# Polynomial-difference avoidance reference

Family 182: Power savings for intersective polynomial differences and prime arguments. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Additive-combinatorics researchers can track density savings for intersective polynomial differences and separately prime arguments.

## Applicability and commercial boundary

Modular-root assumptions and polynomial-specific constants are strong; the claim is not a general anomaly detector or efficient set construction.

## Initial business decision

Research or conditional engineering only until an effective implementation and a recurring buyer problem are identified. No commercial demand or profitability is established. Where a direct product bridge is weak, the legitimate use is a research reference or evidence adapter, rather than a new standalone company.

## Next verification action

Identify an effective polynomial example and check its modular hypotheses.

## Evidence scope

The catalog statement was individually reviewed. The manuscript proof and selected formal statement have not yet been compared in depth for this family. No independent proof verification was run. Pinned source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[A power saving for intersective polynomial differences with an exponent depending only on the degree](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-power-saving-for-intersective-polynomial-differences-with-an-exponent-depending-only-on-the-degree-October-5-2026/power-saving-intersective-polynomial-differences.pdf).