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.

A stable coordinate that is not a coordinate in four variables.