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.
Edge inversions and actions without inversions
Definition
Let act on an oriented graph . An element inverts an oriented edge when
The action is without inversions when no oriented edge is inverted by any group element.
Depends on
Used by
- Groups acting freely without inversions on trees are torsion-free Corollary
- The quotient graph of an action without inversions Definition
- The translation length of a tree automorphism without inversions Definition
- FALSE: every tree action is without edge inversions False statement
- Barycentric subdivision removes edge inversions while preserving the tree Lemma
- Tree automorphisms without inversions are either elliptic or hyperbolic Theorem
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
- Yuriy Tumarkin, Groups Acting on Trees (standard reference, not scraped)
- Jean-Pierre Serre, Trees (standard reference, not scraped)