Add batched cubic sumcheck for K instance triples

[srinathsetty]

Add prove_batched_cubic and evaluation_points_batched_cubic to SumcheckProof and EqSumCheckInstance respectively. These prove sum_x eq(tau,x) * sum_i alpha_i * (A_i(x)*B_i(x) - C_i(x)) = claim for K instances sharing the same sumcheck structure.

The inner polynomial t(X) = sum_i alpha_i*(A_i(X)*B_i(X)-C_i(X)) is degree 2 in X, so BDDT O(1) claim derivation applies unchanged. Includes fallback_eval_inf_batched_cubic for the tau=0 edge case.

[Copilot]

Pull request overview

Adds a new batched cubic sumcheck prover path to support proving a weighted sum of K (A_i, B_i, C_i) instance triples under a shared eq(tau, x) structure, extending Spartan’s sumcheck optimization infrastructure.

Changes:

• Add SumcheckProof::prove_batched_cubic to produce a cubic sumcheck proof for sum_i alpha_i * (A_i*B_i - C_i) under equality-polynomial factoring.
• Add EqSumCheckInstance::evaluation_points_batched_cubic plus a tau=0 fallback path to derive round evaluation points using the existing BDDT O(1) claim derivation.
• Bump crate version to 0.66.0.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 3 comments.

File	Description
src/spartan/sumcheck.rs	Implements batched cubic sumcheck proving and equality-sumcheck evaluation-point derivation for K triples.
Cargo.toml	Version bump to reflect the new public API additions.

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