# Function-field reconstruction formal adapter

Family 009: Function-field reconstruction from Milnor K-theory and Galois data. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Arithmetic researchers can map Milnor K-theory or abelian-by-central Galois data to the correct field/constant reconstruction statement.

## Applicability and commercial boundary

Characteristic matching changes whether one recovers a perfect closure or the original field. Abstract group data may have no practical finite encoding or efficient 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

Specify exact input representation and a finite test example before proposing software reconstruction.

## 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).

[Reconstruction of Function Fields from Mod-ℓ Milnor K-Theory](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Reconstruction-of-Function-Fields-from-Mod-ell-Milnor-K-Theory-October-5-2026/mod-ell-bogomolov-pop.pdf).