Core Interaction Oracle Verifier rbr Knowledge Soundness
Binius.BinaryBasefold.CoreInteraction.coreInteractionOracleVerifier_rbrKnowledgeSoundness
Plain-language statement
Round-by-round knowledge soundness for the core interaction oracle verifier
Exact Lean statement
theorem coreInteractionOracleVerifier_rbrKnowledgeSoundness :
(coreInteractionOracleVerifier 𝔽q β ).rbrKnowledgeSoundness init impl
(pSpec := pSpecCoreInteraction 𝔽q β (h_ℓ_add_R_rate := h_ℓ_add_R_rate))
(relIn := roundRelation (mp := BBF_SumcheckMultiplierParam) 𝔽q β (ϑ:=ϑ)
(h_ℓ_add_R_rate := h_ℓ_add_R_rate) 0)
(relOut := finalSumcheckRelOut 𝔽q β (ϑ:=ϑ) (h_ℓ_add_R_rate := h_ℓ_add_R_rate))
(rbrKnowledgeError := coreInteractionOracleRbrKnowledgeError 𝔽q β (ϑ:=ϑ))Formal artifact
Lean source
theorem coreInteractionOracleVerifier_rbrKnowledgeSoundness : (coreInteractionOracleVerifier 𝔽q β ).rbrKnowledgeSoundness init impl (pSpec := pSpecCoreInteraction 𝔽q β (h_ℓ_add_R_rate := h_ℓ_add_R_rate)) (relIn := roundRelation (mp := BBF_SumcheckMultiplierParam) 𝔽q β (ϑ:=ϑ) (h_ℓ_add_R_rate := h_ℓ_add_R_rate) 0) (relOut := finalSumcheckRelOut 𝔽q β (ϑ:=ϑ) (h_ℓ_add_R_rate := h_ℓ_add_R_rate)) (rbrKnowledgeError := coreInteractionOracleRbrKnowledgeError 𝔽q β (ϑ:=ϑ)) := by unfold coreInteractionOracleVerifier pSpecCoreInteraction apply OracleVerifier.append_rbrKnowledgeSoundness (init:=init) (impl:=impl) (rel₁ := roundRelation 𝔽q β (ϑ:=ϑ) (h_ℓ_add_R_rate := h_ℓ_add_R_rate) 0) (rel₂ := roundRelation (mp := BBF_SumcheckMultiplierParam) 𝔽q β (ϑ:=ϑ) (h_ℓ_add_R_rate := h_ℓ_add_R_rate) (Fin.last ℓ)) (rel₃ := finalSumcheckRelOut 𝔽q β (ϑ:=ϑ) (h_ℓ_add_R_rate := h_ℓ_add_R_rate)) (V₁ := sumcheckFoldOracleVerifier (mp := BBF_SumcheckMultiplierParam) 𝔽q β (h_ℓ_add_R_rate := h_ℓ_add_R_rate) (ϑ:=ϑ) ) (V₂ := finalSumcheckVerifier 𝔽q β (h_ℓ_add_R_rate := h_ℓ_add_R_rate) (ϑ:=ϑ)) (Oₛ₃:=by exact fun i ↦ by exact OracleInterface.instDefault) (rbrKnowledgeError₁ := sumcheckFoldKnowledgeError (mp := BBF_SumcheckMultiplierParam) 𝔽q β (ϑ:=ϑ)) (rbrKnowledgeError₂ := finalSumcheckKnowledgeError (L := L)) (h₁ := by exact sumcheckFoldOracleVerifier_rbrKnowledgeSoundness (mp := BBF_SumcheckMultiplierParam) 𝔽q β (ϑ:=ϑ) (h_ℓ_add_R_rate := h_ℓ_add_R_rate) (init := init) (impl := impl)) (h₂ := by apply finalSumcheckOracleVerifier_rbrKnowledgeSoundness)- Project
- ArkLib
- License
- Apache-2.0
- Commit
- fad5cbf80877
- Source
- ArkLib/ProofSystem/Binius/BinaryBasefold/CoreInteractionPhase.lean:781-808
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