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.

Lexicographic order on exponent tuples and the multidegree of a nonzero polynomial

Definition

For $a, b \in N^{n}$ , write $a >_{l e x} b$ when, at the first coordinate where they differ, the coordinate of $a$ is larger. This is the lexicographic order.

If $0 \neq f = \sum_{a} c_{a} x_{1}^{a_{1}} \dots x_{n}^{a_{n}} \in R [x_{1}, \dots, x_{n}]$ , its leading multidegree is the lexicographically greatest exponent tuple $a$ for which $c_{a} \neq 0$ ; the corresponding monomial and coefficient are its leading monomial and leading coefficient. The maximum exists because a polynomial has finite support.

Lexicographic order on exponent tuples and the multidegree of a nonzero polynomial

Definition

Depends on

Dependency tree · 2 levels

Sources