ExampleConstruction: AI-generatedVerification: AI-adaptedPipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-07

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 boundary Grassmannians Gr(0,V) and Gr(dim V,V)

Example

If $\dim V = n$ , the only $0$ -plane is ${0}$ and the only $n$ -plane is $V$ , so both $Gr (0, V)$ and $Gr (n, V)$ are one point. Their Plucker spaces are $P (Λ^{0} V) = P (k)$ and $P (Λ^{n} V)$ respectively, again one point. There is no $r$ -dimensional subspace when $r < 0$ or $r > n$ , so the stipulated Grassmannian is empty in those cases.

Depends on

The Grassmannian of r-dimensional subspaces of a finite-dimensional vector space

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

4 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

J. S. Milne, Algebraic Geometry, §6m Grassmann varieties (standard reference, not scraped)