# 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](source.json).

[An integral counterexample to Gersten's conjecture](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026.pdf).