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[Super issue] upgrade to recursion v2 #1266

@hero78119

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@hero78119

Recursion dominate in ethproofs e2e around 50% or more compare with base-layer. see benchmark ceno-reth

ceno recursion stick to in-house folk openvm v1.4.1 which is quite old version and prover performance are subjective to degrade compare with multi-variate version like ceno base layer.

openvm are WIP to upgrade to multi-variate develop-v2. To boost ceno recursion performance, we can explore and upgrade recursion to openvm v2 to make us not stuck on low-perf v1.4.1.

Once completed, later we can plan to swap recursion backend proving to ceno as well.

recursion module break down

  • refactor proof-shape + gkr module to fit ceno style
  • main-sumcheck recursion verification
  • PCS: basefold verification
  • precompile rotation argument verification
  • continuation argument verification

base layer change

The goal of base layer change is to reduce dynamism for recursion implementation

  • make num_instance size fixed as size 2 array, constrain num_instance[1] if possible
  • make zkvm proof per chip to be 1 instead of vector
  • main-sumcheck chip various degree => make different degree support for sumcheck

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