Alphabeta Math
ExampleConstruction: AI-generatedVerification: AI-generatedPipeline-generatedprecheck passaudited 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 Turing reduction without a truth table

Example

Set X=0′. The non-domination argument guarantees at least one set Y≤TX which has no everywhere-total oracle functional computing it from X. This is an existence example: a Turing computation may need an oracle-dependent amount of information before it knows its answer.

Facts & Assumptions

Given: X=0′.

Verification

technique · direct
1.1

Some Turing reductions are not truth-table reductions supplies a set Y such that Y≤TX and Y̸≤ttX.

given
2.1

By Truth-table reduction, that failure says no functional computing Y from X is total on every possible oracle.

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