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 & AUTHOR'S NOTE (CRITICAL FOR REVIEWERS):This document represents an early-stage, raw working manuscript published explicitly to establish chronological scientific priority over the derived analytical cascades, theorems, and multi-scale coupling interfaces.The author explicitly states the following operational limitations of the current release: Manuscript Status: The text is currently undergoing rigorous manual refinement, physical dimension checks, and grammatical polishing. A finalized, highly detailed English version (v1.2) is actively being prepared for submission to peer-reviewed physics journals. Computational Architecture (Code v1.0): The embedded Python algorithms (sttm_micro_foam.py and sttm_macro_plateau.py) serve strictly as a Proof of Concept (phenomenological stochastic emulation). The complete deterministic boundary matrices, derived root system projections of the \(E₇₍₇₎\) algebra, and localized boundary condition fixes are currently recorded in the author's physical research journal and have not yet been fully compiled into the executable scripts. Future Roadmap: The upcoming deterministic supercomputing modules, incorporating genuine SPARC tabular imports and individual telescope error matrices to replace stochastic seeding, are within the immediate development pipeline for version 2.0. This draft is open for peer discussion and collaborative analysis of the multi-scale phase transitions. Keywords:Dark Matter Alternatives; 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.