# Stable polynomial coordinate counterexample

Family 049: A stable-coordinate counterexample in four variables. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Help symbolic tools distinguish a polynomial coordinate from one that becomes a coordinate only after adjoining a variable.

## Applicability and commercial boundary

This concerns exact algebraic coordinate transformations, not an arbitrary numerical coordinate warp; fiber isomorphism alone does not supply rectifiability.

## 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 four-variable polynomial and explicit stabilization map.

## 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).

[A stable coordinate that is not a coordinate in four variables](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-stable-coordinate-that-is-not-a-coordinate-in-four-variables-October-5-2026/stable-coordinate-four-variables.pdf).