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.

A-polynomial Newton parallelogram characterization

Open problem

Assume the Axiom of Choice. For a Laurent polynomial f(M,L)=∑i,jcijMiLj, its Newton polygon is the convex hull of the exponent support {(i,j):cij≠0}. For a nontrivial knot K⊂S3, is K a torus knot if and only if the Newton polygon of its ordinary A-polynomial is a parallelogram with nonzero area?

Open problem references

Baldwin and Sivek, Question 1.6

Status

Open. Baldwin–Sivek pose this as Question 1.6 in their 2025 paper. A web search on 2026-10-19 found no later resolution; no proof is asserted here.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

20 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