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Galois homomorphism reconstruction reference
Family 031: Uchida’s conjecture for open homomorphisms of Galois groups. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Arithmetic researchers can record equivariant field embeddings corresponding to the specified open Galois homomorphisms.
Applicability and commercial boundary
Possibly infinite extensions and abstract topological groups may have no efficient input encoding; a unique embedding need not be computably cheap.
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 a restricted finite-data example and exact representation requirements.
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.