Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 573 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.31.0

Lift Context process Round

Prover.liftContext_processRound

Plain-language statement

Lifting the prover intertwines with the process round function

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Exists large of finset cover

ProximityGap.exists_large_of_finset_cover

Plain-language statement

Pigeonhole for finite covers: if U is covered by L indexed subsets and L * B < |U|, then some subset has more than B elements.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Exists Pz of coeffs of close proximity

ProximityGap.exists_Pz_of_coeffs_of_close_proximity

Plain-language statement

There exists a δ-close polynomial P_z for each z from the set S.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Folded rate eq

ProximityGap.folded_rate_eq

Plain-language statement

The rate of the folded RS-code is the same.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Folding preserves distance

ProximityGap.folding_preserves_distance

Plain-language statement

Folding preserves distance from Reed–Solomon codes. For any word f over the smooth coset FFT domain, degree parameter d, folding parameter k, and distance threshold δ satisfying 0 < δ < min (δᵣ(f, RS[d])) (1 - sqrtRate(d)), the probability over a uniformly random folding challenge r : F that the folded word is within relative distance δ of t...

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Fold Word k 1 of sq roots

ProximityGap.foldWord_k_1_of_sq_roots

Plain-language statement

An explicit formula for foldWord when k = 1 that does not use Lagrange interpolation and avoids using log.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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