[recursion] ceno recursion v2#1263
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…value + PublicValues (#1277) This PR refactors how public inputs (PI) are represented and consumed across zkVM proving/verification so that PI handling is circuit-driven and consistent end-to-end. Related to #1263. ### Design rationale Previously, PI transcript absorption and some verifier checks depended on broader/raw PI containers, which made ordering and indexing assumptions harder to audit and keep consistent across: - prover - rust verifier - recursion verifier. This PR moves PI consumption to a canonical, circuit-defined path: - `instance_values` defines which scalar PI values a circuit observes (and in what order). - `instance_openings` defines which PI MLE columns are opened. - PI openings are derived from `PublicValues` MLEs, rather than ad-hoc/raw vectors. This reduces ambiguity in PI ordering/indexing and aligns transcript-visible PI handling with circuit semantics. ### pi update Previous `pi_update` mechanism will trigger verifier failed if a identical public value used > 1 chip because they will be in different opening point, thus evaluation value will be different. This PR fixed the issue, and refactor public value check back to `verify_chip_phase` ### soundness fix This PR also fixed a soundness issue by removing `wit_in_evals` and `fixed_in_evals` from the proof payload. Instead of trusting prover-supplied values for these evaluations, the verifier now deterministically derives them from the sumcheck evaluations during verification. This prevents a malicious prover from introducing mismatches between claimed eval vectors and the actual sumcheck-consistent values. ### Follow up #1280
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Related to #1267