Summary. The Unified Theory of the Background (UT) treats space as a real compressible medium (“O-medium”). Matter corresponds to stable structural defects of this medium; fields are its waves and vortices; gravity emerges as a pressure-gradient effect with Yukawa-type screening that preserves the Newtonian near field while suppressing far-field tails. Linearization reproduces a Maxwell-like sector with wave speed c₀; a coherent (“quantum-limit”) regime introduces a universal action scale χ and an acoustic-metric picture for small disturbances. Two radiation branches are identified: a longitudinal (quadrupole-leading) and a transverse (vortex/Larmor-like) branch. The document is a compact theoretical map and calibration framework for subsequent lab and astrophysical tests, emphasizing falsifiability via cross-linked measurements where one calibration must explain multiple classes of data. Scope & intent. This is a working draft intended for citation and archival purposes (DOI on Zenodo) and for guiding future submissions (e.g., arXiv/journal). It consolidates postulates, neutral terminology, symbol conventions (RU/EN), module cards (MACRO/EM/Inertia/Nuclear/Quantum/Relativistic/Radiation), and a stepwise calibration roster for parameters (c₀, ρ∞, Lρ, κ, κₛ(ρ), χ). It also includes a “paradox → UT mechanism → what to test” map (entanglement, delayed choice, Bentley paradox, singularities, radiation balance) and bridge cards clarifying how UT embeds standard theories without discarding their verified predictions. Validation roadmap (high-level). Proposed checks include: dual-axis cryo-resonators (fix c₀), ring or two-path interferometers + Talbot–Lau (fix χ), screened-field quasi-statics and NV-center probes (inform κ, Lρ), Casimir-offset experiments (inform κ), and astrophysical fits to EHT shadows and galactic rotation curves (constrain Lρ and core radius). Nuclear-scale curvature stiffness κₛ(ρ) is treated as an optional module gated by clear signatures (e.g., heavy-ion EOS, Hoyle-like levels). One calibration set must co-explain multiple datasets; failure triggers a marked “off/rebuild” status for the affected module. Keywords unified theory of the background; O-medium; compressible medium; structural defect; pressure-gradient gravity; Yukawa screening; acoustic metric; Maxwell-like linearization; longitudinal radiation; vortex (transverse) radiation; calibration roster; falsifiability; screening length Lρ; capillarity κ; curvature stiffness κₛ; action scale χ; cryogenic resonator; ring interferometer; Talbot–Lau; NV centers; Casimir offset; EHT shadows; rotation curves; ringdown/Q-factor