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

Abstract & Research Overview

Standard theoretical models effectively utilize the continuous spacetime manifold and the scalar invariant mass metric (the kilogram) to provide predictive power across macroscopic scales. However, standard mass operates mathematically as a zero-dimensional scalar, treating absolute vacuum and localized solid structures identically. This assumption of infinite spatial continuity yields severe mathematical divergences, or singularities, as physical limits approach absolute zero ($r \rightarrow 0$).

This paper proposes a fundamental epistemological shift: mass is modeled not as an intrinsic, invariant solid substance, but rather as Topological Matrix Friction ($\Omega$). 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 purely through observational telescopic kinematics ($K = v^2r$), this framework bypasses the necessity for legacy scalar variables and anthropogenic translation constants ($\text{kg}$, $G$).

Utilizing the strict constraint mechanics of the Unitary Symmetry Law, the exact fractional operators governing structural boundary localization ($\Phi_{\mu} = 0.8$) are mathematically derived. The introduction of Dynamic Centrifugal Balancing, the non-additive Mono-System Law, and Concentric Boundary Dilution (Nested Envelopes) completely replaces classical spacetime curvature. This derives gravitational attenuation, planetary surface tension, and cosmological missing mass strictly through pure geometric constraint parameters without reverse-engineering standard constants.

Key Theoretical Pillars

• Epistemological Independence ($K_{core} = v^2r$): Bypasses the historical "Newtonian patch" of the Gravitational Constant ($G$) and the kilogram. Formulates mechanical processing rates and universe scaling entirely in pure spatial-temporal dimensions ($\text{m}^3/\text{s}^2$).
• The Unitary Symmetry Law ($\Phi_{\mu} = 0.8$): 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 ($T_D = K_{core} / 2\pi R_{obs}$): A flawless dimensional metric ($\text{m}^2/\text{s}^2$) 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. When systems fuse, the spatial matrix optimizes their macro-envelope footprint. This non-linear scaling flawlessly predicts the $\approx 5.62\times$ tension spike at galactic halos, resolving the "missing mass" illusion without hypothetical dark matter particles.
• Concentric Dilution (Nested Envelopes): Replaces the infinite $1/r^2$ 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.
• Scale-Invariant Quantization: Demonstrates that dividing macroscopic Earth kinematics by fundamental Hydrogen node kinematics natively yields the exact atomic nucleon count ($3.57 \times 10^{51}$) by perfectly canceling $G$, rendering the standard kilogram mathematically redundant.

Core Mathematical Equations

• Absolute Kinematic Processing Load: $K_{core} = (v_{orb}^2 \cdot r_{orb}) + (v_{rot}^2 \cdot R_{surface})$
• Inward Core Compression Constraint: $\Phi_{\mu} = \frac{\text{Active Core Dimensions}}{\text{Total Systemic Parameters}} = \frac{4}{5} = 0.8$
• Topological Density (Boundary Tension): $T_D = \frac{K_{core}}{2\pi R_{obs}}$
• Concentric Tension Dilution (Gravity Attenuation): $T_n = \frac{T_0}{R_n^k}$

Research Node & Collaboration

This research paper is published and archived under the open-access initiative of the Anadihilo Research Node. For further resources, code repositories, and continuous updates on discrete spatial matrix mechanics, please visit anadihilo.org.

How to Cite This Work

If you use this framework or references in your research, please cite as follows:

Dagar, N. (2026). The Systemic Mass Unit (SMU): Topological Friction, Dimensional Relativity, and the Mechanics of Discrete Localization. Zenodo preprint. doi:10.5281/zenodo.20510628