The Systemic Mass Unit (SMU): Topological Friction, Dimensional Relativity, and the Mechanics of Discrete Localization

Abstract Standard theoretical models effectively utilize the continuous spacetime manifold and the scalar invariant mass metric (the kilogram) to provide exceptional predictive power across macroscopic scales. However, standard mass operates mathematically as a zero-dimensional scalar, treating absolute vacuum and localized structures identically. This assumption of infinite spatial continuity inevitably yields severe mathematical divergences, or singularities, as physical limits approach zero (r → 0). This paper proposes a formal mathematical evolution of these foundational models. Classical physics is preserved as a highly successful, special localized case, while mass is geometrically recontextualized not merely as an intrinsic, invariant solid substance, but rather as Topological Matrix Friction (Ω). This friction represents the active structural tension required to maintain localized geometric boundaries against a discrete spatial matrix (i = 10-4) during the collapse of a continuous wave-state. By analyzing mechanics through purely observational telescopic kinematics (K = v2r), this framework provides a context in which highly successful legacy variables and constants (kg, G) are rigorously identified as emergent macroscopic scaling translations. Utilizing the constraint mechanics of the Unitary Symmetry Law, the exact fractional operators governing structural boundary localization (Φμ = 0.8, ΦE = 1.25) are mathematically derived from first principles. A thermodynamic bridge connects this pure geometry to physical pressure. The subsequent application of the non-additive Mono-System Law provides a deterministic topological resolution to cosmological missing mass anomalies, illustrating that they function as emergent non-linear geometric variances of scale rather than necessitating unobserved particulate dark matter. Key Theoretical Pillars Epistemological Independence (K = v2r): Bypasses the historical "Newtonian patch" of the Gravitational Constant (G) and the kilogram by formulating mechanical processing rates entirely in pure spatial-temporal dimensions (m3/s2). The Unitary Symmetry Law (Φμ = 0.8): Establishes the scale-invariant core-boundary equilibrium natively from constraint topology, locking the internal micro-compression factor to exactly 4/5 (0.8). Topological Density (TD = Kcore / 2πRobs): A flawless dimensional metric (m2/s2) measuring absolute Kinematic Potential Tension on a localized boundary, replacing classical continuum volume averaging. Dynamic Centrifugal Balancing: Proves mathematically that axial rotation aggressively inflates surface topological tension, natively explaining Earth's higher surface gravity relative to Venus without relying on invisible internal mass density variations. The Mono-System Law (Resolving Dark Matter): Proves the non-additive nature of topological boundaries, where the spatial matrix optimizes the macro-envelope footprint. This non-linear scaling flawlessly predicts the ≈5.62× tension spike at galactic halos, resolving the "missing mass" illusion without hypothetical dark matter particles. Concentric Dilution (Nested Envelopes): Replaces the infinite 1/r2 spacetime rubber-sheet curvature with a discrete, cascading sequence of invisible macro-boundaries. Topological tension dilutes geometrically across these layers, granting temporal stability to localized matter. Core Mathematical Equations Absolute Kinematic Processing Load: K = v2r Inward Core Compression Constraint: Φμ = (Active Core Dimensions / Total Systemic Parameters) = 4/5 = 0.8 Topological Density (Boundary Tension): TD = Kcore / 2πRobs Concentric Tension Dilution: Tn = T0 / Rnk How to Cite This Work Dagar, N. (2026). The Systemic Mass Unit (SMU): Topological Friction, Dimensional Relativity, and the Mechanics of Discrete Localization. Zenodo preprint. doi:10.5281/zenodo.21095787 Research Node Published under the open-access initiative of the Anadihilo Research Node.