# Coarse assembly counterexample ledger

Family 307: Failure of rational injectivity for maximal coarse assembly. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Record rational injectivity failure for assembly maps of specified bounded-degree graph coarse disjoint unions.

## Applicability and commercial boundary

Infinite coarse unions and infinite-order kernel classes are not ordinary finite graph adjacency singularity.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.

## Next verification action

Extract the graph sequence and exact assembly witness.

## Evidence scope

The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Failure of rational injectivity for maximal coarse assembly](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Failure-of-rational-injectivity-for-maximal-coarse-assembly-October-5-2026/paper.pdf).