Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-generatedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-26
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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.

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FALSE: every block is an invariant subset

Statement

Every block is an invariant subset.

Facts & Assumptions

Given: The composite-degree dihedral action from Dihedral actions of prime and composite degree.

[L1]

In the composite dihedral action, a residue class modulo a proper divisor is a block (Dihedral actions of prime and composite degree).

Refutation

technique · direct
1.1

In the action of D6 on Z/6Z, the subset B={0,2,4} is a block by [L1].

L1
2.1

The reflection x↦1−x sends B to {1,3,5}, which is disjoint from B and not equal to it. So B is a block but not an invariant subset.

step 1.1algebra
3.1

This refutes the statement.

step 2.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

3 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