Alphabeta Math
False statementConstruction: Literature-sourcedVerification: Literature-sourcedPipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06
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.

Objectwise isomorphisms X isomorphic to its double dual supply a pivotal structure

Statement

False claim. Objectwise isomorphisms X≅X∨∨ supply a pivotal structure.

Facts & Assumptions

Given: A semisimple multitensor category.

[F1]

Left and right dual objects are isomorphic objectwise (Left and right dual objects are isomorphic in a semisimple multitensor category).

[F2]

Pivotality requires coherent natural monoidal data, not objectwise existence (Objectwise double-dual isomorphisms do not supply a pivotal structure).

Refutation

technique · direct
1.1F1given

[F1] produces isomorphisms separately for objects.

2.1F1F2∎

By [F2], these need not be natural in morphisms or multiplicative under tensor product. They therefore need not form a pivotal structure.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

6 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