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.
Grigorchuk groups of intermediate growth
There exist finitely generated groups of intermediate growth. The first examples were constructed by Grigorchuk.
This page uses that result only as an existence witness. It supplies the standard counterexample to the claim that subexponential growth must already be polynomial.
Depends on
Used by
- FALSE: every subexponential growth group has polynomial growth False statement
Dependency tree · two levels
5 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
- C. Löh, Geometric Group Theory, Sections 5.1-5.3 (standard reference, not scraped)