Proposed
Provider proposes this result; assessment pending ↗
Observed Oct 10, 2026
Bound · version 1
Proposed cubic complex determinantal lower bound
Earlier version 1. View current version 2 →
Statement
For m ≥ 1408, every affine-linear determinant representation, including coefficientwise limits, of the complex m×m permanent has size at least m^3/(5529600e).
Assumptions
- Complex numbers; exact and border affine-linear determinantal representations.
Scope
A proposed bound in an algebraic model; does not separate VP from VNP or Boolean P from NP.
This source presents a theorem with a proposed proof. Its wording does not establish acceptance or independent mathematical review.
Evidence
Source reports
Connections
In this problem · publication v7
P versus NP →
Different statement · related variant · Proposed
This statement contributes context in its stated scope; it does not settle the canonical P versus NP question.
Relationship not independently reviewed. This concerns its use in this problem.
Sources
OpenAI · Mathematics release: complexity proposals →
- Family 108; lean/docs/108.md, PermanentCubic comparator; supporting theorem scope excludes ABP consequences → · Original passage ↗
Recorded wording
For m ≥ 1408, every affine-linear determinant representation, including coefficientwise limits, of the complex m×m permanent has size at least m^3/(5529600e).
paraphrase · Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.
OpenAI internal model; author attribution per manuscript · Project documentation · Publication date Oct 6, 2026
Source-reported preprint/project; independent mathematical assessment pending.
Complex permanent determinantal lower bound — formalization scope ↗Source-reported evidence
Revision & attribution
Source revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. Observed Oct 10, 2026.
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.
Complex permanent determinantal lower bound — formalization scope: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. Pinned provider scope document and comparator links. OpenMath has not executed the code or independently reviewed the mathematical correspondence.
History
Statement versions
Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.
Assessment history · 1
Assessments retained in these publication records. Earlier statement versions retain their own source histories.
Proposed
Provider proposes this result; assessment pending ↗
Observed Oct 10, 2026 · Source passage →
Record details
- Claim ID
- claim-pnp-permanent-proposal
- Statement version
- 1
- SHA-256
- 298b1afd3ad9eee7046acfd85d294c58cd9a6adc33280a1208e02652703c17ec