Batch public input check with ring-switch oracle relation#1441
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The public input consistency check was batched into Phase 2 of the shift reduction protocol. This removes it entirely: the Fiat-Shamir transcript no longer samples inout_eval_point or batch_coeff, the Phase 2 sumcheck claim simplifies from gamma + batch_coeff * public_eval to just gamma, and the eval check simplifies from witness_eval * (monster_eval + batch_coeff * eq_eval) to witness_eval * monster_eval. Public input verification will be handled separately.
[prover] Observe public inputs as B128 on channel
Instead of checking public inputs in the shift reduction protocol, batch the pubcheck with the ring-switch oracle relation during PCS opening. This samples a batch_coeff after ring-switch and modifies both the transparent polynomial (rs_eq_ind + batch_coeff * pubcheck_eq) and the claim (sumcheck_claim + batch_coeff * pubcheck_claim). The pubcheck_eq selects the first 2^log_public_elems entries of the committed polynomial using eq(pubcheck_point || 0, ·).
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Summary
compute_batched_transparenthelper on the prover side andeval_pubcheck_eqhelper on the verifier sideTest plan
cargo test -p binius-prover --test shiftcargo test -p binius-examples --testscargo clippy -p binius-verifier -p binius-prover --tests --benches -- -D warnings