Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: Literature-sourcedPipeline-generatedjudge 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.

The middle form of the bounding disk bundle W2,−1

Example

Assume the Axiom of Choice. For (h,j)=(2,−1) the disk bundle W=W2,−1=D(ξ2,−1) has Euler number ε=h+j=1 and k=h−j=3. The middle form of Middle form and signature of the Milnor disk bundle is generated by the zero section S4⊆W, whose normal bundle is ξ2,−1 with Euler number 1; hence the one-by-one matrix of the form is [1] and the boundary signature is σ(W2,−1)=1. The normalized Thom evaluation ⟨U⌣x,[W,M]⟩=1 gives the same sign in the rank-one computation.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

9 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