The Jacobian Conjecture
A walk down to the determinant and back up again — one main paper, and the notes that came out of writing it.
The main paper
One Formula, Many Worlds
A walk down to the determinant and back up to the broken Jacobian conjecture. Thirteen sections, twenty-two figures, and one ladder with no missing rungs.
The conjecture fell in 2026. This is the expedition that went down after it: what the determinant is actually measuring, why the schoolroom prohibition on dividing by zero is the same rule as Jacobi’s dependence alarm, and what the counterexample looks like when you stand close enough to see its shape.
The main paper is the spine. Everything below came out of writing it — a field appendix that examines the counterexample’s fiber as a single geometric object, a research note seeking expert assessment, and a one-page seed for where the ladder goes next.
The papers
Bracket and Unique MechanismA research note from the Determinant Ladder expedition — observation and programme, seeking expert assessment.
Down the NeedleA field appendix to One Formula, Many Worlds: the fiber of the counterexample as one geometric object · August 2026 · third edition