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.
Oracle and promise conventions are distinct
Statement
A total membership oracle in Relativized complexity class fixes the answer on every query word. A promise target in Promise preserving reduction describes a collection of total completions. Correctness of a promise reduction must hold for each completion, including its arbitrary answers outside the target promise. A promised input to the caller does not by itself guarantee that the caller's queries satisfy the target promise.
Depends on
Used by
Dependency tree · two levels
6 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
- Goldreich, On Promise Problems; §1.2 following Definition1.3, p5. (standard reference, not scraped)