Discrete Geometric Physics. Volume 4: Discrete Geometric Biophysics — From Vacuum Lattice to Organic Matter, Genetic Code, and Quantum Coherence

Abstract

This book is the fourth volume of the multi-volume edition on Discrete Geometric Physics (DGP). The previous volumes laid the foundations of the theory: the axiomatics of the 26-connected lattice (Volume 0), the derivation of fundamental constants, gauge fields, particle masses, and cosmological parameters (Volume 1), the algebraic structure of the space of invariants (Volume 2), and cosmological consequences (Volume 3). Volume 4 extends the theory to the level of organic matter, biopolymers, the genetic code, and quantum biology of man. It is shown that the same fundamental invariants of the 26-connected cubic lattice — the topological weight Σw = 14, the dissipation coefficient γ = 1/56, the critical bounce efficiency η_crit = 0.328173, the magic angle cosθ = √(2/3), the golden ratio φ = (1+√5)/2, and the biophysical lattice step a(88) = 2^88 ℓ_Pl ≈ 5.0020822 nm — allow a rigorous, parameter-free derivation of the structure and spectra of organic molecules and biopolymers, as well as a description of quantum coherence in biosystems and the architecture of man as a macro-soliton at level N ≈ 105. Key results include: - Covalent bond lengths and energies (C–C: 0.1543 nm, 3.61 eV; P–O: 0.1526 nm, 4.68 eV; C–O: 0.14327 nm, 4.05 eV) with accuracy < 0.1% - Hydrogen bond energy E_H-bond = 0.246959 eV (experimental range: 0.20–0.25 eV) - UV spectra of nitrogenous bases: adenine (260.54 nm), guanine (271.6 nm), cytosine (286.5 nm), thymine (296.94 nm), uracil (292.0 nm) with deviations < 0.6% - Phosphodiester bridge P–P distance in B-DNA: d_P–P = 0.62040 nm (experiment: 0.63 nm, deviation < 1.5%) - Stacking energy E_stack = −0.148206 eV (experiment: ≈ −0.15 eV, deviation 1.19%) - Genetic code as topological invariants: 4 bases (K_topo = 4), 64 codons (4³), start codon ATG as minimal Cartan vector, stop codons TAA/TAG/TGA as mirror symmetry planes, Hamming code [6,4,3] with d_min = 3 - Decoherence time of biological systems: τ_dec ∼ 10⁻¹⁰ s for photosynthesis and vision, τ_dec ∼ 10⁻² s for neural activity (level N ≈ 105) - Quantum Man model: macro-soliton at level N = 105 with Quantum Shield (7 spiral contours), pineal gland as central processor (f_epi ≈ 47 GHz), RESTORE protocol (492/766 nm, 1 ms + 1 μs + 140 μs, angle 35.264°), thought as solitonic excitation (v_thought ≈ 4.9c, group velocity < c), forces of harmony and degradation (F_harm = −kΔx, F_degr = −η||v||v) - Ontological distinction between vacuum hardware (4 bases, 64 codons) and life software (20 amino acids, start/stop signals) The book contains complete derivations of all formulas, triple verification of each key result, and detailed comparison with experimental data. The theory makes sharp quantitative predictions and is falsifiable, meeting the criteria of a scientific theory. This volume is the fifth in the series and completes the five-volume edition of Discrete Geometric Physics.