A Geometric Topology of Fiduciary Breach

Pure Mathematics → Applied Mathematical Physics of Legal Relations

Cosmos

This paper develops a rigorous mathematical framework for fiduciary breach using geometric and topological tools drawn from differential geometry, category theory, and the Coulon axiomatic system.

We represent fiduciary duty as a conservative vector field (gradient of a potential function), conduct as a parameterized path in a legal manifold, breach as violation of the differential generator D, and unchaste acts as orientation reversal (negative Jacobian determinant). Harm is quantified as temporal flux through the breach current, and remedy emerges as the unique fixed point of a contracting endomorphism.

The complaint process itself is a colimit assembly of local truth currents (witness testimony, documents, precedents) into a global proof. This synthesis transforms qualitative legal concepts into computable geometric quantities, enabling precise measurement of disloyalty and calculation of remedies.