Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-adaptedPipeline-generatedprecheck passjudge 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.

Lie derivative and interior product commute for all vector fields

Statement

The assertion that LXιY=ιYLX for all vector fields is false.

Facts & Assumptions

Given: The manifolds, forms, vector fields, maps, and coordinates explicitly named in the statement.

[F1]

The preceding result states that With [A,B]=AB−(−1)∣A∣∣B∣BA for homogeneous graded operators, [LX,ιY]=ι[X,Y],[LX,LY]=L[X,Y],ιXιY+ιYιX=0. (Cartan commutator identities).

Refutation

technique · direct
1.1

The Cartan commutator identity is [LX,ιY]=ι[X,Y].

F1given
2.1

For X=∂x and Y=x∂y, the bracket is ∂y, whose contraction is nonzero, so the commutator need not vanish.

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

5 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