Alphabeta Math
CounterexampleConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-28
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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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A stable-letter word need not be Britton-reduced

Statement refuted

Every HNN word containing a stable letter is Britton-reduced.

Facts & Assumptions

Given: An HNN extension in associated-subgroup notation.

[L1]

A pin tct−1 with c∈C− is not Britton-reduced. (HNN words, pins, and Britton-reduced words)

[L2]

Such a pin reduces to the base-group element ϕ(c). (Elementary HNN reductions preserve the represented element)

Counterexample

technique · direct
1.1

Choose any c∈C−. The word tct−1 contains a stable letter, and [L1] says it is a pin, so it is not Britton-reduced.

L1given
2.1

By [L2], the same word reduces to ϕ(c)∈A. Thus it is a concrete counterexample to the statement refuted.

L2step 1.1algebra∎

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