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

MESSAGE TO THE CURATORS OF THE HARVARD–SMITHSONIAN CENTER FOR ASTROPHYSICS ZENODO COMMUNITY Dear Curators, I respectfully submit for your consideration a theoretical chapter entitled "The Geometric Fabric as Active Substrate — Metric Rigidity, Morphic Guidance, and Topological Resonance in Quantum Phenomena," which proposes a unified mechanism for wave-particle duality and quantum entanglement. I wish to be transparent about the nature and scope of this work from the outset. The central proposal is that the geometric substrate underlying spacetime responds actively to informational density through an effective impedance, and that this single mechanism accounts for both the interference suppression observed in double-slit experiments and the Bell-inequality violations observed in entanglement experiments. The impedance tensor and the resulting visibility function are derived from a Lagrangian formulation with Feynman–Vernon influence functional — not postulated. The sigmoidal visibility profile follows analytically from the underdamped-to-overdamped transition of the dissipative wave equation, and its steepness parameter is expressed in terms of experimentally accessible quantities. I am equally transparent about what has not yet been derived. The non-local phase-locking mechanism (Metric Rigidity) is formulated as a topological constraint with a demonstrated no-signalling property, but its full derivation from the substrate topology remains an open problem. The mixing function governing the transition from local to quantum correlations is presented as a first-order approximation; the exact form requires solving the impedance-modulated wave equation in the entangled-pair geometry. These and four further open problems are explicitly catalogued in the manuscript, together with an Epistemic Status Summary table that marks every result as [DERIVED], [ANSATZ], [KNOWN], or [OPEN]. The chapter generates five falsifiable predictions, each with an explicit experimental protocol and a specific falsification criterion. Of particular relevance to the astrophysical community: (1) A quantitative prediction for the velocity dispersion of Cloud-9 RELHIC (σ_v < 25 km/s, versus the ΛCDM virial expectation of 50–70 km/s), testable via 21 cm emission line-width measurements. (2) A cored coherence-density profile for galaxy dark matter haloes, addressing the cusp-core problem, with the caveat that the functional form of σ(r) is not yet derived from first principles. (3) A high-frequency spectral modulation in neutron star merger gravitational wave signals, potentially detectable by next-generation observatories. I make no claim that this work is complete. It is a framework under construction, presented with what I believe is sufficient rigour and sufficient honesty to merit scrutiny. The predictions are on the table; the experiments are feasible; the falsification criteria are explicit. I submit this work in the conviction that science advances through exposure to the most demanding criticism, and I can think of no more demanding forum than yours. I am an independent researcher without institutional affiliation. My prior publications in this programme are available on Zenodo under DOIs 10.5281/zenodo.17911412, 10.5281/zenodo.17928212, and 10.5281/zenodo.17866719. My ORCID is 0009-0008-0050-4424. Zenodo - Harvard Smitsonian Center for Asyrophysic DOI : 10.5281/zenodo.18612504 I welcome any questions, objections, or requests for clarification. With respect, Nelson Karabudak - Independent Researcher nelson.karabudak@gmail.com