Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passaudited 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: the published finite-tree definition already covers Bass-Serre trees

Statement

Every simplicial tree is already a finite tree in the previously published sense.

Facts & Assumptions

Given: The finite-agreement theorem for simplicial trees.

[L1]

The published finite-tree notion agrees with the simplicial-tree notion only for finite oriented graphs. (For finite graphs, the simplicial-tree notion agrees with the published finite-tree notion)

Refutation

technique · direct
1.1

The bi-infinite line is a simplicial tree with infinitely many vertices, so it lies outside the finite scope named in [L1].

L1given
2.1

Therefore [L1] does not identify every simplicial tree with a published finite tree, and the statement is false.

L1step 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