Alphabeta Math
ExampleConstruction: AI-generatedVerification: AI-generatedPipeline-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.

Selecting an admissible contour height

Example

For T≥3, one can choose T′∈[T,T+1] with distance at least c/log⁡T from every zero ordinate in [T−1,T+2], for an absolute c>0.

Verification

Given: the O(log⁡(T+2)) unit-interval zero count.

1.1

The three adjacent unit-interval bounds show that the number of relevant ordinates is at most Clog⁡T after enlarging an absolute constant C to cover 3≤T≤5. Around each such ordinate remove an interval of radius c/log⁡T, where c<1/(2C).

givenconstruct
2.1

The total removed length inside [T,T+1] is at most 2Cc<1. Consequently some T′ remains in that interval, and by construction its distance from every relevant ordinate is at least c/log⁡T.

step 1.1discharge-construct∎

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