644 assets/img/5-Polkadot/Availability_Cores_Deep_Dive/occupying_assigned_cores.svg
 create mode 100644 assets/img/5-Polkadot/Availability_Cores_Deep_Dive/occupying_assigned_cores_on_demand.svg
 create mode 100644 assets/img/5-Polkadot/Availability_Cores_Deep_Dive/occupying_assigned_cores_with_lease.svg

diff --git a/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/exotic_core_scheduling.svg b/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/exotic_core_scheduling.svg
new file mode 100644
index 000000000..9d8cc0abf
--- /dev/null
+++ b/assets/img/5-Polkadot/Availability_Cores_Deep_Dive/exotic_core_scheduling.svg
@@ -0,0 +1 @@
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diff --git a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index 931d4cb7d..c06852ca5 100644
--- a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -46,43 +46,6 @@ Polkadot's primary product is _blockspace_.
 
 ---
 
-## Disecting Polkadot Blockspace
-
-In a parachain block you get:
-
-<pba-flex center>
-
-- Proof of Validity
-    - max size: 5 megabytes
-- Code upgrade 
-    - max size: 4 megabytes
-    - cooldown: 14400 blocks
-- HRMP messages 
-    - Max message size: 102400 bytes
-    - Messages per block per channel: 10
-    - Max channels: 30
-- UMP messages
-    - Max message size: 65531 bytes
-    - Messages per block: 16
-
-</pba-flex>
-
-Notes:
-
-- POV size implicitly limits operations per block
-
-Why not put everything in the POV?
-
-Short answer: Different data availability requirements
-
-Longer answer: Code upgrades and cross consensus messages have different data availability requirements than ordinary parachain operations.
-
-The relay chain needs to keep a copy of the current code for each parachain for PVF execution. 
-
-HRMP and UMP messages must be made available to their recipients, so they need to be cached on the relay chain for an indeterminate period.
-
----
-
 ## Blockspace, Use It or Lose It
 
 Polkadot blockspace is consumed in two ways:
@@ -99,6 +62,7 @@ Polkadot blockspace is consumed in two ways:
 <pba-col center>
 
   - Availability cores are the abstraction we use to allocate Polkadot's blockspace.
+  - Allocated via leases and on-demand claims
   - Cores divide blockspace supply into discrete units, 1 parachain block per relay chain block per core
   - Why "availability"?
   - Why "core"?
@@ -113,11 +77,43 @@ Polkadot blockspace is consumed in two ways:
 
 Notes:
 
-- "Availability", because a core is considered occupied by a parachain block candidate during the period when that candidate is being made available via erasure coding. But cores mediate access to the entire parablock validation pipeline, not just availability.
+- "Availability", because a core is considered occupied by a parachain block candidate while that candidate is being made available. But cores mediate access to the entire parablock validation pipeline, not just availability.
 - "Core", because many candidates can be made available in parallel, mimicking the parallel computation per core in a computer processor.
 
 ---
 
+## Availability
+
+Though cores gate the entire parachain block pipeline, the availability process alone determines when these cores are considered occupied vs free.
+
+To recap, the goals of availability are:
+1. To ensure that approvers will always be able to recover the PoVs to validate their assigned blocks
+2. To ensure that parachain nodes can recover blocks in the case that a parablock author maliciously refuses to share them
+
+---
+
+## The Availability Process
+
+Core States: Free, Scheduled, Occupied
+
+<pba-flex center>
+
+1. Block author places a candidate on-chain as backed, immediately occupying its scheduled core
+1. Candidate backers distribute erasure coded PoV chunks
+1. Validators distribute statements as to which candidates they have chunks for
+1. Availability threshold 2/3 (vs 1/3 needed to reconstruct POV)
+1. Core freed when bitfields indicate availability
+1. Approvers or parachain nodes retrieve PoV chunks as needed
+
+</pba-flex>
+
+Notes:
+- CoreState: Free -> core has not been assigned a parachain via lease or on-demand claim
+- CoreState: Scheduled -> Core has an assigned parachain and is currently unoccupied
+- CoreState: Occupied -> Core has assignment and is occupied by a parablock pending availability
+
+---
+
 ## Cores and Blockspace Over Time
 
 <img rounded style="width: 1100px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Train.jpeg" alt="Train">
@@ -137,6 +133,18 @@ If you have a lease on core 4, then you have the right to fill train car 4 on ea
 
 ---
 
+## The Big Picture
+
+<img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/cores_big_picture.svg" alt="Train">
+
+Notes:
+
+- Which steps of the parachains protocol are missing, and why?
+- Going to dive into each piece
+- Questions?
+
+---
+
 ## Backing Group Formation
 
 <img rounded style="width: 1100px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/validator-groups.png" alt="Train">
@@ -151,7 +159,7 @@ To understand how cores divide up parachains protocol work among validators, we
 
 ## Assigning Backing Groups to Cores
 
-<img rounded style="width: 1500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/pairing_backing_groups_with_cores.svg" alt="Train">
+<img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/pairing_backing_groups_with_cores.svg" alt="Train">
 
 Notes:
 
@@ -182,7 +190,7 @@ Q: Why don't we just have all active validators approve each candidate?
 
 ## Assigning Leases and Claims to Cores
 
-<img rounded style="width: 1500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/pairing_leases_and_claims_with_cores.svg" alt="Train">
+<img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/pairing_leases_and_claims_with_cores.svg" alt="Train">
 
 Notes:
 
@@ -194,28 +202,28 @@ Notes:
 
 ## Putting the Pieces Together
 
-<img rounded style="width: 1500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/cores_big_picture.svg" alt="Train">
+<img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/cores_big_picture.svg" alt="Train">
 
 Notes:
 
-- Depicts how leases are mapped to validator subsets
-
 ---
 
-## Occupying Assigned Cores
+## Occupying Assigned Cores: With Lease
 
-<img rounded style="width: 1500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/occupying_assigned_cores.svg" alt="Train">
+<img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/occupying_assigned_cores_with_lease.svg" alt="">
 
-Notes:
+---
 
-If a parachain has a lease for space in a relay block and that parachain's collators fail to supply a parablock candidate, what does that equate to in our freight train metaphor?
+## Occupying Assigned Cores: On Demand
 
-How about when the same happens for a parachain with an on-demand claim?
+<img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/occupying_assigned_cores_on_demand.svg" alt="">
 
 ---
 
 ## Core States in the Runtime
 
+In file: polkadot/runtime/parachains/src/scheduler.rs
+
 ```rust
 
 #[pallet::storage]
@@ -250,6 +258,8 @@ Notes:
 
 ## Core Assignments in The Runtime
 
+In file: polkadot/runtime/parachains/src/scheduler.rs
+
 ```rust
 
 #[pallet::storage]
@@ -284,6 +294,8 @@ Notes:
 
 ## On-Demand Queue in The Runtime
 
+In file: polkadot/runtime/parachains/src/scheduler.rs
+
 ```rust
 
 #[pallet::storage]
@@ -361,14 +373,10 @@ Notes:
 
 ## Cores and Backing On-Chain, Code
 
-Function `request_backable_candidates` from the Provisioner subsystem
+Function `request_backable_candidates` from the Provisioner subsystem, simplified for readability
 
 ```rust
-
-/// Requests backable candidates from Prospective Parachains subsystem
-/// based on core states.
-///
-/// Should be called when prospective parachains are enabled.
+/// Requests backable candidates based on core states.
 async fn request_backable_candidates(
 	availability_cores: &[CoreState],
 	bitfields: &[SignedAvailabilityBitfield],
@@ -380,19 +388,15 @@ async fn request_backable_candidates(
 	let mut selected_candidates = Vec::with_capacity(availability_cores.len());
 
 	for (core_idx, core) in availability_cores.iter().enumerate() {
-		let (para_id, required_path) = match core {
+		let (para_id) = match core {
 			CoreState::Scheduled(scheduled_core) => {
-				// The core is free, pick the first eligible candidate from
-				// the fragment tree.
-				(scheduled_core.para_id, Vec::new())
+				scheduled_core.para_id
 			},
 			CoreState::Occupied(occupied_core) => {
 				if bitfields_indicate_availability(core_idx, bitfields, &occupied_core.availability)
 				{
 					if let Some(ref scheduled_core) = occupied_core.next_up_on_available {
-						// The candidate occupying the core is available, choose its
-						// child in the fragment tree.
-						(scheduled_core.para_id, vec![occupied_core.candidate_hash])
+						scheduled_core.para_id
 					} else {
 						continue
 					}
@@ -402,7 +406,7 @@ async fn request_backable_candidates(
 					}
 					if let Some(ref scheduled_core) = occupied_core.next_up_on_time_out {
 						// Candidate's availability timed out, practically same as scheduled.
-						(scheduled_core.para_id, Vec::new())
+						scheduled_core.para_id
 					} else {
 						continue
 					}
@@ -416,14 +420,7 @@ async fn request_backable_candidates(
 
 		match candidate_hash {
 			Some(hash) => selected_candidates.push(hash),
-			None => {
-				gum::debug!(
-					target: LOG_TARGET,
-					leaf_hash = ?relay_parent,
-					core = core_idx,
-					"No backable candidate returned by prospective parachains",
-				);
-			},
+			None => (),
 		}
 	}
 
@@ -444,23 +441,6 @@ Notes:
 
 ---
 
-## Cores and Erasure Coding (Availability)
-
-<pba-flex center>
-
-- Core freed when bitfields indicate availability
-- 1/3 needed to reconstruct POV
-- Availability threshold 2/3 
-- But what do bits represent?
-
-</pba-flex>
-
-Notes:
-
-- Available candidate considered included on the relay chain
-
----
-
 ## Cores and Approvals, Disputes, Finality
 
 Each included candidate has already occupied an availability core
@@ -491,27 +471,50 @@ Notes:
 
 ---
 
-## Cores and Roadmap Items
+# Cores and Roadmap Items
 
-<pba-cols>
-<pba-col center>
+<img rounded style="width: 600px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/road.jpeg" alt="">
+
+---
+
+## Exotic core scheduling
+
+<pba-flex center>
 
-- Exotic core scheduling
-	- Multiple cores per parachain
-	- Overlapping leases of many lengths
-	- Lease + On-demand
-- Strided blockspace regions
-	- EX: 2 chains each with 12 sec blocks
-- Cross timeframe cost comparisons
+- Multiple cores per parachain
+- Overlapping leases of many lengths
+- Lease + On-demand
+
+</pba-flex>
+
+<img rounded style="width: 70%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/exotic_core_scheduling.svg" alt="">
+
+---
+
+## Divisible and Marketable Blockspace
+
+<pba-flex center>
+
+- Core sharing via use-threshold blockspace regions
 - Secondary markets for blockspace regions
 
-</pba-col>
-<pba-col center>
+</pba-flex>
 
-<img rounded style="width: 600px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/road.jpeg" alt="Processor cores image">
+---
 
-</pba-col>
-</pba-cols>
+## Blockspace vs Core Time
+
+Blockspace is a universal term for the product of blockchains, while core time is Polkadot's particular abstraction for allocating blockspace or other computation.
+
+Cores can secure computation other than blocks. For example, a smart contract could be deployed on a core directly.
+
+Allocating cores by time rather than for a fixed block size could allow for smaller or larger parachain blocks to be handled seamlessly.
+
+---
+
+## Core Time, and the Polkadot Ubiquitous Computer
+
+TODO
 
 ---
 

From e8a300faf0533f74df1e7e6ac19b528cb2d9bb33 Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Sun, 30 Jul 2023 10:45:59 -0700
Subject: [PATCH 09/17] Revision and extension

---
 .../Deep_Dive_Availability_Cores_Slides.md    | 85 +++++++++++--------
 1 file changed, 50 insertions(+), 35 deletions(-)

diff --git a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index c06852ca5..f5b873895 100644
--- a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -86,7 +86,12 @@ Notes:
 
 Though cores gate the entire parachain block pipeline, the availability process alone determines when these cores are considered occupied vs free.
 
+<pba-flex left>
+
 To recap, the goals of availability are:
+
+</pba-flex>
+
 1. To ensure that approvers will always be able to recover the PoVs to validate their assigned blocks
 2. To ensure that parachain nodes can recover blocks in the case that a parablock author maliciously refuses to share them
 
@@ -101,8 +106,8 @@ Core States: Free, Scheduled, Occupied
 1. Block author places a candidate on-chain as backed, immediately occupying its scheduled core
 1. Candidate backers distribute erasure coded PoV chunks
 1. Validators distribute statements as to which candidates they have chunks for
-1. Availability threshold 2/3 (vs 1/3 needed to reconstruct POV)
-1. Core freed when bitfields indicate availability
+1. Availability threshold is met (2/3 vs the 1/3 needed to reconstruct POV)
+1. Candidate marked as included on chain and core freed
 1. Approvers or parachain nodes retrieve PoV chunks as needed
 
 </pba-flex>
@@ -120,13 +125,15 @@ Notes:
 
 Notes:
 
-- Most apt metaphor: train
+- Metaphor: Freight train
 - Relay block: Train leaving station every 6 seconds
 - Potential Parablock: Car space in scheduled train
 - Availability core: Car index within all trains
 
 If you have a lease on core 4, then you have the right to fill train car 4 on each train with whatever you want to ship.
 
+Q: How would an on-demand claim be represented in this metaphor?
+
 ---
 
 # Mapping Leases and Claims to Validator Subsets
@@ -145,15 +152,15 @@ Notes:
 
 ---
 
-## Backing Group Formation
+## Assigning Leases and Claims to Cores
 
-<img rounded style="width: 1100px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/validator-groups.png" alt="Train">
+<img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/pairing_leases_and_claims_with_cores.svg" alt="Train">
 
 Notes:
 
-To understand how cores divide up parachains protocol work among validators, we first need to understand how those validators are grouped.
-- Validators randomly assigned to groups at start of session.
-- Group count is active validator count / max group size rounded up
+- Leases have indices and pair to cores with the same index
+- Cores not designated as on-demand and without a paired lease are left free, their blockspace wasted
+- When on-demand claims are queued, they are each assigned a designated core in ascending order bounded by the on-demand core count
 
 ---
 
@@ -169,6 +176,17 @@ This prevents a byzantine backing group from interrupting the liveness of any on
 
 ---
 
+## Backing Group Formation
+
+<img rounded style="width: 1100px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/validator-groups.png" alt="Train">
+
+Notes:
+
+- Validators randomly assigned to groups at start of session.
+- Group count is active validator count / max group size rounded up
+
+---
+
 <img rounded style="width: 300px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/dice.jpeg" alt="Train">
 
 ## Assigning Approvers to Cores
@@ -188,18 +206,6 @@ Q: Why don't we just have all active validators approve each candidate?
 
 ---
 
-## Assigning Leases and Claims to Cores
-
-<img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/pairing_leases_and_claims_with_cores.svg" alt="Train">
-
-Notes:
-
-- Leases have indices and pair to cores with the same index
-- Cores for lease without a paired lease are left free, their blockspace wasted
-- When on-demand claims are queued, they are each assigned a designated core in ascending order bounded by the on-demand core count
-
----
-
 ## Putting the Pieces Together
 
 <img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/cores_big_picture.svg" alt="Train">
@@ -212,6 +218,10 @@ Notes:
 
 <img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/occupying_assigned_cores_with_lease.svg" alt="">
 
+Notes:
+
+Q: What step of the parachains protocol takes place between "Supplied backable candidate" and "availability process?
+
 ---
 
 ## Occupying Assigned Cores: On Demand
@@ -250,9 +260,7 @@ pub struct ParathreadEntry {
 
 Notes:
 
-- Vector of possible core occupant types
-- None -> unoccupied
-- retries tracked for on-demand
+Q: When Option is None, what does that indicate?
 
 ---
 
@@ -317,6 +325,7 @@ pub struct QueuedParathread {
 
 Notes:
 
+- Why ParathreadClaimQueue in the code? (Naming change)
 - Vec of queued parathreads
 - `next_core_offset` determines the parathread core which will be pre-assigned the next claim to enter the queue
 
@@ -328,9 +337,9 @@ Notes:
 
 ## How Core Assignments Mediate Backing
 
-Each collation contains a `relay_parent` field corresponding to the included relay block on which that collation is based
+Each parablock candidate is built in the context of a particular `relay_parent`. Important pieces of that context include max PoV size, current parachain runtime code, and backing group assignments.
 
-Validators query their core assignment as of `relay_parent` and refuse to second candidates not assiciated with their backing group
+Validators query their core assignment as of `relay_parent` and refuse to second candidates not assiciated with their backing group.
 
 ---
 
@@ -360,15 +369,18 @@ if Some(candidate.descriptor().para_id) != rp_state.assignment {
 
 <pba-flex center>
 
-- Candidates provided to BABE according to core assignment
+- For each scheduled (un-occupied) core a candidate is retrieved from the off-chain backing process
+- Candidates are provided to block author according to core assignment
 - Backed on-chain -> immediately occupies core
-- Prior occupant must vacate first
 
 </pba-flex>
 
 Notes:
+- Review possible core states
 - Mention time-out vs made available
 
+Q: What does "immediately occupies core" imply?
+
 ---
 
 ## Cores and Backing On-Chain, Code
@@ -489,6 +501,10 @@ Notes:
 
 <img rounded style="width: 70%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/exotic_core_scheduling.svg" alt="">
 
+Notes:
+
+- Each color represents a parachain
+
 ---
 
 ## Divisible and Marketable Blockspace
@@ -500,9 +516,13 @@ Notes:
 
 </pba-flex>
 
+Notes:
+
+- Example: Region spanning 100 blocks. Split the region use so that each of two parties can submit up to 50 parablocks. Ownership proportion is enforced throughout the region such that each party can't submit more than 5 out of the first 10 blocks.
+
 ---
 
-## Blockspace vs Core Time
+## Framing Shift: Blockspace vs Core Time
 
 Blockspace is a universal term for the product of blockchains, while core time is Polkadot's particular abstraction for allocating blockspace or other computation.
 
@@ -512,18 +532,13 @@ Allocating cores by time rather than for a fixed block size could allow for smal
 
 ---
 
-## Core Time, and the Polkadot Ubiquitous Computer
-
-TODO
-
----
-
 ## Resources
 
 <pba-col center>
 
 1. [Implementers Guide: Scheduler Pallet](https://paritytech.github.io/polkadot/book/runtime/scheduler.html)
-1. [Forum Post: Strided Blockspace Regions](https://forum.polkadot.network/t/unifying-bulk-and-mid-term-blockspace-with-strided-regions/2228)
+1. [RFC: Agile Coretime](https://github.com/polkadot-fellows/RFCs/pull/1)
+1. [RFC: Coretime Scheduling Regions](https://github.com/polkadot-fellows/rfcs/pull/3)
 1. [Rob Habermeier's Blog: Polkadot Blockspace Over Blockchains](https://www.rob.tech/polkadot-blockspace-over-blockchains/)
 
 </pba-col>

From dc32c773a8959e28563c7291cd26524974ea35d7 Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Sun, 30 Jul 2023 10:49:41 -0700
Subject: [PATCH 10/17] Blockspace market reason

---
 .../Availability_Cores/Deep_Dive_Availability_Cores_Slides.md   | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index f5b873895..a5d69f2a7 100644
--- a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -509,6 +509,8 @@ Notes:
 
 ## Divisible and Marketable Blockspace
 
+We want Parachains to buy, sell, and split blockspace such that they are allocated exactly as much as fits their needs.<br><br>
+
 <pba-flex center>
 
 - Core sharing via use-threshold blockspace regions

From 4878dd29c64f803374d1861ed1e94fd153e7d71f Mon Sep 17 00:00:00 2001
From: Nuke <nukemandan@protonmail.com>
Date: Mon, 31 Jul 2023 19:23:54 -0600
Subject: [PATCH 11/17] Execution cores polish, fix build (#805)

* fiixes img with closing `/>`, fmt, spelling

* mv files into 7-Polkadot mod

* fix `yarn build` for img paths

* fit code on screen better
---
 .../Deep_Dive_Availability_Cores_Slides.md    | 552 ++++++++++++++++++
 .../7-Polkadot/Polkadot_Decisions_slides.md   |  32 +-
 .../7-Polkadot/assets/Processor_Cores.jpeg    | Bin 0 -> 61058 bytes
 syllabus/7-Polkadot/assets/Train.jpeg         | Bin 0 -> 881404 bytes
 syllabus/7-Polkadot/assets/advantage.png      | Bin 0 -> 327005 bytes
 .../7-Polkadot/assets/cores_big_picture.svg   |   1 +
 syllabus/7-Polkadot/assets/dice.jpeg          | Bin 0 -> 174777 bytes
 .../assets/exotic_core_scheduling.svg         |   1 +
 .../occupying_assigned_cores_on_demand.svg    |   1 +
 .../occupying_assigned_cores_with_lease.svg   |   1 +
 .../pairing_backing_groups_with_cores.svg     |   1 +
 .../pairing_leases_and_claims_with_cores.svg  |   1 +
 syllabus/7-Polkadot/assets/road.jpeg          | Bin 0 -> 33992 bytes
 13 files changed, 574 insertions(+), 16 deletions(-)
 create mode 100644 syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
 create mode 100644 syllabus/7-Polkadot/assets/Processor_Cores.jpeg
 create mode 100644 syllabus/7-Polkadot/assets/Train.jpeg
 create mode 100644 syllabus/7-Polkadot/assets/advantage.png
 create mode 100644 syllabus/7-Polkadot/assets/cores_big_picture.svg
 create mode 100644 syllabus/7-Polkadot/assets/dice.jpeg
 create mode 100644 syllabus/7-Polkadot/assets/exotic_core_scheduling.svg
 create mode 100644 syllabus/7-Polkadot/assets/occupying_assigned_cores_on_demand.svg
 create mode 100644 syllabus/7-Polkadot/assets/occupying_assigned_cores_with_lease.svg
 create mode 100644 syllabus/7-Polkadot/assets/pairing_backing_groups_with_cores.svg
 create mode 100644 syllabus/7-Polkadot/assets/pairing_leases_and_claims_with_cores.svg
 create mode 100644 syllabus/7-Polkadot/assets/road.jpeg

diff --git a/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
new file mode 100644
index 000000000..1e8b7f6f1
--- /dev/null
+++ b/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -0,0 +1,552 @@
+---
+title: Deep Dive, Availability Cores
+description: The Polkadot Abstraction for Flexible Blockspace Allocation
+duration: 1 hour
+---
+
+# Deep Dive, Availability Cores
+
+Notes:
+
+We will present 3 lectures providing a window into Polkadot core, a slice of where we're at and where we're headed.
+
+First a look at availability cores, the abstraction enabling flexible purchases of blockspace under the umbrella of Polkadot shared security.
+
+Lets get to it
+
+---
+
+## Overview
+
+<pba-flex center>
+
+- What do availability cores represent?
+- How do cores map parachain leases and claims to validator subsets?
+- How do cores gate each step of the parachains protocol?
+- What advantages do cores give us now?
+- What roadmap items do cores accommodate?
+
+</pba-flex>
+
+---
+
+## Review, Blockspace
+
+> Blockspace is the capacity of a blockchain<br/>to finalize and commit operations
+
+Polkadot's primary product is _blockspace_.
+
+---
+
+## Blockspace, Use It or Lose It
+
+Polkadot blockspace is consumed in two ways:
+
+<pba-flex center>
+
+1. When the relay chain validates,<br/>includes, and finalizes a parachain block
+1. When the capacity to validate a parachain block<br/> is left unused and expires
+
+</pba-flex>
+
+<img rounded style="width: 500px" src="../../../assets/img/7-Polkadot/OpenGov-PBA2/stopwatch.png" />
+
+---
+
+## Availability Core Defined
+
+<pba-cols>
+<pba-col center>
+
+- Availability cores are the abstraction we use to allocate Polkadot's blockspace.
+- Allocated via leases and on-demand claims
+- Cores divide blockspace supply into discrete units, 1 parachain block per relay chain block per core
+- Why "availability"?
+- Why "core"?
+
+</pba-col>
+<pba-col center>
+
+<img rounded style="width: 500px" src="../assets/Processor_Cores.jpeg" />
+
+</pba-col>
+</pba-cols>
+
+Notes:
+
+- "Availability", because a core is considered occupied by a parachain block candidate while that candidate is being made available. But cores mediate access to the entire parablock validation pipeline, not just availability.
+- "Core", because many candidates can be made available in parallel, mimicking the parallel computation per core in a computer processor.
+
+---
+
+## Availability
+
+Though cores gate the entire parachain block pipeline,<br/> the availability process alone determines when these cores are considered occupied vs free.
+
+To recap, the goals of availability are:
+
+1. To ensure that approvers will always be able to recover the PoVs to validate their assigned blocks
+1. To ensure that parachain nodes can recover blocks in the case that a parablock author maliciously refuses to share them
+
+---
+
+## The Availability Process
+
+Core States: Free, Scheduled, Occupied
+
+<pba-flex center>
+
+1. Block author places a candidate on-chain as backed, immediately occupying its scheduled core
+1. Candidate backers distribute erasure coded PoV chunks
+1. Validators distribute statements as to which candidates they have chunks for
+1. Availability threshold 2/3 (vs 1/3 needed to reconstruct POV)
+1. Core freed when bitfields indicate availability
+1. Approvers or parachain nodes retrieve PoV chunks as needed
+
+</pba-flex>
+
+Notes:
+
+- CoreState: Free -> core has not been assigned a parachain via lease or on-demand claim
+- CoreState: Scheduled -> Core has an assigned parachain and is currently unoccupied
+- CoreState: Occupied -> Core has assignment and is occupied by a parablock pending availability
+
+---
+
+## Cores and Blockspace Over Time
+
+<img rounded style="width: 1100px" src="../assets/Train.jpeg" />
+
+Notes:
+
+- Most apt metaphor: train
+- Relay block: Train leaving station every 6 seconds
+- Potential Parablock: Car space in scheduled train
+- Availability core: Car index within all trains
+
+If you have a lease on core 4, then you have the right to fill train car 4 on each train with whatever you want to ship.
+
+---
+
+# Mapping Leases and Claims to Validator Subsets
+
+---
+
+## The Big Picture
+
+<img rounded style="width: 1100px" src="../assets/cores_big_picture.svg" />
+
+Notes:
+
+- Which steps of the parachains protocol are missing, and why?
+- Going to dive into each piece
+- Questions?
+
+---
+
+## Backing Group Formation
+
+<img rounded style="width: 1100px" src="../assets/validator-groups.png" />
+
+Notes:
+
+To understand how cores divide up parachains protocol work among validators, we first need to understand how those validators are grouped.
+
+- Validators randomly assigned to groups at start of session.
+- Group count is active validator count / max group size rounded up
+
+---
+
+## Assigning Backing Groups to Cores
+
+<img rounded style="width: 1100px" src="../assets/pairing_backing_groups_with_cores.svg" />
+
+Notes:
+
+- Round robin, fixed intervals
+
+This prevents a byzantine backing group from interrupting the liveness of any one parachain for too long.
+
+---
+
+<img rounded style="width: 300px" src="../assets/dice.jpeg" />
+
+## Assigning Approvers to Cores
+
+<pba-flex center>
+
+- Randomness via schnorrkel::vrf
+- Delay tranches add approvers until threshold met
+- Results in 30-40 assigned approvers per core
+- Different assignments each block prevent DOS
+
+</pba-flex>
+
+Notes:
+
+Q: Why don't we just have all active validators approve each candidate?
+
+---
+
+## Assigning Leases and Claims to Cores
+
+<img rounded style="width: 1100px" src="../assets/pairing_leases_and_claims_with_cores.svg" />
+
+Notes:
+
+- Leases have indices and pair to cores with the same index
+- Cores for lease without a paired lease are left free, their blockspace wasted
+- When on-demand claims are queued, they are each assigned a designated core in ascending order bounded by the on-demand core count
+
+---
+
+## Putting the Pieces Together
+
+<img rounded style="width: 1100px" src="../assets/cores_big_picture.svg" />
+
+Notes:
+
+---
+
+## Occupying Assigned Cores: With Lease
+
+<img rounded style="width: 1300px" src="../assets/occupying_assigned_cores_with_lease.svg" />
+
+---
+
+## Occupying Assigned Cores: On Demand
+
+<img rounded style="width: 1100px" src="../assets/occupying_assigned_cores_on_demand.svg" />
+
+---
+
+## Core States in the Runtime
+
+In file: polkadot/runtime/parachains/src/scheduler.rs
+
+<div style="font-size: 0.82em;">
+
+```rust
+
+#[pallet::storage]
+#[pallet::getter(fn availability_cores)]
+pub(crate) type AvailabilityCores<T> = StorageValue<_, Vec<Option<CoreOccupied>>, ValueQuery>;
+
+
+pub enum CoreOccupied {
+    /// A parathread (on-demand parachain).
+    Parathread(ParathreadEntry),
+    /// A lease holding parachain.
+    Parachain,
+}
+
+/// Parathread = on-demand parachain
+pub struct ParathreadEntry {
+	/// The claim.
+	pub claim: ParathreadClaim,
+	/// Number of retries.
+	pub retries: u32,
+}
+
+```
+
+</div>
+
+Notes:
+
+- Vector of possible core occupant types
+- None -> unoccupied
+- Retries tracked for on-demand
+
+---
+
+## Core Assignments in The Runtime
+
+In file: polkadot/runtime/parachains/src/scheduler.rs
+
+<div style="font-size: 0.82em;">
+
+```rust
+
+#[pallet::storage]
+#[pallet::getter(fn scheduled)]
+pub(crate) type Scheduled<T> = StorageValue<_, Vec<CoreAssignment>, ValueQuery>;
+
+pub struct CoreAssignment {
+    /// The core that is assigned.
+    pub core: CoreIndex,
+    /// The unique ID of the para that is assigned to the core.
+    pub para_id: ParaId,
+    /// The kind of the assignment.
+    pub kind: AssignmentKind,
+}
+
+pub enum AssignmentKind {
+	/// A parachain.
+	Parachain,
+	/// A parathread (on-demand parachain).
+	Parathread(CollatorId, u32),
+}
+
+```
+
+</div>
+
+Notes:
+
+- Vec of all core assignments
+- Pairs ParaId with CoreIndex
+- AssignmentKind carries retry info for on-demand
+
+---
+
+## On-Demand Queue in The Runtime
+
+In file: polkadot/runtime/parachains/src/scheduler.rs
+
+<div style="font-size: 0.82em;">
+
+```rust
+
+#[pallet::storage]
+pub(crate) type ParathreadQueue<T> = StorageValue<_, ParathreadClaimQueue, ValueQuery>;
+
+pub struct ParathreadClaimQueue {
+    queue: Vec<QueuedParathread>,
+    // this value is between 0 and config.parathread_cores
+    next_core_offset: u32,
+}
+
+/// A queued parathread (on-demand parachain) entry, pre-assigned to a core.
+pub struct QueuedParathread {
+	claim: ParathreadEntry,
+	core_offset: u32,
+}
+
+```
+
+</div>
+
+Notes:
+
+- Vec of queued parathreads
+- `next_core_offset` determines the parathread core which will be pre-assigned the next claim to enter the queue
+
+---
+
+# How Cores Gate Each Step of the Parachains Protocol
+
+---
+
+## How Core Assignments Mediate Backing
+
+Each collation contains a `relay_parent` field corresponding to the included relay block on which that collation is based
+
+Validators query their core assignment as of `relay_parent` and refuse to second candidates not associated with their backing group
+
+---
+
+## How Core Assignments Mediate Backing (Cont.)
+
+`handle_second_message()` in the Backing Subsystem.
+
+```rust
+
+// Sanity check that candidate is from our assignment.
+if Some(candidate.descriptor().para_id) != rp_state.assignment {
+	gum::debug!(
+		target: LOG_TARGET,
+		our_assignment = ?rp_state.assignment,
+		collation = ?candidate.descriptor().para_id,
+		"Subsystem asked to second for para outside of our assignment",
+	);
+
+	return Ok(())
+}
+
+```
+
+---
+
+## Cores and Backing On-Chain
+
+<pba-flex center>
+
+- Candidates provided to BABE according to core assignment
+- Backed on-chain -> immediately occupies core
+- Prior occupant must vacate first
+
+</pba-flex>
+
+Notes:
+
+- Mention time-out vs made available
+
+---
+
+## Cores and Backing On-Chain, Code
+
+Function `request_backable_candidates` from the Provisioner subsystem, simplified for readability
+
+<div style="font-size: 0.82em;">
+
+```rust
+/// Requests backable candidates based on core states.
+async fn request_backable_candidates(
+	availability_cores: &[CoreState],
+	bitfields: &[SignedAvailabilityBitfield],
+	relay_parent: Hash,
+	sender: &mut impl overseer::ProvisionerSenderTrait,
+) -> Result<Vec<CandidateHash>, Error> {
+	let block_number = get_block_number_under_construction(relay_parent, sender).await?;
+
+	let mut selected_candidates = Vec::with_capacity(availability_cores.len());
+
+	for (core_idx, core) in availability_cores.iter().enumerate() {
+		let (para_id) = match core {
+			CoreState::Scheduled(scheduled_core) => {
+				scheduled_core.para_id
+			},
+			CoreState::Occupied(occupied_core) => {
+				if bitfields_indicate_availability(core_idx, bitfields, &occupied_core.availability)
+				{
+					if let Some(ref scheduled_core) = occupied_core.next_up_on_available {
+						scheduled_core.para_id
+					} else {
+						continue
+					}
+				} else {
+					if occupied_core.time_out_at != block_number {
+						continue
+					}
+					if let Some(ref scheduled_core) = occupied_core.next_up_on_time_out {
+						// Candidate's availability timed out, practically same as scheduled.
+						scheduled_core.para_id
+					} else {
+						continue
+					}
+				}
+			},
+			CoreState::Free => continue,
+		};
+
+		let candidate_hash =
+			get_backable_candidate(relay_parent, para_id, required_path, sender).await?;
+
+		match candidate_hash {
+			Some(hash) => selected_candidates.push(hash),
+			None => (),
+		}
+	}
+
+	Ok(selected_candidates)
+}
+
+```
+
+</div>
+
+Notes:
+
+- Per core
+  - Discuss core states free, scheduled, occupied
+  - Discuss core freeing criteria
+    - `bitfields_indicate_availability`
+      - next_up_on_available
+    - availability time out
+      - next_up_on_timeout
+
+---
+
+## Cores and Approvals, Disputes, Finality
+
+Each included candidate has already occupied an availability core
+
+Approvals, Disputes, and Finality are only provided to included candidates
+
+---
+
+## Advantages Cores Give us Now
+
+<pba-flex center>
+
+1. Improved liveness
+1. Flexibility of market structure
+1. Flexibility of allocation
+1. Intuitive unit of capacity over time
+
+</pba-flex>
+
+<img rounded style="width: 500px" src="../assets/advantage.png" alt="Processor cores image" />
+
+Notes:
+
+1. Regularly rotating pairings between cores and backing groups
+1. Market structures: common good, lease, on-demand
+1. Cores accommodate huge changes in validation recipients from one block to the next
+1. Train metaphor
+
+---
+
+# Cores and Roadmap Items
+
+<img rounded style="width: 600px" src="../assets/road.jpeg" />
+
+---
+
+## Exotic core scheduling
+
+<pba-flex center>
+
+- Multiple cores per parachain
+- Overlapping leases of many lengths
+- Lease + On-demand
+
+</pba-flex>
+
+<img rounded style="width: 700px" src="../assets/exotic_core_scheduling.svg" />
+
+---
+
+## Divisible and Marketable Blockspace
+
+<pba-flex center>
+
+- Core sharing via use-threshold blockspace regions
+- Secondary markets for blockspace regions
+
+</pba-flex>
+
+---
+
+## Blockspace vs Core Time
+
+Blockspace is a universal term for the product of blockchains, while core time is Polkadot's particular abstraction for allocating blockspace or other computation.
+
+Cores can secure computation other than blocks. For example, a smart contract could be deployed on a core directly.
+
+Allocating cores by time rather than for a fixed block size could allow for smaller or larger parachain blocks to be handled seamlessly.
+
+---
+
+## Core Time, and the Polkadot Ubiquitous Computer
+
+TODO
+
+---
+
+## Resources
+
+<pba-col center>
+
+1. [Implementers Guide: Scheduler Pallet](https://paritytech.github.io/polkadot/book/runtime/scheduler.html)
+1. [Forum Post: Strided Blockspace Regions](https://forum.polkadot.network/t/unifying-bulk-and-mid-term-blockspace-with-strided-regions/2228)
+1. [Rob Habermeier's Blog: Polkadot Blockspace Over Blockchains](https://www.rob.tech/polkadot-blockspace-over-blockchains/)
+
+</pba-col>
+
+---
+
+<!-- .slide: data-background-color="#4A2439" -->
+
+# Questions
diff --git a/syllabus/7-Polkadot/Polkadot_Decisions_slides.md b/syllabus/7-Polkadot/Polkadot_Decisions_slides.md
index 89e163e07..06da85e0b 100644
--- a/syllabus/7-Polkadot/Polkadot_Decisions_slides.md
+++ b/syllabus/7-Polkadot/Polkadot_Decisions_slides.md
@@ -68,7 +68,7 @@ Decisions that can be easily changed in the future.
 
 ---
 
-<image src="../../../assets/img/7-Polkadot/less-trust-more-truth.svg" style="width: 1000px; filter: invert();">
+<image src="../../assets/img/7-Polkadot/less-trust-more-truth.svg" style="width: 1000px; filter: invert();">
 
 Notes:
 
@@ -106,7 +106,7 @@ This philosophy is a realization that building a blockchain is trying to build a
 
 <div>
 
-<image src="../../../assets/img/7-Polkadot/trilemma.svg" style="height: 400px;">
+<image src="../../assets/img/7-Polkadot/trilemma.svg" style="height: 400px;">
 
 
 </div>
@@ -159,7 +159,7 @@ What are the type 1 decisions which make Polkadot... Polkadot?
 
 <div>
 
-<img style="width: 400px;" src="../../../assets/img/0-Shared/logo/webassembly-blue.png" />
+<img style="width: 400px;" src="../../assets/img/0-Shared/logo/webassembly-blue.png" />
 
 </div>
 
@@ -189,7 +189,7 @@ These parallel chains (shards) are called Parachains.
 
 <div>
 
-<img style="width: 500px;" src="../../../assets/img/7-Polkadot/decisions/sharding.svg" />
+<img style="width: 500px;" src="../../assets/img/7-Polkadot/decisions/sharding.svg" />
 
 </div>
 
@@ -203,7 +203,7 @@ These parallel chains (shards) are called Parachains.
 
 <div>
 
-<img style="width: 500px;" src="../../../assets/img/7-Polkadot/decisions/app-chain.svg" />
+<img style="width: 500px;" src="../../assets/img/7-Polkadot/decisions/app-chain.svg" />
 
 </div>
 
@@ -234,7 +234,7 @@ Interoperability allows parachains to work together to complete, complex end-to-
 
 <div>
 
-<image src="../../../assets/img/7-Polkadot/xcmp-2.svg" style="height: 500px;">
+<image src="../../assets/img/7-Polkadot/xcmp-2.svg" style="height: 500px;">
 
 A visual of XCMP channels between Parachains.
 
@@ -277,7 +277,7 @@ Polkadot introduces a shared security model so that chains can interact with oth
 
 Polkadot's Shared Security is powered through the creation and allocation of execution cores.
 
-<img style="width: 1000px;" src="../../../assets/img/7-Polkadot/decisions/exotic-scheduling.png" />
+<img style="width: 1000px;" src="../../assets/img/7-Polkadot/decisions/exotic-scheduling.png" />
 
 Execution cores provide blockspace-as-a-service, and are designed to work with any kind of consensus system.
 
@@ -289,7 +289,7 @@ Execution cores provide blockspace-as-a-service, and are designed to work with a
 
 <div>
 
-<image src="../../../assets/img/7-Polkadot/xcmp-finalization.svg" style="height: 500px;">
+<image src="../../assets/img/7-Polkadot/xcmp-finalization.svg" style="height: 500px;">
 
 </div>
 
@@ -317,7 +317,7 @@ This is continuing to evolve with the addition of "accords" / SPREE.
 
 ### Block Production
 
-<img style="width: 500px;" src="../../../assets/img/7-Polkadot/decisions/babe.svg" />
+<img style="width: 500px;" src="../../assets/img/7-Polkadot/decisions/babe.svg" />
 
 Current implementation is BABE, which is forkful with probabilistic finality.
 
@@ -327,7 +327,7 @@ Current implementation is BABE, which is forkful with probabilistic finality.
 
 ### Finality Gadget
 
-<img style="width: 400px;" src="../../../assets/img/7-Polkadot/decisions/grandpa.png" />
+<img style="width: 400px;" src="../../assets/img/7-Polkadot/decisions/grandpa.png" />
 
 Current implementation is GRANDPA, which is robust and scalable against network partitions.
 
@@ -369,7 +369,7 @@ This gives the Polkadot Relay Chain and all connected parachains an evolutionary
 
 <div>
 
-<img style="width: 400px;" src="../../../assets/img/7-Polkadot/decisions/runtime-upgrade.png" />
+<img style="width: 400px;" src="../../assets/img/7-Polkadot/decisions/runtime-upgrade.png" />
 
 </div>
 
@@ -392,7 +392,7 @@ Polkadot and its parachains need to change over time to stay relevant, and the n
 
 <div>
 
-<img style="width: 400px;" src="../../../assets/img/7-Polkadot/decisions/voting.svg" />
+<img style="width: 400px;" src="../../assets/img/7-Polkadot/decisions/voting.svg" />
 
 </div>
 
@@ -414,7 +414,7 @@ It is entirely controlled on-chain by the governance system of Polkadot, which m
 
 <div>
 
-<img style="width: 600px;" src="../../../assets/img/7-Polkadot/decisions/treasury.svg" />
+<img style="width: 600px;" src="../../assets/img/7-Polkadot/decisions/treasury.svg" />
 
 </div>
 
@@ -436,13 +436,13 @@ Polkadot was designed around Parachains, but the exact meaning and manifestation
 
 <div>
 
-<img style="height: 200px;" src="../../../assets/img/7-Polkadot/decisions/original-scheduling.png" />
+<img style="height: 200px;" src="../../assets/img/7-Polkadot/decisions/original-scheduling.png" />
 
 </div>
 
 <div>
 
-<img style="height: 200px;" src="../../../assets/img/7-Polkadot/decisions/exotic-scheduling.png" />
+<img style="height: 200px;" src="../../assets/img/7-Polkadot/decisions/exotic-scheduling.png" />
 
 </div>
 
@@ -469,7 +469,7 @@ Notes:
 
 <div>
 
-<image src="../../../assets/img/7-Polkadot/xcm-stack.svg" style="height: 500px;">
+<image src="../../assets/img/7-Polkadot/xcm-stack.svg" style="height: 500px;">
 
 Instructions to teleport an asset between parachains.
 
diff --git a/syllabus/7-Polkadot/assets/Processor_Cores.jpeg b/syllabus/7-Polkadot/assets/Processor_Cores.jpeg
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new file mode 100644
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diff --git a/syllabus/7-Polkadot/assets/pairing_leases_and_claims_with_cores.svg b/syllabus/7-Polkadot/assets/pairing_leases_and_claims_with_cores.svg
new file mode 100644
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HcmV?d00001


From 2d7c39f90d0e2dd4882a382142eea05aa0ec840b Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Mon, 31 Jul 2023 19:02:05 -0700
Subject: [PATCH 12/17] Fixing content reverted by Nukes correction

---
 .../2-FRAME_Basics/Pallet_Hooks_Slides.md     |  46 +-
 .../Construct_Runtime_slides.md               |  17 +-
 .../Deep_Dive_Availability_Cores_Slides.md    | 552 ------------------
 .../Deep_Dive_Availability_Cores_Slides.md    | 101 ++--
 .../7-Polkadot/Polkadot_Decisions_slides.md   |  23 +-
 syllabus/7-Polkadot/Readme.md                 |   8 +-
 6 files changed, 103 insertions(+), 644 deletions(-)
 delete mode 100644 syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md

diff --git a/syllabus/6-FRAME/2-FRAME_Basics/Pallet_Hooks_Slides.md b/syllabus/6-FRAME/2-FRAME_Basics/Pallet_Hooks_Slides.md
index be2d37ca1..d6d1d85ac 100644
--- a/syllabus/6-FRAME/2-FRAME_Basics/Pallet_Hooks_Slides.md
+++ b/syllabus/6-FRAME/2-FRAME_Basics/Pallet_Hooks_Slides.md
@@ -10,17 +10,17 @@ duration: 1 hour
 
 ## Hooks: All In One
 
-* Onchain / STF
-  * `on_runtime_upgrade`
-  * `on_initialize`
-  * `poll` (WIP)
-  * `on_finalize`
-  * `on_idle`
-* Offchain:
-  * `genesis_build`
-  * `offchain_worker`
-  * `integrity_test`
-  * `try_state`
+- Onchain / STF
+  - `on_runtime_upgrade`
+  - `on_initialize`
+  - `poll` (WIP)
+  - `on_finalize`
+  - `on_idle`
+- Offchain:
+  - `genesis_build`
+  - `offchain_worker`
+  - `integrity_test`
+  - `try_state`
 
 Notes:
 
@@ -96,7 +96,6 @@ fn on_initialize() -> Weight {
 - &shy;<!-- .element: class="fragment" --> Question: If your runtime panics `on_initialize`, how can you recover from it?
 - &shy;<!-- .element: class="fragment" --> Question: If your `on_initialize` consumes more than the maximum block weight?
 
-
 Notes:
 
 - The order comes from `construct_runtime!` macro.
@@ -119,7 +118,7 @@ fn on_finalize() -> Weight {} // ❌
 
 <!-- .element: class="fragment" -->
 
-- Nothing to do with *finality* in the consensus context.
+- Nothing to do with _finality_ in the consensus context.
 
 <!-- .element: class="fragment" -->
 
@@ -190,8 +189,9 @@ graph LR
     end
 
     subgraph Optional
- 	    OnRuntimeUpgrade
-    end
+
+OnRuntimeUpgrade
+end
 
     subgraph BeforeExtrinsics
         OnInitialize
@@ -204,8 +204,8 @@ graph LR
     subgraph Inherents
         Inherent1 --> Inherent2
     end
-</diagram>
 
+</diagram>
 
 Notes:
 
@@ -233,6 +233,7 @@ pub struct GenesisConfig<T: Config> {
   pub bar: Vec<u8>,
 }
 ```
+
 <!-- .element: class="fragment" -->
 
 ```rust
@@ -242,6 +243,7 @@ impl<T: Config> Default for GenesisConfig<T> {
   }
 }
 ```
+
 <!-- .element: class="fragment" -->
 
 ```rust
@@ -252,6 +254,7 @@ impl<T: Config> GenesisBuild<T> for GenesisConfig<T> {
   }
 }
 ```
+
 <!-- .element: class="fragment" -->
 
 ---v
@@ -317,7 +320,6 @@ founders to be careful with this!
 
 https://paritytech.github.io/substrate/master/pallet_examples/index.html
 
-
 ---v
 
 ### Hooks: `offchain_worker`
@@ -325,7 +327,6 @@ https://paritytech.github.io/substrate/master/pallet_examples/index.html
 - Execution entirely up to the client.
 - Has a totally separate thread pool than the normal execution.
 
-
 ```
 --offchain-worker <ENABLED>
     Possible values:
@@ -449,8 +450,9 @@ graph LR
     end
 
     subgraph Optional
- 	    OnRuntimeUpgrade
-    end
+
+OnRuntimeUpgrade
+end
 
     subgraph BeforeExtrinsics
         OnInitialize
@@ -463,6 +465,7 @@ graph LR
     subgraph Inherents
         Inherent1 --> Inherent2
     end
+
 </diagram>
 
 - What other hooks can you think of?
@@ -472,11 +475,10 @@ Notes:
 What other ideas you can think of?
 
 - a hook called once a pallet is first initialized.
-https://github.com/paritytech/substrate/issues/14098
+  https://github.com/paritytech/substrate/issues/14098
 - Local on Post/Pre dispatch: https://github.com/paritytech/substrate/issues/12047
 - Global on Post/Pre dispatch is in fact a signed extension. It has to live in the runtime, because you have to specify order.
 
-
 ---
 
 ## Additional Resources! 😋
diff --git a/syllabus/6-FRAME/3-FRAME_Runtime/Construct_Runtime_slides.md b/syllabus/6-FRAME/3-FRAME_Runtime/Construct_Runtime_slides.md
index 9681d16c0..70a04adc2 100644
--- a/syllabus/6-FRAME/3-FRAME_Runtime/Construct_Runtime_slides.md
+++ b/syllabus/6-FRAME/3-FRAME_Runtime/Construct_Runtime_slides.md
@@ -5,7 +5,6 @@ duration: 1 hour
 instructors: ["Kian Paimani"]
 ---
 
-
 # `construct_runtime!` and Testing 🔨
 
 ---
@@ -73,7 +72,6 @@ impl pallet_dpos::Config for Runtime { .. }
 
 > Anywhere in your pallet code that you have `<T: Config>` can now be replaced with `Runtime`.
 
-
 ```rust[1-2|3-4|5-6]
 // a normal pub function defined in
 frame_system::Pallet::<Runtime>::block_number();
@@ -294,10 +292,10 @@ A test requires a mock runtime, so we need to do a full `construct_runtime` 😱
 
 ### Testing and Mocks
 
-* `u32` account id.
-* `u128` balance.
-* `u32` block number.
-* ...
+- `u32` account id.
+- `u128` balance.
+- `u32` block number.
+- ...
 
 ---
 
@@ -322,7 +320,6 @@ parameter_types! {
 }
 ```
 
-
 ```rust
 impl pallet_template::Config for Runtime {
   type MaxVoters = MyMaxVoters;
@@ -517,7 +514,7 @@ pub fn next_block() {
 
 ### Progressing Blocks
 
-```rust
+````rust
 ```rust
 #[test]
 fn test() {
@@ -537,7 +534,8 @@ fn test() {
     // repeat..
   });
 }
-```
+````
+
 ```
 
 ---
@@ -584,3 +582,4 @@ The `construct_runtime!` itself does a few things under the hood:
 
 - Ordering in `construct_runtime` matters.
 - Pallet parts can be optional in `construct_runtime!`.
+```
diff --git a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
deleted file mode 100644
index a5d69f2a7..000000000
--- a/syllabus/6-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ /dev/null
@@ -1,552 +0,0 @@
----
-title: Deep Dive, Availability Cores
-description: The Polkadot Abstraction for Flexible Blockspace Allocation
-duration: 1 hour
----
-
-# Deep Dive, Availability Cores
-
-Notes:
-
-Hello!
-
-I'm Bradley Olson
-
-Was student at first Academy in Cambridge
-
-Currently on Parachains Core Team at Parity
-
-Will present 3 lectures providing a window into Polkadot core, a slice of where we're at and where we're headed.
-
-First a look at availability cores, the abstraction enabling flexible purchases of blockspace under the umbrella of Polkadot shared security.
-
-Lets get to it
-
----
-
-## Overview
-
-<pba-flex center>
-
-- What do availability cores represent?
-- How do cores map parachain leases and claims to validator subsets?
-- How do cores gate each step of the parachains protocol?
-- What advantages do cores give us now?
-- What roadmap items do cores accomodate?
-
-</pba-flex>
-
----
-
-## Review, Blockspace
-
-> Blockspace is the capacity of a blockchain to finalize and commit operations
-
-Polkadot's primary product is _blockspace_.
-
----
-
-## Blockspace, Use It or Lose It
-
-Polkadot blockspace is consumed in two ways:
-1. When the relay chain validates, includes, and finalizes a parachain block
-2. When the capacity to validate a parachain block is left unused and expires
-
-<img rounded style="width: 500px" src="../../../assets/img/5-Polkadot/OpenGov-PBA2/stopwatch.png" alt="Stopwatch">
-
----
-
-## Availability Core Defined
-
-<pba-cols>
-<pba-col center>
-
-  - Availability cores are the abstraction we use to allocate Polkadot's blockspace.
-  - Allocated via leases and on-demand claims
-  - Cores divide blockspace supply into discrete units, 1 parachain block per relay chain block per core
-  - Why "availability"?
-  - Why "core"?
-
-</pba-col>
-<pba-col center>
-
-<img rounded style="width: 500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Processor_Cores.jpeg" alt="Processor cores image">
-
-</pba-col>
-</pba-cols>
-
-Notes:
-
-- "Availability", because a core is considered occupied by a parachain block candidate while that candidate is being made available. But cores mediate access to the entire parablock validation pipeline, not just availability.
-- "Core", because many candidates can be made available in parallel, mimicking the parallel computation per core in a computer processor.
-
----
-
-## Availability
-
-Though cores gate the entire parachain block pipeline, the availability process alone determines when these cores are considered occupied vs free.
-
-<pba-flex left>
-
-To recap, the goals of availability are:
-
-</pba-flex>
-
-1. To ensure that approvers will always be able to recover the PoVs to validate their assigned blocks
-2. To ensure that parachain nodes can recover blocks in the case that a parablock author maliciously refuses to share them
-
----
-
-## The Availability Process
-
-Core States: Free, Scheduled, Occupied
-
-<pba-flex center>
-
-1. Block author places a candidate on-chain as backed, immediately occupying its scheduled core
-1. Candidate backers distribute erasure coded PoV chunks
-1. Validators distribute statements as to which candidates they have chunks for
-1. Availability threshold is met (2/3 vs the 1/3 needed to reconstruct POV)
-1. Candidate marked as included on chain and core freed
-1. Approvers or parachain nodes retrieve PoV chunks as needed
-
-</pba-flex>
-
-Notes:
-- CoreState: Free -> core has not been assigned a parachain via lease or on-demand claim
-- CoreState: Scheduled -> Core has an assigned parachain and is currently unoccupied
-- CoreState: Occupied -> Core has assignment and is occupied by a parablock pending availability
-
----
-
-## Cores and Blockspace Over Time
-
-<img rounded style="width: 1100px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/Train.jpeg" alt="Train">
-
-Notes:
-
-- Metaphor: Freight train
-- Relay block: Train leaving station every 6 seconds
-- Potential Parablock: Car space in scheduled train
-- Availability core: Car index within all trains
-
-If you have a lease on core 4, then you have the right to fill train car 4 on each train with whatever you want to ship.
-
-Q: How would an on-demand claim be represented in this metaphor?
-
----
-
-# Mapping Leases and Claims to Validator Subsets
-
----
-
-## The Big Picture
-
-<img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/cores_big_picture.svg" alt="Train">
-
-Notes:
-
-- Which steps of the parachains protocol are missing, and why?
-- Going to dive into each piece
-- Questions?
-
----
-
-## Assigning Leases and Claims to Cores
-
-<img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/pairing_leases_and_claims_with_cores.svg" alt="Train">
-
-Notes:
-
-- Leases have indices and pair to cores with the same index
-- Cores not designated as on-demand and without a paired lease are left free, their blockspace wasted
-- When on-demand claims are queued, they are each assigned a designated core in ascending order bounded by the on-demand core count
-
----
-
-## Assigning Backing Groups to Cores
-
-<img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/pairing_backing_groups_with_cores.svg" alt="Train">
-
-Notes:
-
-- Round robin, fixed intervals
-
-This prevents a byzantine backing group from interrupting the liveness of any one parachain for too long.
-
----
-
-## Backing Group Formation
-
-<img rounded style="width: 1100px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/validator-groups.png" alt="Train">
-
-Notes:
-
-- Validators randomly assigned to groups at start of session.
-- Group count is active validator count / max group size rounded up
-
----
-
-<img rounded style="width: 300px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/dice.jpeg" alt="Train">
-
-## Assigning Approvers to Cores
-
-<pba-flex center>
-
-- Randomness via schnorrkel::vrf
-- Delay tranches add approvers until threshold met
-- Results in 30-40 assigned approvers per core
-- Different assignments each block prevent DOS
-
-</pba-flex>
-
-Notes:
-
-Q: Why don't we just have all active validators approve each candidate?
-
----
-
-## Putting the Pieces Together
-
-<img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/cores_big_picture.svg" alt="Train">
-
-Notes:
-
----
-
-## Occupying Assigned Cores: With Lease
-
-<img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/occupying_assigned_cores_with_lease.svg" alt="">
-
-Notes:
-
-Q: What step of the parachains protocol takes place between "Supplied backable candidate" and "availability process?
-
----
-
-## Occupying Assigned Cores: On Demand
-
-<img rounded style="width: 80%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/occupying_assigned_cores_on_demand.svg" alt="">
-
----
-
-## Core States in the Runtime
-
-In file: polkadot/runtime/parachains/src/scheduler.rs
-
-```rust
-
-#[pallet::storage]
-#[pallet::getter(fn availability_cores)]
-pub(crate) type AvailabilityCores<T> = StorageValue<_, Vec<Option<CoreOccupied>>, ValueQuery>;
-
-
-pub enum CoreOccupied {
-    /// A parathread (on-demand parachain).
-    Parathread(ParathreadEntry),
-    /// A lease holding parachain.
-    Parachain,
-}
-
-/// Parathread = on-demand parachain
-pub struct ParathreadEntry {
-	/// The claim.
-	pub claim: ParathreadClaim,
-	/// Number of retries.
-	pub retries: u32,
-}
-
-```
-
-Notes:
-
-Q: When Option is None, what does that indicate?
-
----
-
-## Core Assignments in The Runtime
-
-In file: polkadot/runtime/parachains/src/scheduler.rs
-
-```rust
-
-#[pallet::storage]
-#[pallet::getter(fn scheduled)]
-pub(crate) type Scheduled<T> = StorageValue<_, Vec<CoreAssignment>, ValueQuery>;
-
-pub struct CoreAssignment {
-    /// The core that is assigned.
-    pub core: CoreIndex,
-    /// The unique ID of the para that is assigned to the core.
-    pub para_id: ParaId,
-    /// The kind of the assignment.
-    pub kind: AssignmentKind,
-}
-
-pub enum AssignmentKind {
-	/// A parachain.
-	Parachain,
-	/// A parathread (on-demand parachain).
-	Parathread(CollatorId, u32),
-}
-
-```
-
-Notes:
-
-- Vec of all core assignments
-- Pairs ParaId with CoreIndex
-- AssignmentKind carries retry info for on-demand
-
----
-
-## On-Demand Queue in The Runtime
-
-In file: polkadot/runtime/parachains/src/scheduler.rs
-
-```rust
-
-#[pallet::storage]
-pub(crate) type ParathreadQueue<T> = StorageValue<_, ParathreadClaimQueue, ValueQuery>;
-
-pub struct ParathreadClaimQueue {
-    queue: Vec<QueuedParathread>,
-    // this value is between 0 and config.parathread_cores
-    next_core_offset: u32,
-}
-
-/// A queued parathread (on-demand parachain) entry, pre-assigned to a core.
-pub struct QueuedParathread {
-	claim: ParathreadEntry,
-	core_offset: u32,
-}
-
-```
-
-Notes:
-
-- Why ParathreadClaimQueue in the code? (Naming change)
-- Vec of queued parathreads
-- `next_core_offset` determines the parathread core which will be pre-assigned the next claim to enter the queue
-
----
-
-# How Cores Gate Each Step of the Parachains Protocol
-
----
-
-## How Core Assignments Mediate Backing
-
-Each parablock candidate is built in the context of a particular `relay_parent`. Important pieces of that context include max PoV size, current parachain runtime code, and backing group assignments.
-
-Validators query their core assignment as of `relay_parent` and refuse to second candidates not assiciated with their backing group.
-
----
-
-## How Core Assignments Mediate Backing (Cont.)
-
-`handle_second_message()` in the Backing Subsystem.
-
-```rust
-
-// Sanity check that candidate is from our assignment.
-if Some(candidate.descriptor().para_id) != rp_state.assignment {
-	gum::debug!(
-		target: LOG_TARGET,
-		our_assignment = ?rp_state.assignment,
-		collation = ?candidate.descriptor().para_id,
-		"Subsystem asked to second for para outside of our assignment",
-	);
-
-	return Ok(())
-}
-
-```
-
----
-
-## Cores and Backing On-Chain
-
-<pba-flex center>
-
-- For each scheduled (un-occupied) core a candidate is retrieved from the off-chain backing process
-- Candidates are provided to block author according to core assignment
-- Backed on-chain -> immediately occupies core
-
-</pba-flex>
-
-Notes:
-- Review possible core states
-- Mention time-out vs made available
-
-Q: What does "immediately occupies core" imply?
-
----
-
-## Cores and Backing On-Chain, Code
-
-Function `request_backable_candidates` from the Provisioner subsystem, simplified for readability
-
-```rust
-/// Requests backable candidates based on core states.
-async fn request_backable_candidates(
-	availability_cores: &[CoreState],
-	bitfields: &[SignedAvailabilityBitfield],
-	relay_parent: Hash,
-	sender: &mut impl overseer::ProvisionerSenderTrait,
-) -> Result<Vec<CandidateHash>, Error> {
-	let block_number = get_block_number_under_construction(relay_parent, sender).await?;
-
-	let mut selected_candidates = Vec::with_capacity(availability_cores.len());
-
-	for (core_idx, core) in availability_cores.iter().enumerate() {
-		let (para_id) = match core {
-			CoreState::Scheduled(scheduled_core) => {
-				scheduled_core.para_id
-			},
-			CoreState::Occupied(occupied_core) => {
-				if bitfields_indicate_availability(core_idx, bitfields, &occupied_core.availability)
-				{
-					if let Some(ref scheduled_core) = occupied_core.next_up_on_available {
-						scheduled_core.para_id
-					} else {
-						continue
-					}
-				} else {
-					if occupied_core.time_out_at != block_number {
-						continue
-					}
-					if let Some(ref scheduled_core) = occupied_core.next_up_on_time_out {
-						// Candidate's availability timed out, practically same as scheduled.
-						scheduled_core.para_id
-					} else {
-						continue
-					}
-				}
-			},
-			CoreState::Free => continue,
-		};
-
-		let candidate_hash =
-			get_backable_candidate(relay_parent, para_id, required_path, sender).await?;
-
-		match candidate_hash {
-			Some(hash) => selected_candidates.push(hash),
-			None => (),
-		}
-	}
-
-	Ok(selected_candidates)
-}
-
-```
-
-Notes:
-
-- Per core
-    - Discuss core states free, scheduled, occupied
-    - Discuss core freeing criteria
-        - `bitfields_indicate_availability`
-            - next_up_on_available
-        - availability time out
-            - next_up_on_timeout
-
----
-
-## Cores and Approvals, Disputes, Finality
-
-Each included candidate has already occupied an availability core
-
-Approvals, Disputes, and Finality are only provided to included candidates
-
----
-
-<img rounded style="width: 500px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/advantage.png" alt="Processor cores image">
-
-## Advantages Cores Give us Now
-
-<pba-flex center>
-
-1. Improved liveness 
-1. Flexibility of market structure 
-1. Flexibility of allocation
-1. Intuitive unit of capacity over time
-
-</pba-flex>
-
-Notes:
-
-1. Regularly rotating pairings between cores and backing groups
-1. Market structures: common good, lease, on-demand
-1. Cores accomodate huge changes in validation recipients from one block to the next
-1. Train metaphor 
-
----
-
-# Cores and Roadmap Items
-
-<img rounded style="width: 600px" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/road.jpeg" alt="">
-
----
-
-## Exotic core scheduling
-
-<pba-flex center>
-
-- Multiple cores per parachain
-- Overlapping leases of many lengths
-- Lease + On-demand
-
-</pba-flex>
-
-<img rounded style="width: 70%" src="../../../assets/img/5-Polkadot/Availability_Cores_Deep_Dive/exotic_core_scheduling.svg" alt="">
-
-Notes:
-
-- Each color represents a parachain
-
----
-
-## Divisible and Marketable Blockspace
-
-We want Parachains to buy, sell, and split blockspace such that they are allocated exactly as much as fits their needs.<br><br>
-
-<pba-flex center>
-
-- Core sharing via use-threshold blockspace regions
-- Secondary markets for blockspace regions
-
-</pba-flex>
-
-Notes:
-
-- Example: Region spanning 100 blocks. Split the region use so that each of two parties can submit up to 50 parablocks. Ownership proportion is enforced throughout the region such that each party can't submit more than 5 out of the first 10 blocks.
-
----
-
-## Framing Shift: Blockspace vs Core Time
-
-Blockspace is a universal term for the product of blockchains, while core time is Polkadot's particular abstraction for allocating blockspace or other computation.
-
-Cores can secure computation other than blocks. For example, a smart contract could be deployed on a core directly.
-
-Allocating cores by time rather than for a fixed block size could allow for smaller or larger parachain blocks to be handled seamlessly.
-
----
-
-## Resources
-
-<pba-col center>
-
-1. [Implementers Guide: Scheduler Pallet](https://paritytech.github.io/polkadot/book/runtime/scheduler.html)
-1. [RFC: Agile Coretime](https://github.com/polkadot-fellows/RFCs/pull/1)
-1. [RFC: Coretime Scheduling Regions](https://github.com/polkadot-fellows/rfcs/pull/3)
-1. [Rob Habermeier's Blog: Polkadot Blockspace Over Blockchains](https://www.rob.tech/polkadot-blockspace-over-blockchains/)
-
-</pba-col>
-
----
-
-<!-- .slide: data-background-color="#4A2439" -->
-
-# Questions
\ No newline at end of file
diff --git a/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index 1e8b7f6f1..58a50f7f9 100644
--- a/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -8,7 +8,15 @@ duration: 1 hour
 
 Notes:
 
-We will present 3 lectures providing a window into Polkadot core, a slice of where we're at and where we're headed.
+Hello!
+
+I'm Bradley Olson
+
+Was student at first Academy in Cambridge
+
+Currently on Parachains Core Team at Parity
+
+Will present 3 lectures providing a window into Polkadot core, a slice of where we're at and where we're headed.
 
 First a look at availability cores, the abstraction enabling flexible purchases of blockspace under the umbrella of Polkadot shared security.
 
@@ -86,7 +94,7 @@ Though cores gate the entire parachain block pipeline,<br/> the availability pro
 To recap, the goals of availability are:
 
 1. To ensure that approvers will always be able to recover the PoVs to validate their assigned blocks
-1. To ensure that parachain nodes can recover blocks in the case that a parablock author maliciously refuses to share them
+2. To ensure that parachain nodes can recover blocks in the case that a parablock author maliciously refuses to share them
 
 ---
 
@@ -99,14 +107,13 @@ Core States: Free, Scheduled, Occupied
 1. Block author places a candidate on-chain as backed, immediately occupying its scheduled core
 1. Candidate backers distribute erasure coded PoV chunks
 1. Validators distribute statements as to which candidates they have chunks for
-1. Availability threshold 2/3 (vs 1/3 needed to reconstruct POV)
-1. Core freed when bitfields indicate availability
+1. Availability threshold is met (2/3 vs the 1/3 needed to reconstruct POV)
+1. Candidate marked as included on chain and core freed
 1. Approvers or parachain nodes retrieve PoV chunks as needed
 
 </pba-flex>
 
 Notes:
-
 - CoreState: Free -> core has not been assigned a parachain via lease or on-demand claim
 - CoreState: Scheduled -> Core has an assigned parachain and is currently unoccupied
 - CoreState: Occupied -> Core has assignment and is occupied by a parablock pending availability
@@ -119,13 +126,15 @@ Notes:
 
 Notes:
 
-- Most apt metaphor: train
+- Metaphor: Freight train
 - Relay block: Train leaving station every 6 seconds
 - Potential Parablock: Car space in scheduled train
 - Availability core: Car index within all trains
 
 If you have a lease on core 4, then you have the right to fill train car 4 on each train with whatever you want to ship.
 
+Q: How would an on-demand claim be represented in this metaphor?
+
 ---
 
 # Mapping Leases and Claims to Validator Subsets
@@ -144,16 +153,15 @@ Notes:
 
 ---
 
-## Backing Group Formation
+## Assigning Leases and Claims to Cores
 
-<img rounded style="width: 1100px" src="../assets/validator-groups.png" />
+<img rounded style="width: 1100px" src="../assets/pairing_leases_and_claims_with_cores.svg" />
 
 Notes:
 
-To understand how cores divide up parachains protocol work among validators, we first need to understand how those validators are grouped.
-
-- Validators randomly assigned to groups at start of session.
-- Group count is active validator count / max group size rounded up
+- Leases have indices and pair to cores with the same index
+- Cores not designated as on-demand and without a paired lease are left free, their blockspace wasted
+- When on-demand claims are queued, they are each assigned a designated core in ascending order bounded by the on-demand core count
 
 ---
 
@@ -169,6 +177,17 @@ This prevents a byzantine backing group from interrupting the liveness of any on
 
 ---
 
+## Backing Group Formation
+
+<img rounded style="width: 1100px" src="../assets/validator-groups.png" />
+
+Notes:
+
+- Validators randomly assigned to groups at start of session.
+- Group count is active validator count / max group size rounded up
+
+---
+
 <img rounded style="width: 300px" src="../assets/dice.jpeg" />
 
 ## Assigning Approvers to Cores
@@ -188,18 +207,6 @@ Q: Why don't we just have all active validators approve each candidate?
 
 ---
 
-## Assigning Leases and Claims to Cores
-
-<img rounded style="width: 1100px" src="../assets/pairing_leases_and_claims_with_cores.svg" />
-
-Notes:
-
-- Leases have indices and pair to cores with the same index
-- Cores for lease without a paired lease are left free, their blockspace wasted
-- When on-demand claims are queued, they are each assigned a designated core in ascending order bounded by the on-demand core count
-
----
-
 ## Putting the Pieces Together
 
 <img rounded style="width: 1100px" src="../assets/cores_big_picture.svg" />
@@ -212,6 +219,10 @@ Notes:
 
 <img rounded style="width: 1300px" src="../assets/occupying_assigned_cores_with_lease.svg" />
 
+Notes:
+
+Q: What step of the parachains protocol takes place between "Supplied backable candidate" and "availability process?
+
 ---
 
 ## Occupying Assigned Cores: On Demand
@@ -254,9 +265,7 @@ pub struct ParathreadEntry {
 
 Notes:
 
-- Vector of possible core occupant types
-- None -> unoccupied
-- Retries tracked for on-demand
+Q: When Option is None, what does that indicate?
 
 ---
 
@@ -329,6 +338,7 @@ pub struct QueuedParathread {
 
 Notes:
 
+- Why ParathreadClaimQueue in the code? (Naming change)
 - Vec of queued parathreads
 - `next_core_offset` determines the parathread core which will be pre-assigned the next claim to enter the queue
 
@@ -340,9 +350,9 @@ Notes:
 
 ## How Core Assignments Mediate Backing
 
-Each collation contains a `relay_parent` field corresponding to the included relay block on which that collation is based
+Each parablock candidate is built in the context of a particular `relay_parent`. Important pieces of that context include max PoV size, current parachain runtime code, and backing group assignments.
 
-Validators query their core assignment as of `relay_parent` and refuse to second candidates not associated with their backing group
+Validators query their core assignment as of `relay_parent` and refuse to second candidates not assiciated with their backing group.
 
 ---
 
@@ -372,16 +382,18 @@ if Some(candidate.descriptor().para_id) != rp_state.assignment {
 
 <pba-flex center>
 
-- Candidates provided to BABE according to core assignment
+- For each scheduled (un-occupied) core a candidate is retrieved from the off-chain backing process
+- Candidates are provided to block author according to core assignment
 - Backed on-chain -> immediately occupies core
-- Prior occupant must vacate first
 
 </pba-flex>
 
 Notes:
-
+- Review possible core states
 - Mention time-out vs made available
 
+Q: What does "immediately occupies core" imply?
+
 ---
 
 ## Cores and Backing On-Chain, Code
@@ -477,7 +489,7 @@ Approvals, Disputes, and Finality are only provided to included candidates
 
 </pba-flex>
 
-<img rounded style="width: 500px" src="../assets/advantage.png" alt="Processor cores image" />
+<img rounded style="width: 500px" src="../assets/advantage.png" />
 
 Notes:
 
@@ -504,12 +516,18 @@ Notes:
 
 </pba-flex>
 
-<img rounded style="width: 700px" src="../assets/exotic_core_scheduling.svg" />
+<img rounded style="width: 1500" src="../assets/exotic_core_scheduling.svg" />
+
+Notes:
+
+- Each color represents a parachain
 
 ---
 
 ## Divisible and Marketable Blockspace
 
+We want Parachains to buy, sell, and split blockspace such that they are allocated exactly as much as fits their needs.<br><br>
+
 <pba-flex center>
 
 - Core sharing via use-threshold blockspace regions
@@ -517,9 +535,13 @@ Notes:
 
 </pba-flex>
 
+Notes:
+
+- Example: Region spanning 100 blocks. Split the region use so that each of two parties can submit up to 50 parablocks. Ownership proportion is enforced throughout the region such that each party can't submit more than 5 out of the first 10 blocks.
+
 ---
 
-## Blockspace vs Core Time
+## Framing Shift: Blockspace vs Core Time
 
 Blockspace is a universal term for the product of blockchains, while core time is Polkadot's particular abstraction for allocating blockspace or other computation.
 
@@ -529,18 +551,13 @@ Allocating cores by time rather than for a fixed block size could allow for smal
 
 ---
 
-## Core Time, and the Polkadot Ubiquitous Computer
-
-TODO
-
----
-
 ## Resources
 
 <pba-col center>
 
 1. [Implementers Guide: Scheduler Pallet](https://paritytech.github.io/polkadot/book/runtime/scheduler.html)
-1. [Forum Post: Strided Blockspace Regions](https://forum.polkadot.network/t/unifying-bulk-and-mid-term-blockspace-with-strided-regions/2228)
+1. [RFC: Agile Coretime](https://github.com/polkadot-fellows/RFCs/pull/1)
+1. [RFC: Coretime Scheduling Regions](https://github.com/polkadot-fellows/rfcs/pull/3)
 1. [Rob Habermeier's Blog: Polkadot Blockspace Over Blockchains](https://www.rob.tech/polkadot-blockspace-over-blockchains/)
 
 </pba-col>
diff --git a/syllabus/7-Polkadot/Polkadot_Decisions_slides.md b/syllabus/7-Polkadot/Polkadot_Decisions_slides.md
index 06da85e0b..452067c29 100644
--- a/syllabus/7-Polkadot/Polkadot_Decisions_slides.md
+++ b/syllabus/7-Polkadot/Polkadot_Decisions_slides.md
@@ -48,7 +48,6 @@ Decisions that cannot easily be changed in the future.
 - Must be a part of the original protocol design.
 - Changes might as well be considered a new protocol.
 
-
 </pba-col>
 <pba-col>
 
@@ -108,7 +107,6 @@ This philosophy is a realization that building a blockchain is trying to build a
 
 <image src="../../assets/img/7-Polkadot/trilemma.svg" style="height: 400px;">
 
-
 </div>
 
 <div>
@@ -123,7 +121,6 @@ This philosophy is a realization that building a blockchain is trying to build a
 
 </div>
 
-
 ---
 
 ## In one sentence...
@@ -144,8 +141,7 @@ Polkadot tries to accomplish that mission by solving three problems:
 2. Shared Security
 3. Interoperability
 
-</pba-flex>
----
+## </pba-flex>
 
 ## The Decisions
 
@@ -217,7 +213,6 @@ Specialized solutions for problems are more performant than generalized solution
 
 </div>
 
-
 ---
 
 ## Interoperability
@@ -246,7 +241,6 @@ A visual of XCMP channels between Parachains.
 
 ## Shared Security
 
-
 <div class="grid grid-cols-2">
 
 <div>
@@ -269,7 +263,7 @@ Notes:
 
 Security in proof-of-stake networks depends on economics, so there can only exist a limited amount of security in the world because economic value is, by definition, limited. As the number of blockchains increases due to scaling issues on single chains, their economic value — and therefore their security — gets spread out over multiple chains, leaving each one weaker than before.
 
-Polkadot introduces a shared security model so that chains can interact with others while knowing full well that their interlocutors have the same security guarantees as their own chain. Bridge-based solutions — where each chain handles its own security — force the receiver to trust the sender.  Polkadot’s security model provides the necessary guarantees to make cross-chain messages meaningful without trusting the security of the sender.
+Polkadot introduces a shared security model so that chains can interact with others while knowing full well that their interlocutors have the same security guarantees as their own chain. Bridge-based solutions — where each chain handles its own security — force the receiver to trust the sender. Polkadot’s security model provides the necessary guarantees to make cross-chain messages meaningful without trusting the security of the sender.
 
 ---
 
@@ -344,7 +338,7 @@ Current implementation is GRANDPA, which is robust and scalable against network
 Polkadot has a strong belief that light clients are a necessary component for a Web3 future. It has been uncompromising in enabling first class light client support as a primary part of its development process:
 
 - In-Browser Wasm Client (Substrate Connect)
-	- Wasm state transition function too!
+  - Wasm state transition function too!
 - Consensus data integrated into block headers
 - Merkle Tries and other LC compatible data structures
 - Maximizing statically known metadata to offset reliance on full nodes.
@@ -473,7 +467,6 @@ Notes:
 
 Instructions to teleport an asset between parachains.
 
-
 </div>
 
 <div>
@@ -506,8 +499,8 @@ The staking system is a critical focus of the network, and we have one of the mo
 <div class="col-span-2">
 
 - NPoS over DPoS to better allocate stake.
-	- We see ~25% more stake behind the elected set on NPoS compared with DPoS.
-	- At the cost of complexity and scaling.
+  - We see ~25% more stake behind the elected set on NPoS compared with DPoS.
+  - At the cost of complexity and scaling.
 - Economic incentives to distribute funds evenly across validators.
 - Super-linear slashing system to discourage validator centralization.
 - Actual value being generated by staking, justifying rewards.
@@ -568,11 +561,11 @@ What questions should you ask when learning about the decisions of a Protocol?
 
 - What is (the decision)?
 - What do we need to consider when making (the decision)?
-	- Is it a Type 1 or Type 2 decision?
+  - Is it a Type 1 or Type 2 decision?
 - What decisions has (chain) decided to make and why?
-	- What tradeoffs have they chosen?
+  - What tradeoffs have they chosen?
 - What decisions have others decided to make?
-	- How might those decisions be better or worse?
+  - How might those decisions be better or worse?
 - Where can the blockchain community still improve on (the decision)?
 
 ---
diff --git a/syllabus/7-Polkadot/Readme.md b/syllabus/7-Polkadot/Readme.md
index 8add4dd92..e9adc4aac 100644
--- a/syllabus/7-Polkadot/Readme.md
+++ b/syllabus/7-Polkadot/Readme.md
@@ -26,8 +26,8 @@ Draw content from:
 
 **Morning**
 
-9:00  Discussion - Parachains Protocol AMA (.5 hr) @JoshOrndorff<br>
-9:30  Lecture - Blockspace (.5 hr) @rphmeier<br>
+9:00 Discussion - Parachains Protocol AMA (.5 hr) @JoshOrndorff<br>
+9:30 Lecture - Blockspace (.5 hr) @rphmeier<br>
 10:00 Lecture - Deep dive: Execution cores (1 hr) @BradleyOlson64<br>
 11:00 Coffee Break (15 m)<br>
 11:15 Lecture - Deep dive: Cumulus (1.25 hr) @BradleyOlson64<br>
@@ -42,8 +42,8 @@ Draw content from:
 
 **Morning**
 
-9:00  Lecture - Cross-Chain Message Passing (45 m) @rphmeier<br>
-9:45  Lecture + Exercise - Zombienet (1.5 hr) @pepoviola<br>
+9:00 Lecture - Cross-Chain Message Passing (45 m) @rphmeier<br>
+9:45 Lecture + Exercise - Zombienet (1.5 hr) @pepoviola<br>
 11:15 Coffee Break (15 m)<br>
 11:30 Lecture - Shallow Dive: Asynchronous Backing (30 m) @BradleyOlson64<br>
 12:00 Lecture - Light Clients (1 hr) @wirednkod<br>

From 9e9f949c4a2dca6c1599115ad373b83f2a043b67 Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Mon, 31 Jul 2023 19:02:58 -0700
Subject: [PATCH 13/17] fmt

---
 .../Availability_Cores/Deep_Dive_Availability_Cores_Slides.md   | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index 58a50f7f9..9ea4e1dd0 100644
--- a/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -114,6 +114,7 @@ Core States: Free, Scheduled, Occupied
 </pba-flex>
 
 Notes:
+
 - CoreState: Free -> core has not been assigned a parachain via lease or on-demand claim
 - CoreState: Scheduled -> Core has an assigned parachain and is currently unoccupied
 - CoreState: Occupied -> Core has assignment and is occupied by a parablock pending availability
@@ -389,6 +390,7 @@ if Some(candidate.descriptor().para_id) != rp_state.assignment {
 </pba-flex>
 
 Notes:
+
 - Review possible core states
 - Mention time-out vs made available
 

From cc4556bc3e6271317bab8d95a73ba99eabf3af65 Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Mon, 31 Jul 2023 19:08:15 -0700
Subject: [PATCH 14/17] Less text on slide

---
 .../Deep_Dive_Availability_Cores_Slides.md                  | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index 9ea4e1dd0..d4891748c 100644
--- a/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -351,10 +351,14 @@ Notes:
 
 ## How Core Assignments Mediate Backing
 
-Each parablock candidate is built in the context of a particular `relay_parent`. Important pieces of that context include max PoV size, current parachain runtime code, and backing group assignments.
+Each parablock candidate is built in the context of a particular `relay_parent`. 
 
 Validators query their core assignment as of `relay_parent` and refuse to second candidates not assiciated with their backing group.
 
+Notes:
+
+- Relay parent context: max PoV size, current parachain runtime code, and backing group assignments.
+
 ---
 
 ## How Core Assignments Mediate Backing (Cont.)

From 541bc0fc8def3675484a4d9df7c52457dfe39c01 Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Wed, 2 Aug 2023 20:00:01 -0700
Subject: [PATCH 15/17] Core time added fragments to slides

---
 .../Deep_Dive_Availability_Cores_Slides.md    | 165 ++++++++----------
 1 file changed, 75 insertions(+), 90 deletions(-)

diff --git a/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index d4891748c..9d06228f3 100644
--- a/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -30,9 +30,13 @@ Lets get to it
 
 - What do availability cores represent?
 - How do cores map parachain leases and claims to validator subsets?
+<!-- .element: class="fragment" data-fragment-index="1" -->
 - How do cores gate each step of the parachains protocol?
+<!-- .element: class="fragment" data-fragment-index="2" -->
 - What advantages do cores give us now?
+<!-- .element: class="fragment" data-fragment-index="3" -->
 - What roadmap items do cores accommodate?
+<!-- .element: class="fragment" data-fragment-index="4" -->
 
 </pba-flex>
 
@@ -52,12 +56,14 @@ Polkadot blockspace is consumed in two ways:
 
 <pba-flex center>
 
-1. When the relay chain validates,<br/>includes, and finalizes a parachain block
+1. When the relay chain validates, includes, <br/> and finalizes a parachain block
 1. When the capacity to validate a parachain block<br/> is left unused and expires
+<!-- .element: class="fragment" data-fragment-index="1" -->
 
 </pba-flex>
 
 <img rounded style="width: 500px" src="../../../assets/img/7-Polkadot/OpenGov-PBA2/stopwatch.png" />
+<!-- .element: class="fragment" data-fragment-index="1" -->
 
 ---
 
@@ -68,9 +74,13 @@ Polkadot blockspace is consumed in two ways:
 
 - Availability cores are the abstraction we use to allocate Polkadot's blockspace.
 - Allocated via leases and on-demand claims
+<!-- .element: class="fragment" data-fragment-index="1" -->
 - Cores divide blockspace supply into discrete units, 1 parachain block per relay chain block per core
+<!-- .element: class="fragment" data-fragment-index="2" -->
 - Why "availability"?
+<!-- .element: class="fragment" data-fragment-index="3" -->
 - Why "core"?
+<!-- .element: class="fragment" data-fragment-index="4" -->
 
 </pba-col>
 <pba-col center>
@@ -92,9 +102,12 @@ Notes:
 Though cores gate the entire parachain block pipeline,<br/> the availability process alone determines when these cores are considered occupied vs free.
 
 To recap, the goals of availability are:
+<!-- .element: class="fragment" data-fragment-index="1" -->
 
 1. To ensure that approvers will always be able to recover the PoVs to validate their assigned blocks
-2. To ensure that parachain nodes can recover blocks in the case that a parablock author maliciously refuses to share them
+<!-- .element: class="fragment" data-fragment-index="2" -->
+2. To ensure that parachain nodes can recover blocks in the case that a parablock author fails to share them, through malintent or malfunction
+<!-- .element: class="fragment" data-fragment-index="3" -->
 
 ---
 
@@ -105,11 +118,17 @@ Core States: Free, Scheduled, Occupied
 <pba-flex center>
 
 1. Block author places a candidate on-chain as backed, immediately occupying its scheduled core
+<!-- .element: class="fragment" data-fragment-index="1" -->
 1. Candidate backers distribute erasure coded PoV chunks
+<!-- .element: class="fragment" data-fragment-index="2" -->
 1. Validators distribute statements as to which candidates they have chunks for
+<!-- .element: class="fragment" data-fragment-index="3" -->
 1. Availability threshold is met (2/3 vs the 1/3 needed to reconstruct POV)
+<!-- .element: class="fragment" data-fragment-index="4" -->
 1. Candidate marked as included on chain and core freed
+<!-- .element: class="fragment" data-fragment-index="5" -->
 1. Approvers or parachain nodes retrieve PoV chunks as needed
+<!-- .element: class="fragment" data-fragment-index="6" -->
 
 </pba-flex>
 
@@ -128,6 +147,7 @@ Notes:
 Notes:
 
 - Metaphor: Freight train
+- Relay chain: Train station
 - Relay block: Train leaving station every 6 seconds
 - Potential Parablock: Car space in scheduled train
 - Availability core: Car index within all trains
@@ -162,7 +182,7 @@ Notes:
 
 - Leases have indices and pair to cores with the same index
 - Cores not designated as on-demand and without a paired lease are left free, their blockspace wasted
-- When on-demand claims are queued, they are each assigned a designated core in ascending order bounded by the on-demand core count
+- When on-demand claims are queued, they are each assigned a designated core in ascending order, looping when reaching the last core
 
 ---
 
@@ -202,23 +222,17 @@ Notes:
 
 </pba-flex>
 
-Notes:
-
-Q: Why don't we just have all active validators approve each candidate?
-
 ---
 
 ## Putting the Pieces Together
 
 <img rounded style="width: 1100px" src="../assets/cores_big_picture.svg" />
 
-Notes:
-
 ---
 
 ## Occupying Assigned Cores: With Lease
 
-<img rounded style="width: 1300px" src="../assets/occupying_assigned_cores_with_lease.svg" />
+<img rounded style="width: 1100px" src="../assets/occupying_assigned_cores_with_lease.svg" />
 
 Notes:
 
@@ -238,13 +252,9 @@ In file: polkadot/runtime/parachains/src/scheduler.rs
 
 <div style="font-size: 0.82em;">
 
-```rust
-
-#[pallet::storage]
-#[pallet::getter(fn availability_cores)]
+```rust[1|3-8|5,10-16]
 pub(crate) type AvailabilityCores<T> = StorageValue<_, Vec<Option<CoreOccupied>>, ValueQuery>;
 
-
 pub enum CoreOccupied {
     /// A parathread (on-demand parachain).
     Parathread(ParathreadEntry),
@@ -259,7 +269,6 @@ pub struct ParathreadEntry {
 	/// Number of retries.
 	pub retries: u32,
 }
-
 ```
 
 </div>
@@ -276,10 +285,7 @@ In file: polkadot/runtime/parachains/src/scheduler.rs
 
 <div style="font-size: 0.82em;">
 
-```rust
-
-#[pallet::storage]
-#[pallet::getter(fn scheduled)]
+```rust[1|3-10|9,12-17]
 pub(crate) type Scheduled<T> = StorageValue<_, Vec<CoreAssignment>, ValueQuery>;
 
 pub struct CoreAssignment {
@@ -297,7 +303,6 @@ pub enum AssignmentKind {
 	/// A parathread (on-demand parachain).
 	Parathread(CollatorId, u32),
 }
-
 ```
 
 </div>
@@ -316,9 +321,7 @@ In file: polkadot/runtime/parachains/src/scheduler.rs
 
 <div style="font-size: 0.82em;">
 
-```rust
-
-#[pallet::storage]
+```rust[1|3-7|4,9-13]
 pub(crate) type ParathreadQueue<T> = StorageValue<_, ParathreadClaimQueue, ValueQuery>;
 
 pub struct ParathreadClaimQueue {
@@ -332,7 +335,6 @@ pub struct QueuedParathread {
 	claim: ParathreadEntry,
 	core_offset: u32,
 }
-
 ```
 
 </div>
@@ -345,7 +347,7 @@ Notes:
 
 ---
 
-# How Cores Gate Each Step of the Parachains Protocol
+## How Cores Gate Each Step of the Parachains Protocol
 
 ---
 
@@ -354,6 +356,7 @@ Notes:
 Each parablock candidate is built in the context of a particular `relay_parent`. 
 
 Validators query their core assignment as of `relay_parent` and refuse to second candidates not assiciated with their backing group.
+<!-- .element: class="fragment" data-fragment-index="1" -->
 
 Notes:
 
@@ -361,13 +364,11 @@ Notes:
 
 ---
 
-## How Core Assignments Mediate Backing (Cont.)
+### How Core Assignments Mediate Backing (Cont.)
 
 `handle_second_message()` in the Backing Subsystem.
 
-```rust
-
-// Sanity check that candidate is from our assignment.
+```rust[1|6]
 if Some(candidate.descriptor().para_id) != rp_state.assignment {
 	gum::debug!(
 		target: LOG_TARGET,
@@ -378,7 +379,6 @@ if Some(candidate.descriptor().para_id) != rp_state.assignment {
 
 	return Ok(())
 }
-
 ```
 
 ---
@@ -387,9 +387,11 @@ if Some(candidate.descriptor().para_id) != rp_state.assignment {
 
 <pba-flex center>
 
-- For each scheduled (un-occupied) core a candidate is retrieved from the off-chain backing process
+- For each scheduled (un-occupied) core, a candidate is retrieved from the off-chain backing process
 - Candidates are provided to block author according to core assignment
+<!-- .element: class="fragment" data-fragment-index="1" -->
 - Backed on-chain -> immediately occupies core
+<!-- .element: class="fragment" data-fragment-index="2" -->
 
 </pba-flex>
 
@@ -404,75 +406,50 @@ Q: What does "immediately occupies core" imply?
 
 ## Cores and Backing On-Chain, Code
 
-Function `request_backable_candidates` from the Provisioner subsystem, simplified for readability
-
 <div style="font-size: 0.82em;">
 
-```rust
-/// Requests backable candidates based on core states.
-async fn request_backable_candidates(
-	availability_cores: &[CoreState],
-	bitfields: &[SignedAvailabilityBitfield],
-	relay_parent: Hash,
-	sender: &mut impl overseer::ProvisionerSenderTrait,
-) -> Result<Vec<CandidateHash>, Error> {
-	let block_number = get_block_number_under_construction(relay_parent, sender).await?;
-
-	let mut selected_candidates = Vec::with_capacity(availability_cores.len());
-
-	for (core_idx, core) in availability_cores.iter().enumerate() {
-		let (para_id) = match core {
-			CoreState::Scheduled(scheduled_core) => {
-				scheduled_core.para_id
-			},
-			CoreState::Occupied(occupied_core) => {
-				if bitfields_indicate_availability(core_idx, bitfields, &occupied_core.availability)
-				{
-					if let Some(ref scheduled_core) = occupied_core.next_up_on_available {
-						scheduled_core.para_id
-					} else {
-						continue
-					}
+Code determining whether to back a candidate and which, greatly simplified
+
+```rust[1|25|2-4|5-13|13-23|1,28-29]
+	let (para_id) = match core {
+		CoreState::Scheduled(scheduled_core) => {
+			scheduled_core.para_id
+		},
+		CoreState::Occupied(occupied_core) => {
+			if current_occupant_made_available(core_idx, &occupied_core.availability)
+			{
+				if let Some(ref scheduled_core) = occupied_core.next_up_on_available {
+					scheduled_core.para_id
 				} else {
-					if occupied_core.time_out_at != block_number {
-						continue
-					}
-					if let Some(ref scheduled_core) = occupied_core.next_up_on_time_out {
-						// Candidate's availability timed out, practically same as scheduled.
-						scheduled_core.para_id
-					} else {
-						continue
-					}
+					continue
 				}
-			},
-			CoreState::Free => continue,
-		};
-
-		let candidate_hash =
-			get_backable_candidate(relay_parent, para_id, required_path, sender).await?;
-
-		match candidate_hash {
-			Some(hash) => selected_candidates.push(hash),
-			None => (),
-		}
-	}
-
-	Ok(selected_candidates)
-}
+			} else {
+				if occupied_core.time_out_at != current_block {
+					continue
+				}
+				if let Some(ref scheduled_core) = occupied_core.next_up_on_time_out {
+					scheduled_core.para_id
+				} else {
+					continue
+				}
+			}
+		},
+		CoreState::Free => continue,
+	};
 
+	let candidate_hash =
+		get_backable_candidate(relay_parent, para_id, required_path, sender).await?;
 ```
 
 </div>
 
 Notes:
 
-- Per core
-  - Discuss core states free, scheduled, occupied
-  - Discuss core freeing criteria
-    - `bitfields_indicate_availability`
-      - next_up_on_available
-    - availability time out
-      - next_up_on_timeout
+- Discuss core freeing criteria
+- `bitfields_indicate_availability`
+	- next_up_on_available
+- availability time out
+	- next_up_on_timeout
 
 ---
 
@@ -490,8 +467,11 @@ Approvals, Disputes, and Finality are only provided to included candidates
 
 1. Improved liveness
 1. Flexibility of market structure
+<!-- .element: class="fragment" data-fragment-index="1" -->
 1. Flexibility of allocation
+<!-- .element: class="fragment" data-fragment-index="2" -->
 1. Intuitive unit of capacity over time
+<!-- .element: class="fragment" data-fragment-index="3" -->
 
 </pba-flex>
 
@@ -518,7 +498,9 @@ Notes:
 
 - Multiple cores per parachain
 - Overlapping leases of many lengths
+<!-- .element: class="fragment" data-fragment-index="1" -->
 - Lease + On-demand
+<!-- .element: class="fragment" data-fragment-index="2" -->
 
 </pba-flex>
 
@@ -550,10 +532,13 @@ Notes:
 ## Framing Shift: Blockspace vs Core Time
 
 Blockspace is a universal term for the product of blockchains, while core time is Polkadot's particular abstraction for allocating blockspace or other computation.
+<!-- .element: class="fragment" data-fragment-index="1" -->
 
 Cores can secure computation other than blocks. For example, a smart contract could be deployed on a core directly.
+<!-- .element: class="fragment" data-fragment-index="2" -->
 
 Allocating cores by time rather than for a fixed block size could allow for smaller or larger parachain blocks to be handled seamlessly.
+<!-- .element: class="fragment" data-fragment-index="3" -->
 
 ---
 

From 3aebc59520f0c84977f75b424ba0f2852157e08f Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Wed, 2 Aug 2023 21:08:54 -0700
Subject: [PATCH 16/17] Partially address comments

---
 .../Deep_Dive_Availability_Cores_Slides.md    |  56 ++++++++++++++----
 syllabus/7-Polkadot/assets/free.png           | Bin 0 -> 5193 bytes
 syllabus/7-Polkadot/assets/occupied.png       | Bin 0 -> 4132 bytes
 syllabus/7-Polkadot/assets/scheduled.png      | Bin 0 -> 3068 bytes
 4 files changed, 44 insertions(+), 12 deletions(-)
 create mode 100644 syllabus/7-Polkadot/assets/free.png
 create mode 100644 syllabus/7-Polkadot/assets/occupied.png
 create mode 100644 syllabus/7-Polkadot/assets/scheduled.png

diff --git a/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index 9d06228f3..01e50235c 100644
--- a/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -111,9 +111,43 @@ To recap, the goals of availability are:
 
 ---
 
-## The Availability Process
+## Core States
+
+<pba-cols>
+<pba-col center>
+
+Free
+
+<img rounded style="height: 300px" src="../assets/free.png" />
+
+</pba-col>
+<pba-col center>
+
+Scheduled
+
+<img rounded style="height: 300px" src="../assets/scheduled.png" />
+
+</pba-col>
+
+<pba-col center>
+
+Occupied
+
+<img rounded style="height: 300px" src="../assets/occupied.png" />
+
+</pba-col>
+</pba-cols>
+
+Notes:
+
+- Before going any farther we need to talk about core states
+- CoreState: Free -> core has not been assigned a parachain via lease or on-demand claim
+- CoreState: Scheduled -> Core has an assigned parachain and is currently unoccupied
+- CoreState: Occupied -> Core has assignment and is occupied by a parablock pending availability
 
-Core States: Free, Scheduled, Occupied
+---
+
+## The Availability Process
 
 <pba-flex center>
 
@@ -132,12 +166,6 @@ Core States: Free, Scheduled, Occupied
 
 </pba-flex>
 
-Notes:
-
-- CoreState: Free -> core has not been assigned a parachain via lease or on-demand claim
-- CoreState: Scheduled -> Core has an assigned parachain and is currently unoccupied
-- CoreState: Occupied -> Core has assignment and is occupied by a parablock pending availability
-
 ---
 
 ## Cores and Blockspace Over Time
@@ -146,8 +174,8 @@ Notes:
 
 Notes:
 
-- Metaphor: Freight train
-- Relay chain: Train station
+- Metaphor: Freight trains
+- Relay chain: Train loading bay
 - Relay block: Train leaving station every 6 seconds
 - Potential Parablock: Car space in scheduled train
 - Availability core: Car index within all trains
@@ -206,6 +234,7 @@ Notes:
 
 - Validators randomly assigned to groups at start of session.
 - Group count is active validator count / max group size rounded up
+- Groups are partitioned such that the largest group and smallest group have a size difference of 1
 
 ---
 
@@ -216,9 +245,12 @@ Notes:
 <pba-flex center>
 
 - Randomness via schnorrkel::vrf
-- Delay tranches add approvers until threshold met
-- Results in 30-40 assigned approvers per core
+- Approver assignments activated with delay tranches until threshold met
+<!-- .element: class="fragment" data-fragment-index="1" -->
+- Results in 30-40 approvers checking each block
+<!-- .element: class="fragment" data-fragment-index="2" -->
 - Different assignments each block prevent DOS
+<!-- .element: class="fragment" data-fragment-index="3" -->
 
 </pba-flex>
 
diff --git a/syllabus/7-Polkadot/assets/free.png b/syllabus/7-Polkadot/assets/free.png
new file mode 100644
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From e6963959fdd3bb02ae32e56517de666ae4840e1f Mon Sep 17 00:00:00 2001
From: BradleyOlson64 <lotrftw9@gmail.com>
Date: Wed, 2 Aug 2023 22:44:35 -0700
Subject: [PATCH 17/17] Final touch up

---
 .../Deep_Dive_Availability_Cores_Slides.md    | 79 ++++++++-----------
 1 file changed, 31 insertions(+), 48 deletions(-)

diff --git a/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md b/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
index 01e50235c..132e4021e 100644
--- a/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
+++ b/syllabus/7-Polkadot/Availability_Cores/Deep_Dive_Availability_Cores_Slides.md
@@ -24,6 +24,17 @@ Lets get to it
 
 ---
 
+## Addressing the Dual Naming
+
+<pba-flex center>
+
+- In the code: Availability core
+- Outside the code: Execution core
+
+</pba-flex>
+
+---
+
 ## Overview
 
 <pba-flex center>
@@ -102,6 +113,7 @@ Notes:
 Though cores gate the entire parachain block pipeline,<br/> the availability process alone determines when these cores are considered occupied vs free.
 
 To recap, the goals of availability are:
+
 <!-- .element: class="fragment" data-fragment-index="1" -->
 
 1. To ensure that approvers will always be able to recover the PoVs to validate their assigned blocks
@@ -177,7 +189,7 @@ Notes:
 - Metaphor: Freight trains
 - Relay chain: Train loading bay
 - Relay block: Train leaving station every 6 seconds
-- Potential Parablock: Car space in scheduled train
+- Parachain block: One train car worth of cargo
 - Availability core: Car index within all trains
 
 If you have a lease on core 4, then you have the right to fill train car 4 on each train with whatever you want to ship.
@@ -347,47 +359,16 @@ Notes:
 
 ---
 
-## On-Demand Queue in The Runtime
-
-In file: polkadot/runtime/parachains/src/scheduler.rs
-
-<div style="font-size: 0.82em;">
-
-```rust[1|3-7|4,9-13]
-pub(crate) type ParathreadQueue<T> = StorageValue<_, ParathreadClaimQueue, ValueQuery>;
-
-pub struct ParathreadClaimQueue {
-    queue: Vec<QueuedParathread>,
-    // this value is between 0 and config.parathread_cores
-    next_core_offset: u32,
-}
-
-/// A queued parathread (on-demand parachain) entry, pre-assigned to a core.
-pub struct QueuedParathread {
-	claim: ParathreadEntry,
-	core_offset: u32,
-}
-```
-
-</div>
-
-Notes:
-
-- Why ParathreadClaimQueue in the code? (Naming change)
-- Vec of queued parathreads
-- `next_core_offset` determines the parathread core which will be pre-assigned the next claim to enter the queue
-
----
-
 ## How Cores Gate Each Step of the Parachains Protocol
 
 ---
 
 ## How Core Assignments Mediate Backing
 
-Each parablock candidate is built in the context of a particular `relay_parent`. 
+Each parablock candidate is built in the context of a particular `relay_parent`.
 
 Validators query their core assignment as of `relay_parent` and refuse to second candidates not assiciated with their backing group.
+
 <!-- .element: class="fragment" data-fragment-index="1" -->
 
 Notes:
@@ -419,8 +400,8 @@ if Some(candidate.descriptor().para_id) != rp_state.assignment {
 
 <pba-flex center>
 
-- For each scheduled (un-occupied) core, a candidate is retrieved from the off-chain backing process
-- Candidates are provided to block author according to core assignment
+- For each core that is either unoccupied or is about to be a new candidate is found
+- A candidate for the parachain scheduled next on that core is provided to the block author
 <!-- .element: class="fragment" data-fragment-index="1" -->
 - Backed on-chain -> immediately occupies core
 <!-- .element: class="fragment" data-fragment-index="2" -->
@@ -479,9 +460,9 @@ Notes:
 
 - Discuss core freeing criteria
 - `bitfields_indicate_availability`
-	- next_up_on_available
+  - next_up_on_available
 - availability time out
-	- next_up_on_timeout
+  - next_up_on_timeout
 
 ---
 
@@ -497,13 +478,9 @@ Approvals, Disputes, and Finality are only provided to included candidates
 
 <pba-flex center>
 
-1. Improved liveness
-1. Flexibility of market structure
+1. Predictability of parachain execution
+1. Predictability of allocation
 <!-- .element: class="fragment" data-fragment-index="1" -->
-1. Flexibility of allocation
-<!-- .element: class="fragment" data-fragment-index="2" -->
-1. Intuitive unit of capacity over time
-<!-- .element: class="fragment" data-fragment-index="3" -->
 
 </pba-flex>
 
@@ -511,10 +488,9 @@ Approvals, Disputes, and Finality are only provided to included candidates
 
 Notes:
 
-1. Regularly rotating pairings between cores and backing groups
-1. Market structures: common good, lease, on-demand
-1. Cores accommodate huge changes in validation recipients from one block to the next
-1. Train metaphor
+- Regularly rotating pairings between cores and backing groups lessen the impact of potential bad validator subsets
+- Cores accommodate advance allocation making costs for parachains predictable
+- Core time can be resold or split for precise allocation
 
 ---
 
@@ -541,6 +517,10 @@ Notes:
 Notes:
 
 - Each color represents a parachain
+  Metaphor:
+- Multiple cars on the same train
+- Overlapping time spans of rights to fill different train cars
+- Long term rights to one car and buy rights to others for just one train
 
 ---
 
@@ -564,12 +544,15 @@ Notes:
 ## Framing Shift: Blockspace vs Core Time
 
 Blockspace is a universal term for the product of blockchains, while core time is Polkadot's particular abstraction for allocating blockspace or other computation.
+
 <!-- .element: class="fragment" data-fragment-index="1" -->
 
 Cores can secure computation other than blocks. For example, a smart contract could be deployed on a core directly.
+
 <!-- .element: class="fragment" data-fragment-index="2" -->
 
 Allocating cores by time rather than for a fixed block size could allow for smaller or larger parachain blocks to be handled seamlessly.
+
 <!-- .element: class="fragment" data-fragment-index="3" -->
 
 ---