Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-05
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.
The annihilator bundle of a distribution
Definition
Let be a smooth distribution on . Its annihilator bundle is the subset
Equivalently, the fibre over is the annihilator subspace .
Depends on
- Smooth distributions on a manifold
- A smooth distribution is exactly a locally framed constant-rank family of tangent spaces
- Dual and Hom vector bundles
- The annihilator $U^\circ\leq V^*$ of $U\leq V$ and the preannihilator ${}^\circ S\leq V$ of $S\leq V^*$
- Assuming countable choice, the cotangent bundle has a canonical smooth 2n-manifold structure
Used by
Dependency tree · two levels
20 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
- John M. Lee, Introduction to Smooth Manifolds, 2nd ed. (standard reference, not scraped)
- Will J. Merry, Differential Geometry (standard reference, not scraped)