Triadic Mesh Dynamics: A Discrete Ontology of Space Based on Oriented 2-Simplices

Triadic Mesh Dynamics (TMD) is a discrete geometric framework in which physical space is composed of independent oriented 2‑simplices (“triads”). Local orientation dynamics governed by CAG, DAG, and DAP rules give rise to emergent curvature, torsion, geodesics, matter-like topological defects, quantum-like path-sum behaviour, and gauge-like structures. Without assuming a metric, connection, or Hilbert space at the fundamental level, TMD provides a unified discrete origin for geometry, matter, time, and quantum phenomena. This preprint presents the refined formulation of TMD, its mathematical structure, emergent continuum limits, numerical simulation framework, and phenomenological predictions, together with a historical appendix documenting the original version of the theory.