This work presents a unified, minimal-ontology framework in which space is modeled as a real, compressible medium governed by extended barotropic hydrodynamics with gradient elasticity. From this single dynamical system, three major physical regimes emerge without additional postulates: (i) Maxwell-type electrodynamics as the linear transverse-wave limit; (ii) screened (Yukawa-type) gravity as the hydrostatic response to density deficits; and (iii) quantum-coherent dynamics as the weak-contrast, phase-coherent limit in which the gradient-elastic term becomes equivalent to the Bohm/Bogoliubov potential. A key feature of the framework is its strict quantitative falsifiability. All observable phenomena depend on the same small set of medium parameters . These parameters cannot be adjusted independently across domains: the action scale must satisfy , the gravitational screening length and SD-core radius must satisfy , and the electromagnetic wave speed must match the barotropic derivative. Any mismatch—across interferometry, EM dispersion, gravitational profiles, or structural-defect core measurements—falsifies the model outright. The article provides a stepwise calibration and verification program (T1–T6), enabling independent determination of each parameter and a unified cross-domain consistency check. This over-constrained structure makes the theory experimentally vulnerable in a way rarely achievable in foundational physics. The manuscript is intended as a clean, self-contained reference document (v1.0) for further development, experimental evaluation, and comparison with observational data. Keywords compressible medium; structural defects; gradient elasticity; capillarity; screened gravity; Yukawa potential; finite-core solutions; emergent electrodynamics; acoustic metric; emergent quantum mechanics; Bohm potential; Bogoliubov limit; interferometry; NV centers; unified physics; continuum foundations; phase coherence; dispersion relation; analogue models; falsifiable theory.