# Big integer asymptotic feasibility worksheet

Family 109: Integer multiplication below $`n\log n`$. First review, 8 October 2026.

## Problem and potential new use

A commercialization team can quantify the extremely small log-exponent saving and avoid treating it as an immediate arithmetic optimization.

## Applicability and commercial boundary

The saving parameter is 2^-182 in a finite-tape bit model. No practical crossover or library benchmark is established.

## 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

Read the machine construction and document precisely which constants would be needed to estimate crossover.

## 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.