trailGao's tangent-sweep construction produces constant-Jacobian counterexamples of arbitrarily large geometric degree in every dimension greater than two
The Jacobian conjecture is false in every dimension n ≥ 3
Non-invertible constant-Jacobian polynomial self-maps of ℂ³ exist in every geometric degree at least three
Direct route through the curve-type direction field· for
The monomial-twist side conditions in Gao's tangent-sweep construction are solvable for sweep data of arbitrarily high degree in every dimension at least four
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Gallagher's July 2026 construction yields a generically d-to-one Keller map of C³ for every integer d at least three
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Gao's explicit four- and five-dimensional Keller maps F4, F5, F6, F7 have constant Jacobian determinant and generic fiber sizes 5, 10, 6 and 12
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Degenerate route through suspension of the three-dimensional family· for
A counterexample to the Jacobian conjecture in dimension n yields a counterexample in every dimension m ≥ n by adjoining identity coordinates
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claim · empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →claim page ↗︎
Gao's tangent-sweep construction produces constant-Jacobian counterexamples of arbitrarily large geometric degree in every dimension greater than two
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this rests on ↓
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