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A Three-Dimensional Keller Counterexample

The map and the claim
Direct exact certificate
Structural determinant certificate
The exact three-point fiber
Determinant-one integral normalization
Binary cubics and the complete fiber description
Discriminant and behavior at infinity
Dimensions, reductions, and consequences
The plane problem after the threefold example
Exact obstructions to descending the cubic construction
Two exact plane near-models
The factorization–resultant route to the plane problem
Exact Poisson obstructions on the exceptional pseudo-plane
Focused program for dimension two
Adversarial checks and common objections
Literature and provenance audit
One map, three public descriptions
Reproducibility
Research directions
Claims and risk register
Exact SymPy verification
References

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Last updated on 2026-07-21.