DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-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.

Oracle-c.e. completeness

Definition

An $A$ -c.e. set $K$ is $A$ -c.e.-complete when for every $A$ -c.e. set $W$ there is a total $A$ -computable function $f$ such that $n \in W ⟺ f (n) \in K .$ We write this $W \leq_{m}^{A} K$ .

Depends on

Relative computability and relative enumerability

Used by

Relative halting is oracle-c.e.-complete Theorem

Dependency tree · one level

1 result within one dependency step 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

Ludovic Patey, Computability Theory, §4.2 (standard reference, not scraped)