Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-adaptedPipeline-generatedprecheck passjudge pass (gpt-6.1-sol)
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.

Thom space of a trivial line bundle

Example

For the supplied product line B×R, its Thom space is ΣB+. This is the line case of the AT trivial line/plane computation, used here to specify the framed normal target.

Facts & Assumptions

Given: A product line with its specified trivialization.

[F1]

Trivial Thom spaces as suspension smash products gives the natural quotient.

Verification

1.1F1

The disk bundle is B×[−1,1] and the sphere bundle is B×{−1,1}. Collapsing both boundary copies to the one Thom basepoint gives B+∧([−1,1]/{−1,1}).

2.1F1step 1.1∎

The interval quotient is the based circle, so the result is B+∧S1=ΣB+. For a point base this is S1; for empty base it is a point. The trivialization records which fiber direction is positive, even though the underlying homeomorphism type does not remember its sign.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

3 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