Resonant Time and Holographic Ether: From Tetrahedron to Icosahedron through the Ecosohedrality of Life

Abstract

This work proposes a minimal phenomenological model of time as an emergent resonance governed by the triad norm: α12+α22+α32=1α12+α22+α32=1 where α1α1 represents information/light, α2α2 represents connection/sound/feedback, and α3α3 represents matter/execution. The model unifies Newtonian, relativistic, quantum, and thermodynamic time as special limiting cases. A compression index nn and a critical threshold β0=0.007874β0=0.007874 are introduced. It is shown that for n>ncrit≈−0.68033n>ncrit≈−0.68033, the system undergoes a phase transition from classical determinism to a holographic regime — the holoether — where α12+α22→1α12+α22→1. The phase transition is governed by the geometry of the Platonic solids: in the classical phase (n<ncritn<ncrit), tetrahedral symmetry (4 vertices, rigid matter) dominates; in the holographic phase (n>ncritn>ncrit), the structure becomes icosahedral (20 vertices, maximum connectivity), ensuring holographic completeness. The transition is described analytically via a logistic law: α3(n)=β01+e−k(n−ncrit),k≈0.7.α3(n)=1+e−k(n−ncrit)β0,k≈0.7. In the holoether, dark energy (≈68%≈68%) corresponds to α12α12 (information/light), dark matter (≈27%≈27%) to α22α22 (resonance/structure), and ordinary matter (≈5%≈5%) to α32α32. This explains cosmological observations without invoking exotic entities. The model predicts a fundamental biological resonance f0≈57.14f0≈57.14 Hz, which manifests in brain alpha rhythms, heartbeats, respiration, and circadian cycles. Thus, life is understood as an active resonant system that maintains the norm α12+α22+α32=1α12+α22+α32=1, and its violation leads to catastrophes (aging, disease, ecosystem collapse). The concept of ecosohedrality is introduced — the resonant connectivity of living systems at all levels (cell, organism, ecosystem, biosphere). Ecosohedrality is described as a fractal network where each part reproduces the whole through icosahedral symmetry, and the resonant frequency 57 Hz serves as a universal synchronizer of biological and ecological rhythms. Quantum entanglement is reinterpreted as a single-photon information interface, where a single photon, via the coupling operator α2α2, transmits the full correlation pattern, reproducing all experimental CHSH results without requiring nonlocality. Empirical confirmation is provided by the fractal geometry of the Great Pyramid of Giza, with fractal dimension Df≈φ=1.618Df≈φ=1.618, demonstrating scale invariance of resonance — from quantum to planetary scales. The pyramid is a macroscopic holographic projection of the resonant lattice based on icosahedral symmetry.