Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 049-01. A stable coordinate that is not a coordinate in four variables
Manuscript map · lines 3495–3504
OpenAI@2026-10-07#rem:oai-p-049-01
Authors: OpenAI. Family 049.
Title: A stable coordinate that is not a coordinate in four variables.
Abstract: We construct an explicit degree-five polynomial over ${}mathbf C$ that is not a coordinate in four variables but becomes one after adjoining a single variable. This gives a counterexample to the stable coordinate conjecture in four variables. Every fiber is isomorphic to affine three-space, yet its embedding in affine four-space is not rectifiable. Thus the example also disproves the Abhyankar–Sathaye embedding conjecture in ambient dimension four.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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