DefinitionDefinition: Literature-sourcedProof: AI-generatedjudge pass (z-ai/glm-5.2)audited 2026-07-31

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.

Universal net: eventually in every subset or eventually in its complement

Definition

A net $x : D \to X$ is universal if, for every subset $S \subseteq X$ , it is eventually in $S$ or eventually in $X ∖ S$ .

The two alternatives cannot both occur: directedness would give an index after both thresholds, whose value would belong to the empty intersection $S \cap (X ∖ S)$ .

Depends on

A net is eventually or frequently in a subset of its codomain

Universal net: eventually in every subset or eventually in its complement

Definition

Depends on

Dependency tree · 2 levels

Sources