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 70.46%. Comparing base (368e404) to head (2b646d4).

Additional details and impacted files

@@            Coverage Diff            @@
##               main     #179   +/-   ##
=========================================
  Coverage     70.46%   70.46%           
  Complexity     1040     1040           
=========================================
  Files           282      282           
  Lines         11314    11314           
  Branches       1082     1030   -52     
=========================================
  Hits           7972     7972           
  Misses         2875     2875           
  Partials        467      467           

Flag	Coverage Δ
hardhat	98.70% <ø> (ø)
kotlin	67.94% <ø> (ø)