Alphabeta MathHow 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.
Descending-diagram crossing-change sequence
Definition
Input a valid finite planar code for one regular oriented knot diagram and a basepoint in the interior of an edge, away from every crossing and bend. Traverse the oriented code once starting at the basepoint. At each crossing, consider the first branch reached by this traversal. If that branch is under, record the crossing and exchange its over/under label; otherwise leave the crossing unchanged. Return the finite list of recorded crossing changes and the updated planar code. For a code with no crossings, return the empty list and the unchanged code. The input is the valid finite code defined for an oriented knot diagram; this procedure has no invalid-input branch.
Depends on
Used by
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
- Ozsváth, Stipsicz, and Szabó, Grid Homology for Knots and Links (standard reference, not scraped)
- Danny Calegari, Introduction to Knot Theory (standard reference, not scraped)