Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 130-02. Finite tensor savings and exact Fourier circuits
Manuscript map · lines 4935–4944
OpenAI@2026-10-07#rem:oai-p-130-02
Authors: OpenAI. Family 130.
Title: Finite tensor savings and exact Fourier circuits.
Abstract: We construct exact nonuniform Fourier circuits of size $o(n{}log n)$ along an unbounded sequence of lengths, counting every addition, subtraction, and scalar multiplication. This refutes the ${}Omega(n{}log n)$ lower bound in the unrestricted complex linear-circuit model. The construction uses a finite tensor saving: a tensor power of some invertible nonmonomial complex matrix can be computed with fewer matrix calls than the standard tensor-axis algorithm on the same coordinates, when invertible monomial maps are allowed freely between calls.
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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