Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-generatedPipeline-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-01
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: naturality of the long exact sequence follows without checking the connecting square

Statement

Naturality of the long exact sequence follows without checking the connecting square.

Facts & Assumptions

Given: A morphism of short exact sequences of complexes.

[A1]

The statement refuted is: naturality of the long exact sequence follows without checking the connecting square.

[L1]

The connecting square itself requires a separate naturality theorem (Naturality of the homology connecting morphism).

[L2]

The long exact ladder is natural only after that connecting square is included (The long exact homology sequence is natural).

Refutation

technique · direct
1.1A1L1givenalgebra

The ordinary homology squares commute formally, but [L1] shows that the square involving the connecting morphisms is an additional theorem rather than an automatic byproduct.

2.1A1L1L2step 1.1algebra∎

Because [L2] depends on that separate connecting-square result, [A1] omits a necessary part of the proof of naturality. Therefore [A1] is false.

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