# 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](source.json) for the exact manuscripts and available scope notes.