Alphabeta Math
Open problemQuestion: Literature-sourcedProof: Not applicablePipeline-generated‡ sources checked 2026-10-22‡ unresolved
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.

This problem is unresolved. Its sources and status may be reviewed, but no solution is accepted here. It cannot be used as a proof premise.

Do exactly two boundary slopes characterize torus knots?

Open problem

Assume the Axiom of Choice. If a nontrivial knot K⊂S3 has exactly two distinct boundary slopes, must K be a torus knot? The two slopes of a nontrivial torus knot Tp,q are 0 and pq in the meridian-longitude convention where a[λ]+b[μ] has slope b/a.

Status

Open. Baldwin–Sivek describe the two-boundary-slope statement as a folklore conjecture and give only a partial result for nontrivial fibered non-torus knots. A web search on 2026-10-19 found 2-bridge partial results but no resolution for all knots. No proof is asserted here.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

17 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