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The precise statements and locators cited in this P versus NP research record.
Source-reported preprint/project; independent mathematical assessment pending.
3 cited passages ↓1 problem ↓Record fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb ↓
The exact passages cited in OpenMath. Each passage identifies how its wording was recorded.
A fixed language in P requires more than 2^{A√n} depth-three OR–AND–OR gates for every fixed A > 0, at every sufficiently large input length.
Passage ID: pnp-entry-depth-three-proposal:v1
Source item: depth-three-proposal
Source record: pnp-openai@fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
For m ≥ 1408, every affine-linear determinant representation, including coefficientwise limits, of the complex m×m permanent has size at least m^3/(5529600e).
Passage ID: pnp-entry-permanent-proposal:v1
Source item: permanent-proposal
Source record: pnp-openai@fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
For every fixed ε, δ in (0,1/2), there is a deterministic polynomial-time reduction from binary 3SAT to unique games over a fixed alphabet, with completeness at least 1−ε and soundness at most δ.
Passage ID: pnp-entry-ugc-proposal:v1
Source item: ugc-proposal
Source record: pnp-openai@fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Explicit citations in versioned problem publications. A citation records a use; it does not confer proof or independent verification.
Problem publication v14
Source assessment
Proposed
Provider proposes this result; assessment pending
Restricted depth only; not a fixed n^{1/2+ε} exponent and not unrestricted circuits.
Observed Oct 10, 2026
Source assessment
Proposed
Provider proposes this result; assessment pending
A proposed bound in an algebraic model; does not separate VP from VNP or Boolean P from NP.
Observed Oct 10, 2026
Source assessment
Proposed
Provider proposes this result; assessment pending
Provider proposal for Unique Games hardness; a hardness reduction does not prove P ≠ NP.
Observed Oct 10, 2026
History
New AI-produced complexity proposals
Linked manuscripts, code and data. External proof reports, statement correspondence and OpenMath execution are separate checks.
Project notes
Source-reported evidence
Pinned provider scope document and comparator links. OpenMath has not executed the code or independently reviewed the mathematical correspondence.
Resource revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Project notes
Source-reported evidence
Pinned provider scope document and comparator links. OpenMath has not executed the code or independently reviewed the mathematical correspondence.
Resource revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Project notes
Source-reported evidence
Pinned provider scope document and comparator links. OpenMath has not executed the code or independently reviewed the mathematical correspondence.
Resource revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Source-reported evidence
Pinned provider manuscript; the proposed result has not received independent OpenMath mathematical review. See the matching formalization scope document separately.
Resource revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Source-reported evidence
Pinned provider manuscript; the proposed result has not received independent OpenMath mathematical review. See the matching formalization scope document separately.
Resource revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Source-reported evidence
Pinned provider manuscript; the proposed result has not received independent OpenMath mathematical review. See the matching formalization scope document separately.
Resource revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Recorded authorship
OpenAI internal model; author attribution per manuscript
OpenAI reports internal-model production and accompanying formalizations at mixed stages of assessment. These Claims remain proposed in this curation; external formal evidence does not become an OpenMath check.
OpenMath source records preserve exact citations. Observation dates order these records; they do not establish the latest upstream paper or proof.
OpenAI · Mathematics release: complexity proposals
Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.
Source terms ↗