Alphabeta Math
ExampleConstruction: 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.

Changing representatives of a degree comparison

Example

Let A~=A⊕∅ and B~=B⊕∅. The tags can be ignored or supplied as constant 0 bits, so A≡TA~ and B≡TB~. Thus a comparison A≤TB gives the same degree comparison when these particular representatives are replaced by A~ and B~.

Facts & Assumptions

Given: sets A,B⊆N and their zero-padded tagged versions.

Verification

technique · direct
1.1

A A~-oracle decides A by even queries, while an A-oracle decides A~ by querying A on even inputs and returning 0 on odd inputs. Thus A≡TA~, and likewise B≡TB~.

givenconstruct
2.1

The degree order is representative-independent now yields A≤TB iff A~≤TB~.

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