Full Oracle Reduction perfect Completeness
Binius.BinaryBasefold.FullBinaryBasefold.fullOracleReduction_perfectCompleteness
Plain-language statement
Perfect completeness for the full Binary Basefold protocol (reduction)
Exact Lean statement
theorem fullOracleReduction_perfectCompleteness :
OracleReduction.perfectCompleteness
(oracleReduction := fullOracleReduction 𝔽q β γ_repetitions (ϑ:=ϑ)
(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 := acceptRejectOracleRel)
(init := init)
(impl := impl)Formal artifact
Lean source
theorem fullOracleReduction_perfectCompleteness : OracleReduction.perfectCompleteness (oracleReduction := fullOracleReduction 𝔽q β γ_repetitions (ϑ:=ϑ) (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 := acceptRejectOracleRel) (init := init) (impl := impl) := by apply OracleReduction.append_perfectCompleteness (R₁ := CoreInteraction.coreInteractionOracleReduction 𝔽q β (h_ℓ_add_R_rate := h_ℓ_add_R_rate) (ϑ:=ϑ) ) (R₂ := QueryPhase.queryOracleReduction 𝔽q β γ_repetitions (h_ℓ_add_R_rate := h_ℓ_add_R_rate) (ϑ:=ϑ)) (Oₛ₃ := fun _ => OracleInterface.instDefault) (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) (h₁ := by apply CoreInteraction.coreInteractionOracleReduction_perfectCompleteness 𝔽q β (h_ℓ_add_R_rate := h_ℓ_add_R_rate) (ϑ:=ϑ) ) (h₂ := by apply QueryPhase.queryOracleProof_perfectCompleteness 𝔽q β γ_repetitions (ϑ:=ϑ) (h_ℓ_add_R_rate := h_ℓ_add_R_rate) init impl )- Project
- ArkLib
- License
- Apache-2.0
- Commit
- fad5cbf80877
- Source
- ArkLib/ProofSystem/Binius/BinaryBasefold/General.lean:110-136
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Affine gaps lifted to interleaved codes
affine_gaps_lifted_to_interleaved_codes
Project documentation
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.
Gadget Decompose coeff
ArkLib.Lattices.Ajtai.gadgetDecompose_coeff
Plain-language statement
The k-th coefficient (k < deg φ) of a gadget-decomposition block is exactly the corresponding digit of the corresponding input coefficient.
Source project: ArkLib
Person-level attribution pending.
Gadget Decompose lawful
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.