DefinitionDefinition: AI-adaptedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-12

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.

A dovetailing schedule

Definition

For each stage $s \in N$ , let $S_{s} : = {(i, t) \in N^{2} : i + t = s} .$ Inside $S_{s}$ , order the pairs lexicographically by $i$ and then by $t$ .

The sequence $S_{0}, S_{1}, S_{2}, \dots$ is the stage-sum dovetailing schedule. Running task $i$ for one more local step at each occurrence of a pair $(i, t)$ means that global stage $s$ performs exactly the finitely many local simulations whose task index and local time sum to $s$ .

Remarks

Every stage is finite, so one global stage can be completed before the next begins.
The point of the schedule is fairness: no fixed finite amount of work on a fixed task is postponed forever.

Depends on

Sequences of reals: bounded, eventually, frequently, tails, subsequences

Used by

Dependency tree · two levels

8 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

John Watrous, Introduction to the Theory of Computing, Lecture 17: More undecidable languages; reductions (standard reference, not scraped)
Jean Gallier and Jocelyn Quaintance, Introduction to the Theory of Computation: Some Notes for CIS511 (standard reference, not scraped)