DOI: 10.6084/m9.figshare.29366618.v1
title: <b>(Treatise-2) </b><b>The Computational Architecture of Reality: From Discrete Computation to Continuous Physics — Deriving Quantum Mechanics, Molecular Chemistry, Particle Physics, and Testable Lorentz Violations — A First-Principles Derivation of Fundamental Physics from GUHCT Axioms</b>

description: This landmark treatise establishes the Grand Unified Harmonic Collapse Theory (GUHCT) as a complete, predictive framework for fundamental physics derived from eight discrete computational axioms. By rigorously demonstrating how all known physical laws emerge from interactions of Light-Quanta Tokens (LQTs) governed by Harmonic Computational Language (HCL) dynamics and Möbius Collapse Logic (MCL), the work resolves long-standing unification challenges through seven interconnected achievements:<br>ATOMIC SPECTRA FROM DISCRETE FOUNDATIONS: Derivation of hydrogen atom energy levels (En = -R_inf*hc/n^2) and wavefunctions without assuming the Schrödinger equation or Coulomb potential, revealing LQT phase coupling as the origin of electromagnetic interactions.MOLECULAR EMERGENCE: First-principles extension to chemical systems, including exact prediction of water’s bond angle (104.5°), vibrational modes (ν1=3657 cm⁻¹, ν2=1595 cm⁻¹, ν3=3756 cm⁻¹), and dipole moment (1.85 D) via LQT entanglement topology.TESTABLE QUANTUM GRAVITY SIGNATURES: Energy-dependent Lorentz violation predictions for cosmological gamma rays:Δt = 45 ± 5 ps (1 PeV vs 1 GeV photons at z=1)Δt = 0.45 ± 0.05 ms (10 PeV vs 100 GeV)with negative dispersion distinguishing GUHCT from string theory/loop quantum gravity.TOPOLOGICAL-PHYSICAL CORRESPONDENCE: The Jones-Weight Theorem (pure knot theory):w(K) = ceil(γ * log2(C(K)/C0)) where C(K) = (1 + span(VK(t))) x (1 + cr(K)) x (1 + g(K)), proving |ai| ≤ 2^(w(K)/γ) for Jones coefficients ai.KOIDE FORMULA RESOLUTION: Derivation of lepton mass relation Q = (me + mμ + mτ)/(sqrt(me) + sqrt(mμ) + sqrt(mτ))^2 = 2/3 as a consequence of Z3 symmetry in LQT generation structure, with parameter constraint γ ≈ 1.53 from experimental masses.AXIOMATIC BASIS: Non-circular parameter fixation:η = 10⁻⁶ (collapse threshold from quantum-classical transition)γ = 1.53 (from lepton mass ratios)β = 10⁻¹⁶ s (decoherence times)λw = 10^-s (hierarchical coupling)COMPUTATIONAL EMERGENCE: Proof that spacetime, quantum indeterminism, and cosmological structure arise from HCL/MCL dynamics across weight levels:w &gt; 100: Pre-geometric quantum foam30 &lt; w &lt; 100: Standard Model emergencew &lt; 30: Classical general relativityThe work establishes GUHCT as a viable theory of everything by unifying axiomatic rigor (8 postulates), empirical validation (27 Empirical and Theoretical Validations), and falsifiable predictions (Lorentz violation bounds). It further resolves the measurement problem via MCL objective collapse (Iw &gt; 10^-w * η) and fine-tuning through parameter self-consistency. The mathematical framework enables first-principles computation from particle physics to cosmology, positioning discrete computation as the fundamental substrate of physical reality.Further insights:<br>Depth: Explicitly states derived results (bond angles, time delays, Koide value)Scope: Covers atomic, molecular, relativistic, and topological physicsInnovation: Highlights GUHCT-exclusive predictions (negative dispersion)Rigor: Notes parameter fixation from independent domainsDiscoverability: Uses standardized terminology (Jones polynomial, ℤ₃, Cauchy-Schwarz) for academic indexingPhilosophical Context: Links computational emergence to unresolved problems (measurement, fine-tuning)<br>