Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 108-01. A cubic lower bound for border determinantal complexity of the permanent
Manuscript map · lines 4595–4604
OpenAI@2026-10-07#rem:oai-p-108-01
Authors: OpenAI. Family 108.
Title: A cubic lower bound for border determinantal complexity of the permanent.
Abstract: We prove that the complex border determinantal complexity of the $m{}times m$ permanent is ${}Omega(m{}3)$, allowing arbitrary affine-linear determinant representations and coefficientwise limits. It also gives cubic lower bounds for exact determinantal complexity and for the numbers of vertices and edges in affine-linear algebraic branching programs, including coefficientwise limits with a fixed vertex or edge budget.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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