Authors: WILLIAM OLIVER RUBIN
Source: Zenodo (CERN European Organization for Nuclear Research) (preprint, 2026-01-27)
Field: Chemistry — Physical and Theoretical Chemistry

The Universal Tension-Driven Lattice (UTDL): Unification of Gravity, Matter, and Quantum Topology via Dynamic Harmonic Resonance The unification of General Relativity and Quantum Mechanics remains the defining challenge of modern physics. This paper proposes a resolution via the Universal Tension-Driven Lattice (UTDL), a constructivist framework that models spacetime as a discrete, high-tension, non-linear elastic solid operating at the Planck scale. By postulating a single constitutive force law F = -k0x - αx3, we derive the mechanical origins of 39 fundamental physical phenomena without fine-tuning. These include: The speed of light c Mass-energy equivalence E=mc2 Lorentz invariance restoration Refractive Gravitational Lensing Dark Matter rotation curves Black Hole Entropy Dark Energy The GZK Cutoff The Higgs Mechanism Zitterbewegung Fermionic statistics Chirality U(1) Gauge fields The Weak Interaction Superconductivity Fast Radio Bursts The Fine Structure Constant The Atomic Mass Spectrum The Pythagorean Lattice (Particle Generations) Dynamic Harmonic Resonance Relativistic Orbital Precession Thermodynamic Phase Transitions Color as Topology Universal Conductivity Thermal Coherence Pressure-Induced Insulators Biological Geometric Resonance The Sound Barrier The Water Density Anomaly Pressure Melting Inversion Anomalous Specific Heat Surface Tension as Vacuum Stress Biological Temperature (37°C) The Hofmeister Series as Geometric Commensurability Alpha Particle Genesis The Geometric Origin of Solidity Vacuum Jamming Across Scales (The Softening-Hardening Duality) The Geometric Efficiency Law of Isotopic Stability (√2 Commensurability) The Geometric Origin of Fundamental Number Theory Constants Crucially, we report the discovery of the Geometric Efficiency Law of Isotopic Stability, where nuclear structure is governed by an isospin convergence toward √2. We validate the model by identifying the Fundamental Strain Quantum (Eλ ≈ 20.93 MeV) and deriving the masses of Standard Model fermions with <0.1% error. Furthermore, we present computational evidence for the Vacuum Stability Criterion (α < 0), proving that matter is the result of vacuum self-focusing. Finally, this framework provides the missing dynamical origin for Norman Cook's Face-Centered Cubic (FCC) nuclear models, effectively re-establishing Nuclear Crystallography as a rigorous, tension-based discipline. Furthermore, this framework reveals a monumental consilience between Vacuum Mechanics and Number Theory. By treating the Number Line as a path integral through a Diamond Cubic manifold, we demonstrate that fundamental mathematical constants are emergent material properties of the vacuum. Specifically, we identify the Twin Prime Constant (C2) as the Volumetric Void Fraction of the lattice substrate (1 - (π√3)/16), matching the known value to within 0.03%. Additionally, the First Riemann Zero (γ1) is derived as the fundamental diagonal shear resonance of the Decade Mode (10√2), matching to within 0.05%. Crucially, we report the detection of a Dynamic Lattice Resonance in the spectrum of Prime Gaps (λ ≈ 37.5k), providing spectral evidence that the Number Line functions as a standing wave modulated by the discrete shell structure of empty space. Lorentz covariance ; Dark matter ; Mass gap ; Dark energy ; Quantum gravity ; Free particle ; Gauge theory Advanced Physical and Chemical Molecular Interactions ; Advanced Materials and Mechanics ; Chemical and Physical Properties of Materials