DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06

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.

Limit-computable functions

Definition

A total function $f : N \to N$ is limit computable when there is a total computable $g (x, s)$ such that for every $x$ the sequence $g (x, 0), g (x, 1), \dots$ is eventually constant with eventual value $f (x)$ . No computable function selecting a stabilization stage is included in this definition.

Depends on

Computable and partial computable functions

Used by

A limit approximation computed from the halting oracle Example
False: a limit-computable function has a known stabilization stage False statement
Shoenfield's limit lemma Theorem

Dependency tree · two levels

2 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

Ludovic Patey, Computability Theory, §4.7 (standard reference, not scraped)