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.
FALSE: the O'Nan-Scott theorem requires the classification of finite simple groups
Statement
False claim: the O'Nan-Scott theorem itself requires the classification of finite simple groups.
Facts & Assumptions
Given: The structural O'Nan-Scott theorem and its later applications.
The O'Nan-Scott theorem gives a structural classification of finite primitive groups of degree at least (The O'Nan-Scott classification of finite primitive groups).
The classification of finite simple groups enters later refinements rather than the structural reduction itself.
Refutation
The theorem [L1] is already a completed structural classification of finite primitive permutation groups.
The sourced boundary fact [A1] states that CFSG is used later, not in the theorem itself. So the claim is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
8 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
- Leonard H. Soicher, Primitive permutation groups (standard reference, not scraped)