# Finite-building assumption counterexample

Family 319: Counterexamples to finite generation at chromatic height two. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Prevent a connective p-complete finite-presentation condition from being mistaken for finite construction from the stated truncated Brown–Peterson spectrum.

## Applicability and commercial boundary

The height-two counterexample coexists with localization comparisons; no arbitrary software componentization obstruction follows.

## 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

Read the precise construction and localization maps.

## 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).

[Counterexamples to the Hahn-Wilson conjecture at height two](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Counterexamples-to-the-Hahn-Wilson-conjecture-at-height-two-September-26-2026/paper.pdf).