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

For Volume 1: This volume presents the complete axiomatic foundation of Discrete Geometric Physics (DGP) — a new fundamental theory in which space, time, matter, and all interactions emerge from a single geometric structure: a 26‑connected cubic lattice with the topological invariant Σw = 14. All fundamental constants are derived from the lattice geometry without empirical fitting: the gravitational constant G, the masses of elementary particles (proton, neutron, electron, Higgs boson), the gauge constants of SU(3)×SU(2)×U(1), the parameters of dark matter and dark energy, and the fundamental optical scale λ₀ = 766.490234 nm. The latter arises as a solution to a variational problem of minimising the energy of solitons and serves as a dynamic resonance centre connecting lattice geometry with atomic physics, the solar spectrum, the biological optical window, and the evolution of the Universe. Three potassium modes (766, 799, 813 nm) are introduced as a natural splitting of this fundamental resonance. The theory gives testable predictions and contains no fitting parameters (except ρ_DE, which is fixed from observations). This volume covers the full axiomatics, the bounce mechanism of the origin of time, the derivation of gauge fields, gravity, the mass spectrum, the information structure of the lattice, and cosmological consequences. For Volume 2: This volume extends Discrete Geometric Physics (DGP) to the full hierarchy of scales — from the Planck length to the size of the Universe and beyond, from chaos (N → −∞) to infinity (N → +∞). It shows that the Universe is a self‑similar hierarchical structure, where each level N generates the physical laws of the next level. The volume covers the ontological transition from the ∞‑groupoid (chaos) to structured matter, the formation of the first atoms under the selection of the fundamental spectrum λ₀, the emergence of physical laws from local lattice rules, cosmological evolution as the growth of the hierarchy level N(t), the resolution of the Hubble tension through a scale‑dependent gravitational constant, and the role of consciousness, mathematics, and ontology within the DGP framework. All parameters remain fixed geometric invariants and are not fitted. The theory gives testable predictions and opens the way to understanding the Universe as a self‑computing structure.