perf: GKR - Section 3.2 of Gru24

[Tabaie]

Section 3.2 of https://eprint.iacr.org/2024/108.pdf describes a clever optimization on Zero-Check reducing the degree of round polynomials and thus saving an entire gate evaluation pass and a multiplication pass at every round. This is not available when claims from multiple evaluation points are folded, in which case factoring out parts of the eq term is not possible.

[peter941221]

I took a narrow v1 pass on this and opened a PR:

• https://github.com/Consensys/gnark/pull/1744

Scope-wise, I kept it intentionally strict:

• only enable the Section 3.2 optimization when the whole GkrSumcheckLevel collapses to one distinct GkrClaimSource
• keep folded multi-source levels on the legacy path

Implementation-wise, this is not just a degree constant tweak:

• add a schedule-side single-source eligibility boundary
• switch eligible levels to the weighted Section 3.2 verifier recurrence
• update both verifier surfaces together:
  • native verifier
  • in-circuit verifier
• use a reduced eq-table prover path that strips one current-variable eq factor per round

I also added a couple of reviewer-confidence checks around the trickiest algebraic edge:

• direct coeff == 1 weighted-reconstruction tests for the native verifier path
• a matching frontend / circuit-side verifier test

On the evidence side, the regenerated vectors shrink exactly on the eligible levels and stay unchanged on legacy-only shapes.

If you'd prefer, I can also split the write-up further or add a short code comment around the optimized final-check path.