added verifier check in sticker, fixed the edge case in product

[Soleimani193]

This PR adds the verifier check for the local opening in the stitcker compiler.
It also addresses the edge case 0^0=1 in the symbolic.NewProduct()

Checklist

• I wrote new tests for my new core changes.
• I have successfully ran tests, style checker and build against my new changes locally.
• I have informed the team of any breaking changes if there are any.

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 70.59%. Comparing base (5fad7f7) to head (2d6be64).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff            @@
##               main     #204   +/-   ##
=========================================
  Coverage     70.59%   70.59%           
  Complexity     1059     1059           
=========================================
  Files           291      291           
  Lines         11960    11960           
  Branches       1103     1051   -52     
=========================================
  Hits           8443     8443           
  Misses         3039     3039           
  Partials        478      478           

Flag	Coverage Δ
hardhat	98.67% <ø> (ø)
kotlin	68.28% <ø> (ø)

[gusiri]

LGTM