Spacetime Elastic-Curvature Heterogeneity as a Falsifiable Alternative to Particle Dark Matter: A Symmetry-Breaking Scalar-Field Framework for the Cosmic Cloud-Desert Morphology

The particle dark matter paradigm remains observationally unconfirmed at the laboratory level despite four decades of direct-detection effort, motivating continued exploration of field-theoretic alternatives. This paper develops the Spacetime Elastic-Curvature Domain (SECD) hypothesis: a real scalar order-parameter field κ(x), undergoing spontaneous breaking of a discrete Z2 symmetry in the early universe, conformally modulates the effective gravitational coupling and freezes into a percolating network of high-coupling "cloud" domains and low-coupling "desert" domains via a Kibble-type causal quench. We derive the model from an explicit action, obtain and rigorously verify an exact analytic domain-wall (kink) solution, perform dimensional and limiting-case analysis, and numerically implement the associated non-conserved (Model-A) phase-ordering dynamics. All reported numerical results are produced by an executed, unit-tested, fully reproducible Python pipeline (fixed seed) operating on a synthetic realization of the proposed mechanism; no observational catalogue is fitted in this paper, and this limitation is stated explicitly and repeatedly rather than obscured. The simulation reproduces a percolating cloud/desert morphology and a curvature-driven coarsening law with a numerically extracted growth exponent z = 0.353 ± 0.026 (Monte Carlo over 12 realizations), below the asymptotic Model-A expectation z = 1/2; a dedicated resolution study attributes part of this deviation to lattice pinning of sub-resolved domain walls and demonstrates partial convergence toward z = 1/2 with improved grid resolution, a limitation we discuss candidly rather than mask. One-at-a-time and approximate variance-based (correlation-ratio) sensitivity analyses identify the vacuum expectation value v and gradient-energy coefficient as the dominant controls on the emergent domain scale. We derive concrete, falsifiable observational discriminants, including a predicted absence of coherent weak-lensing convergence in desert-classified void interiors, a specific domain-wall-network gravitational-wave background scaling, and a bound from the classical cosmological domain-wall problem that constrains the wall tension to values that, we show, are difficult to reconcile simultaneously with Mpc-scale correlation lengths and the observed CMB temperature anisotropy budget, and we present this tension as a first-order theoretical challenge to the hypothesis rather than resolving it by fiat. We conclude that the SECD framework is a mathematically well-posed, internally falsifiable, and computationally reproducible research program, but that it does not, in its present form, constitute an empirically competitive alternative to ΛCDM, and we specify the numerical simulations and observational campaigns required to change that assessment.