Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-generatedPipeline-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-06
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.

Reading a c.e. definition as a Sigma_1^0 formula

Example

The halting set is expressed by ⟨e,x⟩∈K  ⟺  ∃s T(e,x,s), where s encodes a complete halting computation history.

Facts & Assumptions

Given: the fixed computation-history coding for K.

Verification

technique · direct
1.1

Validity of a proposed finite history is primitive recursive, so the displayed formula has one leading unbounded existential quantifier over a bounded matrix.

givenconstruct
2.1

Hence it is a Σ10 presentation. The witness is precisely the finite accepting computation used by the recognizer of K.

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

6 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