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.
The simplicial path metric on a tree
Definition
Let be a simplicial tree. By A simplicial graph is a tree exactly when every two vertices are joined by a unique reduced path, every two vertices are joined by a unique reduced path. Define the simplicial path metric
to be the length of that unique reduced path.
The fact that this definition is geodesic and integer-valued is proved in
The path metric on a simplicial tree is geodesic and integer-valued ↗, recorded here in
justified_by.
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
- Jean-Pierre Serre, Trees (standard reference, not scraped)