Alphabeta Math
DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16
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 degree [K:F]=dim⁡FK of a finite field extension

Definition

Let K/F be a field extension. Scalar multiplication by F⊆K, together with addition in K, makes K an F-vector space. The extension is finite when this vector space is finite-dimensional. In that case its degree is

[K:F]:=dim⁡FK.

No numerical degree is assigned here to an infinite-dimensional extension.

Depends on

Dependency tree · 2 levels

Sources