Prover: beta v1 setup

[gusiri]

This PR implements issue(s) #

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 71.18%. Comparing base (7a4d510) to head (77ed108).
Report is 4 commits behind head on main.

Additional details and impacted files

@@             Coverage Diff              @@
##               main     #179      +/-   ##
============================================
+ Coverage     71.04%   71.18%   +0.13%     
- Complexity     1072     1074       +2     
============================================
  Files           291      291              
  Lines         11964    11965       +1     
  Branches       1050     1050              
============================================
+ Hits           8500     8517      +17     
+ Misses         2988     2974      -14     
+ Partials        476      474       -2     

Flag	Coverage Δ
hardhat	98.67% <ø> (ø)
kotlin	68.92% <ø> (+0.14%)	⬆️

see 6 files with indirect coverage changes