Ontological Mapping of Mathematics for Cross-Disciplinary Linkages and Research

A map of how major areas of mathematics connect (arithmetic, spectral theory, algebraic geometry, category theory, dynamics and mathematical physics), built both as an expository survey and as an executable typed graph. Nodes are kinds of mathematical object; edges are bridges, each labeled three ways: whether the correspondence is a theorem, a conjecture or a heuristic; whether its computation is exact or only numerically tested; and whether the underlying statement has a machine-checked proof. Each executable step tests itself against an independent reference. The engine computes the L-function of an elliptic curve from point counts and matches published values of L(E,1) and L′(E,1), rejects a wrong conductor by two independent checks, reproduces the Gauss–Kuzmin–Wirsing eigenvalue, recovers the Martin–Odlyzko–Wolfram cycle structure of cellular automaton rule 90, and returns the Hilbert–Pólya problem as an open question rather than an answer. This record contains the manuscript (PDF, version 4) and the Python source code of the engine with tests (zip). AI assistance in preparing this work is disclosed in the acknowledgments.