Alphabeta Math
CounterexampleConstruction: AI-generatedVerification: AI-generatedPipeline-generatedprecheck passjudge 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.

A finite oracle-query transcript

Statement refuted

A computation deciding whether 7 belongs to its oracle must read every bit of that oracle.

Counterexample

technique · direct

Given: an oracle X.

1.1

The machine that queries only 7 and returns the answer decides this predicate for every oracle X. Its transcript has the single query 7.

givenconstruct
2.1

Any two oracles agreeing at 7 give exactly the same run and output, even if they differ elsewhere. This finite witness refutes the claimed whole-oracle read.

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

4 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