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K-theory localization information-loss fixture
Family 209: Integral counterexamples to Gersten’s conjecture. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Algebra researchers can test the false universal injectivity assumption when passing specified ramified local rings to fraction fields.
Applicability and commercial boundary
The degrees-three/five mixed-characteristic examples do not imply every localization loses information or constitute ordinary file/data loss.
Initial business decision
Research reference or conditional symbolic/verification engineering. No practical implementation, recurring buyer need or profitability has been demonstrated; a weak business bridge is explicitly deferred.
Next verification action
Extract the explicit rings and nonzero classes with exact symbolic witnesses.
Evidence scope
The catalog statement was individually reviewed. Main-paper proof, construction effectiveness and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.