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.
Cyclically reduced words
Definition
A reduced word is cyclically reduced when it is empty or its first letter is not the formal inverse of its last letter. Equivalently, every cyclic rotation of the word is reduced.
If as a literal concatenation of words, the word is a cyclic permutation of . This includes itself by taking or empty.
Depends on
Used by
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 7 results over 4 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.
Sources
- Alexei Myasnikov and Vladimir Shpilrain, Combinatorics over Free Groups, §2.2.1 (standard reference, not scraped)
- Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial Group Theory (standard reference, not scraped)