Exact Fourier algorithm feasibility worksheet

Family 130: Exact Fourier transforms below $n\log n$. First review, 8 October 2026.

Problem and potential new use

Algebraic-complexity researchers can study exact circuits and uniform programs with a formally stated asymptotic saving.

Applicability and commercial boundary

The saving is 10^-13 in an exact-complex model with unrestricted coefficients, not a floating-point FFT speed claim.

Initial business decision

Defer performance product. Buyer demand and profitability remain hypotheses. This first pass does not establish a validated commercial market.

Next verification action

Inspect numerical conditioning, preparation costs and any finite-size construction before a hardware proposal.

Evidence scope

Catalog statement reviewed; inspect linked opportunity dossier for any deeper source review. This record alone does not establish full manuscript or proof verification.

Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata for the exact manuscripts and available scope notes.