Special Theory of Dark Matter (STDM): Theory of Non-Local Planckian Nodes and Macroscopic Topological Projection

Title of Preprint: Special Theory of Dark Matter (STDM): Theory of Non-Local Planckian Nodes and Macroscopic Topological Projection (Working Manuscript / Version 1. 1) Abstract: This paper presents the foundational mathematical framework of the Macroscopic Topological Projection (MTO) formalism, which aims to resolve the global cosmological and galactic-scale constraints (such as the core-cusp problem and flat rotation curves) through the intrinsic quantum elasticity of the spacetime fabric, entirely eliminating the need for hypothetical non-baryonic dark matter particles. Utilizing non-commutative geometry (Alain Connes spectral triad) and deformation quantization (Maxim Kontsevich integration), we describe the sub-Planckian vacuum space as a highly entangled Yang-Mills gauge network governed by the exceptional Lie group \ (E₇ (₇) \). Via the Witten-Kontsevich bridge, the topological vacuum invariants (Jones polynomials) are shown to be strictly isomorphic to the generalized tau-functions of the infinite integrable Kadomtsev-Petviashvili (KP-2) hierarchy. METHODOLOGICAL DISCLAIMER Macroscopic Topological Projection; Integrable Systems; Kadomtsev–Petviashvili Hierarchy; Non-Commutative Geometry; Exceptional Lie Groups; SPARC Database; Open Science. Code Availability: The foundational DSP analyzer and primary instrumental framework that yielded the core empirical breakthroughs for the STDM model is open-source and available at: https: //github. com/alekssan8183269-lang/stdm-topological-framework. The continuous density distributions derived via multi-scale 21D vacuum shear tomography strongly demonstrate a coherent wave-like (gravitational) topology rather than localized non-baryonic particles. These critical visual and numerical markers established the empirical baseline for shifting the dark matter paradigm toward the intrinsic quantum elasticity of the spacetime fabric. - Completed the high-precision academic translation of Part I (Sections 1. 1 to 2. 9 & Appendix A) into the comprehensive English framework under the Physical Review style format. - Fully translated the Theoretical Reviewer's Guide, the analytical derivation of Milgrom's constant a0, and the multi-scale gauge reduction cascade. - Fixed minor typographical layout artifacts and verified the strict LaTeX compilation parameters for all underlying vector equations.