Research proof index

Coordinate-wise special soundness of SendClaim. The verifier is a pure pass-through with no challenge rounds, so CWSS collapses (via the oracle no-challenge bridge) to a transcript-level obligation. The extractor is trivial (e := fun _ _ => (), there is no witness); since the output oracle statements at inl are the input oracles unchanged and `t...

The pure pass-through oracle verifier's underlying non-oracle verifier returns the statement together with the output oracle statements (input oracles at inl, the message at inr 0).

Coordinate-wise special soundness of SendSingleWitness. The oracle verifier has no challenge rounds, so CWSS collapses (via the oracle no-challenge bridge coordinateWiseSpecialSound_of_isEmpty_challengeIdx) to a transcript-level extraction obligation on the combined statement Statement × (∀ i, OStatement i). The extractor is `e := fun _ tr => tr...

Coordinate-wise special soundness of SendWitness. The verifier has no challenge rounds, so CWSS collapses (via the no-challenge bridge coordinateWiseSpecialSound_of_isEmpty_challengeIdx) to a transcript-level extraction obligation. The extractor is e := fun _ tr => tr 0: the witness is the (single) prover message. Since the verifier is pure wi...

Singleton bound for arbitrary codes

Lemma 5.4: Round-by-round soundness of the STIR IOPP Consider parameters: ι = {ιᵢ}_{i = 0, ..., M} be smooth evaluation domains P : Params ι F containing required protocol parameters - initial degree, folding parameters foldingParamᵢ, embedding φᵢ, repetition parameters repeatParamᵢ hParams : ParamConditions ι P, stating conditions that parame...