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.
Why a hierarchy separation is not a P versus NP separation
Example
The separation compares two deterministic resource budgets. It says nothing about whether a language with a polynomial verifier has a deterministic polynomial-time decider.
Facts & Assumptions
Given: the displayed deterministic hierarchy separation.
Verification
Both sides of the displayed separation are deterministic classes.
The missing assertion would have to relate one of these classes to , whose definition allows existential certificates. No such relation appears in the hierarchy statement, so the P-versus-NP implication is absent.
Depends on
Used by
Nothing in the library uses this result yet.
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
- Arora and Barak, Computational Complexity, Chapter 3 (standard reference, not scraped)