Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-generatedPipeline-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-06
How 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.

Lie type is developed here through Lie algebras

Statement

This page develops the finite simple groups of Lie type through their Lie-algebra structure.

Facts & Assumptions

Given: Inspect the named-family carrier Finite simple groups of Lie type as named families.

Refutation

technique · direct
1.1

It records only the source table's family names and conventions. It does not define root data, Chevalley groups, or the Lie-algebra constructions from which the families arise.

given
2.1

The claim that this page develops the groups through Lie-algebra structure is therefore false.

step 1.1contradiction∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · one level

1 result within one dependency step 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