The Geometric Fabric as Active Substrate Metric Rigidity, Morphic Guidance, and Topological Resonance in Quantum Phenomena

The Geometric Fabric as Active Substrate — Metric Rigidity, Morphic Guidance, and Topological Resonance in Quantum Phenomena DOI : 10.5281/zenodo.18611549 Description: This chapter presents a unified treatment of wave-particle duality and quantum entanglement within the Karabdak Unified Theory (KUT). Both phenomena are shown to emerge from a single mechanism: the active response of the Geometric Fabric to informational density, formalised through an effective impedance tensor Z_eff(I) derived from a Feynman–Vernon influence functional. The argument proceeds in four stages: (i) the Bell–CHSH–Fine impossibility results are reproduced and contextualised, establishing that local passive substrates are bounded by S ≤ 2 with irreducibly triangular correlations; (ii) a microscopic Lagrangian derivation yields the impedance modulation and a visibility function whose sigmoidal form is derived from the overdamped regime of the dissipative wave equation, with a steepness parameter expressed in measurable quantities; (iii) the non-local phase-locking mechanism (Metric Rigidity) is formulated as a topological constraint compatible with no-signalling, and the Information Saturation parameter ξ is derived from the impedance function; (iv) the framework is confronted with five cosmological scenarios — Cloud-9 RELHIC (with quantitative velocity dispersion estimate), the Bullet Cluster, CMB anomalies, galaxy rotation curves, and neutron star mergers. Five falsifiable predictions with explicit experimental protocols and falsification criteria are presented. An epistemic status convention ([DERIVED], [ANSATZ], [KNOWN], [OPEN]) is maintained throughout, with a summary table identifying what has been demonstrated and what remains open. This chapter consolidates and supersedes two prior publications: — N. Karabudak, "The Morphic Origin of Quantum Entanglement — Topological Resonance in the Geometric Fabric" (Vers. 2), DOI: 10.5281/zenodo.17911412 — N. Karabudak, "The Morphic Resolution of the Young's Slits Paradox" (Full Vers. 3), DOI: 10.5281/zenodo.17928212 Upload type: Publication / Working paper Publication date: 2026-02-11 Creators: Dr. Karabudak, Nelson (ORCID: 0009-0008-0050-4424) Keywords: Quantum Mechanics, Entanglement, Wave-Particle Duality, Bell Inequality, CHSH Bound, Metric Rigidity, Geometric Fabric, Morphic Potential, Karabdak Unified Theory, Falsifiable Predictions, Topological Resonance, Feynman–Vernon Influence Functional