Emergence of Geometry and a Gravitational Analogue from Persistent Classical Transport

This paper presents a regime-based account of the emergence of geometry and gravitational behaviour from persistent classical transport within a variational dissipative–conservative framework governed by irreversible constraint accumulation. Once stable transport paths dominate, exclusion and compatibility relations between trajectories admit an effective geometric description, with curvature arising as a measure of transport constraint rather than as a fundamental field. Gravitational behaviour is interpreted as an analogue phenomenon reflecting the organisation of persistent motion, not as a new interaction or a modification of general relativity. The contribution is explanatory and foundational, positioning geometry and gravity as downstream regime descriptions rather than fundamental ontologies, and setting the stage for a principled treatment of extreme constraint regimes such as black holes.