Topological Substrate Mechanics (TSM) 2.1 A Predictive Fractional-Substrate Framework for Emergent Dark Matter

Title: Topological Substrate Mechanics 2.1: A Fractional-Operator Framework for Emergent Dark Matter Resource Type: Preprint / Technical Report Authors: Baggott, Brandyn Abstract: This paper introduces Topological Substrate Mechanics (TSM) 2.1, a covariant modified gravity framework that interprets dark matter phenomena as an emergent property of a nonlocal gravitational substrate rather than a beyond-standard-model particle species. Central to the framework is the application of a fractional d'Alembertian operator, ^α (with α ≈ 0.675), which characterizes the spectral dimension of the gravitational vacuum. We demonstrate that this fractional scaling provides a topological origin for the observed 5.1:1 dark-to-baryonic mass ratio, derived via entropic scaling relations in a 2.7-dimensional substrate manifold. This process, termed "Superfluid Mitosis," describes the secondary distributed tension gradients induced by baryonic density. The framework incorporates a density-triggered screening mechanism to ensure consistency with General Relativity in high-curvature environments, such as the Solar System. Preliminary results indicate that the model naturally recovers the Baryonic Tully-Fisher Relation (BTFR) and provides a mechanism for resolving the S₈ and H₀ tensions through scale-dependent growth Geff(k). We address theoretical stability through a spectral representation that bypasses Ostrogradsky instabilities and discuss the model's potential for falsification via upcoming CMB and LSS surveys.