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.

Reconstruction of Function Fields from Mod-ℓ Milnor K-Theory.