Mathematical Abstraction of the Theory of Manifold Interfaces

This paper presents the mathematical abstraction of the Theory ofManifold Interfaces. Philosophical, cognitive, and metaphysical termsare relegated to the level of interpretation, while the formal core is de-fined through state sets, relations, boundary structures, transitions, in-terfaces, paths, flows, patterns, order preservation, losses, conductivity,and integrity. The central technical maneuver consists of defining an in-terface as a boundary-indexed transition, of which a function is a specialcase. The document contains definitions, axioms, propositions, proofs,and a categorical extension suitable for preprint publication.