The Geometry of Silence: Resolving the UDG Dark Matter Deficiency via Sexagesimal Phase-Locking in the $\mathcal{M}_{60}$ Manifold (Vols. I-III)

This repository contains the complete analytical framework, scientific manuscript, and supplementary technical documentation for the Sexagesimal Harmonic Algorithm (ASHM) and the López Standard applied to extragalactic kinematics. The ongoing crisis in standard ΛCDM cosmology—exemplified by the anomalous absence of dark matter in the Ultra-Diffuse Galaxies (UDGs) NGC 1052-DF2 and NGC 1052-DF4—is resolved through a deterministic, non-exotic geometric model. Instead of invoking fine-tuned particle halos or exotic dark sectors, this research demonstrates that "dark matter" signatures are emergent macroscopic manifestations of spatial geometric tension, termed Accumulated Dissonance (ΔD). This friction arises primarily from base-10 numerical truncation and rounding errors forced onto an inherently discrete, radix-60 space-time metric (the M60 Manifold). Key highlights of the uploaded manuscript:• Vol. I: Analytical foundations of the M60 manifold, velocity dispersion invariance formulas, and the zero-dissonance boundary condition.• Vol. II: Observational verification protocols mapping high-resolution spectroscopy from the W. M. Keck Observatory and sub-arcsecond astrometry from the Hubble Space Telescope (HST/ACS) into a modular, sexagesimal phase space.• Vol. III: Wide-field environmental mapping using the Dark Energy Camera Legacy Survey (DECaLS) to model dissonance transfer mechanics and phase cleansing via cosmic macro-sinks (NGC 1052). The repository includes the explicit mathematical proofs confirming that when a galactic structure crystallizes precisely atop a primary sexagesimal node, its accumulated dissonance collapses to zero (ΔD ≡ 0). Consequently, the system operates under absolute harmonic equilibrium, matching pure baryonic Newton-López dynamics without requiring speculative mass fields.