Full Oracle Verifier rbr Knowledge Soundness
Binius.BinaryBasefold.FullBinaryBasefold.fullOracleVerifier_rbrKnowledgeSoundness
Plain-language statement
Round-by-round knowledge soundness for the full Binary Basefold oracle verifier
Exact Lean statement
theorem fullOracleVerifier_rbrKnowledgeSoundness :
(fullOracleVerifier 𝔽q β γ_repetitions (ϑ:=ϑ)
(h_ℓ_add_R_rate := h_ℓ_add_R_rate) ).rbrKnowledgeSoundness init impl
(relIn := roundRelation (mp := BBF_SumcheckMultiplierParam) 𝔽q β (ϑ:=ϑ)
(h_ℓ_add_R_rate := h_ℓ_add_R_rate) 0)
(relOut := acceptRejectOracleRel)
(rbrKnowledgeError := fullRbrKnowledgeError 𝔽q β γ_repetitions (ϑ:=ϑ)
(h_ℓ_add_R_rate := h_ℓ_add_R_rate))Formal artifact
Lean source
theorem fullOracleVerifier_rbrKnowledgeSoundness : (fullOracleVerifier 𝔽q β γ_repetitions (ϑ:=ϑ) (h_ℓ_add_R_rate := h_ℓ_add_R_rate) ).rbrKnowledgeSoundness init impl (relIn := roundRelation (mp := BBF_SumcheckMultiplierParam) 𝔽q β (ϑ:=ϑ) (h_ℓ_add_R_rate := h_ℓ_add_R_rate) 0) (relOut := acceptRejectOracleRel) (rbrKnowledgeError := fullRbrKnowledgeError 𝔽q β γ_repetitions (ϑ:=ϑ) (h_ℓ_add_R_rate := h_ℓ_add_R_rate)) := by apply OracleVerifier.append_rbrKnowledgeSoundness (init:=init) (impl:=impl) (rel₁ := roundRelation (mp := BBF_SumcheckMultiplierParam) 𝔽q β (ϑ:=ϑ) (h_ℓ_add_R_rate := h_ℓ_add_R_rate) 0) (rel₂ := finalSumcheckRelOut 𝔽q β (ϑ:=ϑ) (h_ℓ_add_R_rate := h_ℓ_add_R_rate)) (rel₃ := acceptRejectOracleRel) (V₁ := CoreInteraction.coreInteractionOracleVerifier 𝔽q β (h_ℓ_add_R_rate := h_ℓ_add_R_rate) (ϑ:=ϑ) ) (V₂ := QueryPhase.queryOracleVerifier 𝔽q β γ_repetitions (h_ℓ_add_R_rate := h_ℓ_add_R_rate) (ϑ:=ϑ)) (Oₛ₃:=by exact fun i ↦ by exact OracleInterface.instDefault) (rbrKnowledgeError₁ := CoreInteraction.coreInteractionOracleRbrKnowledgeError 𝔽q β (ϑ:=ϑ)) (rbrKnowledgeError₂ := QueryPhase.queryRbrKnowledgeError 𝔽q β γ_repetitions (h_ℓ_add_R_rate := h_ℓ_add_R_rate)) (h₁ := by apply CoreInteraction.coreInteractionOracleVerifier_rbrKnowledgeSoundness) (h₂ := by apply QueryPhase.queryOracleVerifier_rbrKnowledgeSoundness)- Project
- ArkLib
- License
- Apache-2.0
- Commit
- fad5cbf80877
- Source
- ArkLib/ProofSystem/Binius/BinaryBasefold/General.lean:151-174
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This lemma proves the final algebraic step in the DG25 Theorem 3.1 proof. It shows that if R > e + 1, then e * (R / (R - 1)) < e + 1. The intuition is that the fraction R / (R - 1) is always greater than 1, but as R gets larger, it gets closer to 1. The hypothesis R > e + 1 provides a strong enough bound to ensure the product e * (fraction) do...
Source project: ArkLib
Person-level attribution pending.
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Plain-language statement
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Source project: ArkLib
Person-level attribution pending.
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ArkLib.Lattices.Ajtai.gadgetDecompose_lawful
Plain-language statement
The base-b gadget decomposition is a lawful gadget decomposition.
Source project: ArkLib
Person-level attribution pending.