Four-Variable Jacobian Conjecture in a Topological Quantum Model of Intersecting Fields

This preprint introduces in a visual and conceptual way a model of two intersecting curved fields with a shared nucleus, whose quantized dynamics offer potential cases of the four-variable Jacobian conjecture and a nonlinear Hodge cycle.

The Kummer type geometry of the model suggests a unified framework where abstract mathematical developments like Tomita-Takesaki, Gorenstein, and Dolbeault theories, can be conceptually linked to the Jacobian, Hodge, and Riemann conjectures.

Other mathematical physics topics, like the mass gap problem, reflection positivity, the emergence of imaginary time, or t-duality, are also considered within this context.

The fields model also lays the foundation of a novel deterministic quantum atomic system with a supersymmetric dual nucleus structure of matter and mirror antimatter.