GEOMETRIC TORSION AND ORBITAL PHASE HOLONOMY A D4 (600-CELL) PROJECTION MODEL IN GLOBAL SEISMICITY

================================================================================ GEOMETRIC TORSION AND ORBITAL PHASE HOLONOMY A D4 (600-CELL) PROJECTION MODEL IN GLOBAL SEISMICITY================================================================================ Author: Lluís Morató de DalmasesDate: April 1, 2026Version: Complete Archive (v4.0)DOI: https://doi.org/10.5281/zenodo.19369125 ================================================================================ ABSTRACT================================================================================ We investigate whether global seismicity exhibits statistically significant spatialcorrelations with a geometric structure derived from the projection of the four-dimensional {3,3,5} polytope (600-cell). Using an exact construction of the H₄ rootsystem, we project the 120 vertices of the 600-cell onto the unit sphere and interpretthem as a global node set. For the full dataset (M ≥ 6, 2010-2025), no statisticallysignificant deviation from randomness is observed (p = 0.187, Z = 1.32σ). However,for high-magnitude events (M ≥ 8, 1900-2025), a weak but statistically significantdeviation is detected (p = 0.042, Z = 2.03σ). Based on this historical signal,we identify a double resonance mechanism for 2026: Phase A (August, N-120 Azores)acts as a Riemann Silence filter, followed by Phase B (October, N-056 San Francisco)as a torsional saturation rupture. Additionally, we present experimental validationof the CronNet torsional resonance at 54.545 Hz using LIGO O3 data, demonstratingcross-coherence C_xy = 0.823 between Hanford and Livingston detectors. All code and data are provided for full reproducibility. Keywords: 600-cell, H₄ symmetry, earthquake distribution, statistical geophysics, spherical geometry, torsion field, LIGO, gravitational waves, GNSS, Riemann zeros, D4 polytope, geometric projection ================================================================================ TABLE OF CONTENTS================================================================================ 1. INTRODUCTION ................................................. [Section 1]2. GEOMETRIC FRAMEWORK: THE 600-CELL ........................... [Section 2] 2.1 Vertex Generation (H₄ Root System) ...................... [2.1] 2.2 Stereographic Projection ................................ [2.2] 2.3 Node Coordinates on Earth's Sphere ...................... [2.3]3. DATA AND METHODS ............................................ [Section 3] 3.1 Seismic Data (USGS Catalog) ............................. [3.1] 3.2 Angular Distance Metric ................................. [3.2] 3.3 Random Control Distribution ............................. [3.3] 3.4 Kolmogorov-Smirnov Test ................................. [3.4]4. RESULTS: STATISTICAL ANALYSIS ............................... [Section 4] 4.1 Dataset A: M ≥ 6 (2010-2025, N = 1,482) ................ [4.1] 4.2 Dataset B: M ≥ 8 (1900-2025, N = 94) ................... [4.2] 4.3 Temporal Stability Analysis ............................. [4.3] 4.4 Bootstrap Confidence Intervals .......................... [4.4]5. DISCUSSION .................................................. [Section 5] 5.1 Absence of Global Signal ................................ [5.1] 5.2 Threshold Behavior in Extreme Events .................... [5.2] 5.3 Limitations ............................................. [5.3]6. PREDICTIVE MODEL: DOUBLE RESONANCE 2026-2027 ................ [Section 6] 6.1 Phase A: The Atlantic Trigger (August 2026) ............. [6.1] 6.2 Phase B: The Pacific Saturation (October 2026) .......... [6.2] 6.3 Secondary Window: November 2027 ........................ [6.3] 6.4 Unified Prediction Table ................................ [6.4] 6.5 Torsional Stress Function ............................... [6.5] 6.6 Model Validation Criteria ............................... [6.6]7. EXPERIMENTAL VALIDATION: CRONNET RESONANCE ................... [Section 7] 7.1 Theoretical Prediction (54.545 Hz) ...................... [7.1] 7.2 LIGO Data Analysis Methodology .......................... [7.2] 7.3 Phase Extraction via Hilbert Transform .................. [7.3] 7.4 Cross-Coherence Results ................................. [7.4] 7.5 GNSS Correlation ........................................ [7.5]8. QUATERNIONIC FRAMEWORK ...................................... [Section 8] 8.1 Angular Defect from Tetrahedral Geometry ................ [8.1] 8.2 Geometric-Planetary Torsion Model (GPTM) ................ [8.2] 8.3 Projection Factor Derivation ............................ [8.3] 8.4 Morató Equation of State ................................ [8.4]9. LUNAR GRAVITY ANALYSIS ...................................... [Section 9] 9.1 GRAIL Data and Spherical Harmonics ...................... [9.1] 9.2 Spectral Peaks and Mascon Identification ................ [9.2] 9.3 Kaula Spectrum Comparison ............................... [9.3]10. CONCLUSION ................................................. [Section 10]11. CODE ARCHIVE ............................................... [Section 11]12. REFERENCES ................................................. [Section 12]13. ACKNOWLEDGMENTS ............................................ [Section 13] ================================================================================ 1. INTRODUCTION================================================================================ Earthquake occurrence is generally understood as a consequence of tectonic stressaccumulation and release within the lithosphere [1]. While large-scale patterns suchas plate boundaries are well established, the statistical distribution of seismicevents remains complex and partially stochastic, exhibiting power-law scaling andclustering behavior [2, 3]. This work explores a complementary hypothesis: that global seismicity may exhibitweak statistical correlations with high-dimensional geometric structures.Specifically, we test whether the projection of the four-dimensional 600-cell({3,3,5}) onto the Earth's surface produces a node set that correlates withearthquake locations. The 600-cell is a regular four-dimensional polytope with 120 vertices correspondingto the H₄ root system, a structure of significant mathematical interest [4]. Itsprojection into three dimensions yields a set of points that can be mapped onto theunit sphere. While no physical mechanism is proposed, the existence of such ageometric structure raises the empirical question: do earthquake epicenters showany statistical preference for these projected locations? Importantly, we do not assume a deterministic mechanism. The objective is strictlyto evaluate whether any statistically detectable spatial modulation exists, usingrigorous statistical methods and transparent reporting of both positive and nullresults. Additionally, we extend this framework to: • The detection of a torsional resonance at 54.545 Hz in LIGO data, • The formulation of a quaternionic geometric-harmonic model for solar-terrestrial dynamics, • The development of the Geometric-Planetary Torsion Model (GPTM) for orbital perturbations, • A spectral analysis of lunar mass concentrations using GRAIL data. ================================================================================ 2. GEOMETRIC FRAMEWORK: THE 600-CELL================================================================================ 2.1 Vertex Generation (H₄ Root System) The 600-cell is a regular four-dimensional polytope with 120 vertices, 720 edges,and 600 tetrahedral cells. Its vertices correspond to the H₄ root system, which canbe constructed using the golden ratio φ = (1 + √5)/2 ≈ 1.618034. The 120 vertices can be generated from the following coordinate sets: (1) 8 vertices: (±1, 0, 0, 0) and all permutations (2) 16 vertices: (±½, ±½, ±½, ±½) (all sign combinations) (3) 96 vertices: (0, ±½, ±φ/2, ±1/(2φ)) and all even permutations All vertices are normalized to lie on the unit 3-sphere: |v| = 1. 2.2 Stereographic Projection We project each vertex v ∈ ℝ⁴ into three dimensions using stereographic projectionfrom the south pole: x = v₁ / (1 - v₄) y = v₂ / (1 - v₄) z = v₃ / (1 - v₄) The resulting points are then normalized onto the unit sphere: n_k = (x, y, z) / √(x² + y² + z²), k = 1, …, 120 This defines a set of 120 nodes on the sphere. 2.3 Node Coordinates on Earth's Sphere For comparison with earthquake epicenters, we convert each node to sphericalcoordinates: Longitude: θ_k = arctan2(y_k, x_k) (degrees) Latitude: φ_k = arcsin(z_k) (degrees) The complete set of 120 node coordinates (latitude, longitude) is provided in thesupplementary material. ================================================================================ 3. DATA AND METHODS================================================================================ 3.1 Seismic Data (USGS Catalog) Two datasets are analyzed, obtained from the USGS Earthquake Catalog [5]: Dataset A (Global seismicity): M ≥ 6, 2010-2025, N = 1,482 events. This provides a modern, well-detected sample of moderate-to-large earthquakes. Dataset B (Large earthquakes): M ≥ 8, 1900-2025, N = 94 events. This captures the most extreme seismic events, albeit with a smaller sample size. For each earthquake, epicenter coordinates (latitude λ, longitude θ) are useddirectly. 3.2 Angular Distance Metric For each earthquake i with spherical coordinates (φ_i, θ_i) and each node k withcoordinates (φ_k, θ_k), we compute the angular distance: d_ik = arccos[ sin φ_i sin φ_k + cos φ_i cos φ_k cos(θ_i - θ_k) ] The nearest-neighbor distance for earthquake i is: d_i = min_k d_ik This yields a distribution of nearest-neighbor