DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-07

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Two-query linear self-correction

Definition

For fixed oracle $f : F_{2}^{n} \to F_{2}$ , $n \geq 0$ , and a requested point $x$ , the two-query self-corrector chooses uniform $y \in F_{2}^{n}$ and returns ${Corr}_{f} (x; y) = f (y) + f (x + y) in F_{2} .$ It uses $n$ random bits and two oracle calls, possibly at the same location. Linearity and distance have the conventions of The BLR linearity test over F_2. Correctness will require proximity of the fixed oracle to a linear function. This procedure does not assume that the original value $f (x)$ is correct.

Depends on

The BLR linearity test over F_2

Used by

Pointwise correctness under less than quarter noise Theorem

Dependency tree · two levels

2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Arora and Barak, Computational Complexity, January 2007 web draft, §18.4.1 Local decoding of Walsh-Hadamard code pp.364–365 (standard reference, not scraped)