Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-adaptedaudited 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.

Sequential repetition of a constant-gap protocol

Example

For a protocol with completeness 3/4 and soundness 1/4, run k independent copies and accept a strict majority.

Verification

Given: the repeated protocol with odd k.

1.1

Its honest and cheating parameters satisfy the hypotheses c>1/2>s of Sequential repetition amplifies completeness and soundness gaps.

given
2.1

Thus each error probability is exponentially small in k; choosing an odd k with that bound below 10−6 gives completeness at least 1−10−6 and soundness at most 10−6.

step 1.1choose∎

Depends on

Used by

Nothing in the library uses this result yet.

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