Math RefereeAn explicit noncoordinate polynomial with affine three-space zero fibre
A polynomial zero fibre and an ambient coordinate obstruction
The proposed argument
The manuscript defines a polynomial from a cusp relation and a shifted auxiliary algebra. A local lifting lemma identifies its zero-fibre quotient with a polynomial extension of a two-variable ring. An ambient polynomial identity supplies a critical point on another fibre, and a Jacobian argument is used to rule out a coordinate. Adjoining variables gives the higher-dimensional statements; the appendix records both coordinate maps.
The reading guide describes the manuscript’s argument. Independent human assessment remains pending. Review assessments and source checks are available separately. The appendix is Appendix A in the PDF; the source map preserves its native label app:coordinates.
Reading order
- 01
Define the construction and scope
Introduce the cusp polynomials and the coordinate/zero-fibre distinction.
- 02
Establish the lifting parameter
Replace the cusp presentation by a single free polynomial parameter over the base ring.
- 03
Identify the fibre and apply the obstruction
Combine the base-algebra shift with lifting and the ambient critical-point identity.
- 04
Record explicit coordinate maps
Give the forward map, inverse map and Bezout certificate.
Follow the dependencies
Open the full map ↗Select a claim to see its prerequisites and consumers. Edge labels distinguish proof inputs, source references, background and exclusions.
Your independent assessment
Reconstruct the base-ring parametrization and the lifting lemma. Check both polynomial inverse maps, the unit-ideal identity and the ambient critical-point obstruction. Keep the zero-fibre calculation distinct from the behavior of other fibres.