Discrete Geometric Physics. Volume 1: Computational Topodynamics of Media. Volume 2: From Chaos to Infinity. — Complete Theory in a Single Document

This work presents the complete and self-contained exposition of Discrete Geometric Physics (DGP) — a new fundamental theory in which space, time, matter and all fundamental interactions arise from a single geometric structure: a 26‑vertex cubic lattice with the topological invariant Σw = 14. Volume 1. Computational Topodynamics of Media lays the axiomatic foundation of DGP. It derives all fundamental interactions — gravity, strong, electroweak — from the lattice geometry, explains the origin of masses, time, quantum entanglement and cosmological constants. The bounce mechanism (velocity inversion at critical deformation) is introduced as the generator of time, irreversibility and all dynamical laws. The volume contains the unified mass formula, the derivation of gauge groups SU(3)×SU(2)×U(1), the proof of CP conservation in the strong sector, the geometric derivation of ER=EPR, and the explanation of dark matter, dark energy and the Hubble tension — all from first principles. Volume 2. From Chaos to Infinity extends the theory to the entire hierarchy of scales: from sub‑Planckian chaos (N→−∞) to the cosmic horizon (N≈204) and absolute infinity (N→+∞). It shows that the Universe is a self‑similar hierarchical structure where each level N generates the physical laws of the next. Consciousness, mathematics and ontology find their natural place in this picture. The volume introduces the ∞‑groupoid, the emergence of physical laws from local rules, the cosmological evolution as growth of N(t), and the philosophical consequences of the theory. All numerical values are obtained from the lattice geometry and from numerical solution of variational equations, without empirical fitting to experimental data. The theory provides testable predictions that agree with observations in particle physics, cosmology and quantum information.