Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-adaptedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-04‡ rests on unproved material
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.

‡ Rests on 1 statement not proved in this library. Every dependency marked ‡ below is recorded with a citation but is not established here, because the track that would prove it has not yet been developed in this library. Everything else in this proof is proved here.

FALSE: Schur-Zassenhaus conjugacy needs no solvability or deeper input

Statement

The conjugacy part of Schur-Zassenhaus needs neither a solvability hypothesis nor any deeper finite-group input.

Facts & Assumptions

Given: The local page boundary for Schur-Zassenhaus conjugacy.

[L1]

This page proves complement conjugacy when the kernel or quotient is solvable (Schur-Zassenhaus conjugacy when the kernel or quotient is solvable).

‡ [L2]

The stronger clean theorem is recorded separately as a source-cited boundary item (The full Schur-Zassenhaus conjugacy theorem ‡).

Refutation

technique · direct
1.1

Fact [L1] shows that the local proof package carries an explicit solvability hypothesis.

givenL1
2.1

Fact [L2] records that the full unrestricted conjugacy theorem sits beyond that local proof boundary. So the claim that no solvability qualification or deeper input is involved is false.

L1‡ L2step 1.1∎

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