A Topological Unification of Matter, Dark Energy, and the Spacetime Metric

This document presents an exploratory theoretical framework in which space–time is modeled as an effective elastic medium capable of supporting stable excitations and persistent defects. In this picture, ordinary matter is associated with stable localized excitations (“nodes”), while dark matter is interpreted as defects of the underlying medium, produced when excitations fail to stabilize under strong constraints. A relaxation mechanism (“healing”) may locally reduce the gravitational effect of these defects in baryon-dense environments. The work is motivated by a qualitative generative scenario, intended as a guiding intuition rather than a validated cosmological model. The primary goal of the document is not to propose a replacement for ΛCDM, but to test whether a minimal effective translation of this idea is compatible with well-established physical constraints. In particular, the document focuses on: compatibility with precision constraints (electromagnetism, weak equivalence principle, gravitational wave speed), explicit exclusion of new long-range propagative forces coupled to charged particles, based on a detailed derivation of spectroscopic bounds (hydrogen 1S–2S transition), consistency with a minimal effective field theory description, preliminary internal coherence tests at mesoscopic and macroscopic scales (lensing and linear structure growth). All assumptions, constraints, and derivations are stated explicitly, and supporting calculations and data tables are provided as supplementary material to facilitate critical review. The author is not a professional physicist but an engineer by training, and this work is shared as a contribution for open discussion. Feedback, criticism, and identification of decisive observational or theoretical tests are explicitly encouraged.