# Character variety integral-point provenance

Family 027: Potential integral density on curve character varieties. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Algebraic geometry researchers can record potential Zariski density under one number-field ring and prescribed boundary classes.

## Applicability and commercial boundary

Zariski density is not quantitative Euclidean sampling or an efficient integral point enumerator.

## Initial business decision

Research infrastructure or conditional engineering until a computable implementation, effective bounds and a recurring buyer need are demonstrated. No commercial novelty or profitability is established.

## Next verification action

Specify exact finite coordinate data and inspect an effective construction.

## Evidence scope

The catalog statement was individually reviewed. Manuscript proof and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Integral points on character varieties of curves](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Integral-points-on-character-varieties-of-curves-September-25-2026/paper.pdf).