Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-08-31
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: an unbracketed three-fold tensor product is already well defined in any monoidal category

Statement

False claim: in any monoidal category, the expression A⊗B⊗C is already a defined object before any coherence theorem is invoked.

Facts & Assumptions

Given: The bracketing discipline fixed on this page.

[L1]

Before coherence, only parenthesised tensor words are defined expressions; unbracketed strings are not yet defined (Unbracketed tensor strings are not yet defined on this page).

Refutation

technique · direct
1.1

The claim suppresses the choice between (A⊗B)⊗C and A⊗(B⊗C).

given
1.2

But [L1] says the page does not identify those expressions automatically before coherence.

L1
2.1

Therefore the claim is false.

step 1.1step 1.2∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

2 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