DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedverified 2026-09-26 (gpt-6-sol)

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.

MajoritySAT

Definition

On a well-formed NumberSAT input consisting of a formula $φ$ and a declared list $(x_{1}, \dots, x_{n})$ of $n$ distinct variables, MajoritySAT asks whether $N u m b e r S A T (φ, (x_{1}, \dots, x_{n})) > 2^{n - 1}$ . Every malformed input is a no-instance. At $n = 0$ the inequality is equivalent to the empty assignment satisfying $φ$ .

Depends on

NumberSAT

Used by

MajoritySAT is PP-complete Corollary

Dependency tree · one level

1 result within one dependency step 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: A Modern Approach (standard reference, not scraped)
Lance Fortnow, Counting Complexity (standard reference, not scraped)