Alphabeta MathHow 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.
The Church-Turing thesis
Definition
The Church-Turing thesis is the informal claim that every effectively calculable procedure can be carried out by a Turing machine. Equivalently, every effectively calculable partial function between a finitely encoded domain and codomain is computable in the sense of Partial functions computed by a machine under fixed encodings.
Remarks
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This is a thesis relating an informal pre-mathematical notion, "effective calculability," to a formal model of computation.
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Because one side of the claim is informal, the thesis is not itself a theorem of the formal Turing-machine definition.
Depends on
Used by
Dependency tree · two levels
4 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
- A. M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem (standard reference, not scraped)
- Richard Zach, Sets, Logic, Computation: An Open Introduction to Metalogic (standard reference, not scraped)
- Charles Brubaker and Lance Fortnow, Church-Turing Thesis lesson notes (standard reference, not scraped)