Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-28
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.

FALSE: every word containing a stable letter is nontrivial

Statement

Every HNN word that contains a stable letter represents a nonidentity element.

Facts & Assumptions

Given: An HNN extension in associated-subgroup notation.

[L1]

A pin is a subword tct−1 with c∈C− or t−1dt with d∈C+. (HNN words, pins, and Britton-reduced words)

[L2]

Britton's lemma applies only to words that are already Britton-reduced. (Britton's lemma)

Refutation

technique · direct
1.1

For any c∈C−, the word tct−1 contains a stable letter and is a pin by [L1].

L1given
2.1

By the defining relator it equals ϕ(c)∈A, so it can even represent the identity when c=e. Thus [L2] does not justify the stated claim, and the statement is false.

L1L2step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

4 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