# Atypical subvariety provenance library

Family 016: Zilber–Pink in abelian varieties and the Siegel threefold. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Arithmetic geometry researchers can track finite maximal atypical structures under the specified abelian and A2 curve cases.

## Applicability and commercial boundary

Finiteness does not imply efficient enumeration or apply to arbitrary higher-dimensional Shimura subvarieties.

## 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

Inspect effective height bounds and a concrete computational example.

## 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).

[The abelian Zilber–Pink conjecture](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Abelian-Zilber-Pink-Conjecture-September-24-2026/paper.pdf).