# Arithmetic cycle specialization provenance

Family 001: Milne’s rationality conjecture and algebraic specialization. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Arithmetic-geometry researchers can track rational pairings and single-cycle specialization across cohomology realizations.

## Applicability and commercial boundary

The dependence on family 032 and exact good-reduction hypotheses matter. An existence statement supplies no efficient cycle generator or database reconstruction algorithm.

## 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

Map every dependency and specialization hypothesis before a symbolic adapter.

## 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).

[Milne's rationality conjecture for abelian varieties](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Milnes-rationality-conjecture-for-abelian-varieties-October-7-2026/paper.pdf).