Matter-Space Coupling Framework: Deriving General Relativity as the IR Limit of Causal Substrate Dynamics

We present the Matter-Space Coupling Framework (MSCF), in which spacetime emerges from causal structure generated by matter-events. MSCF is not a parameterized modification of general relativity. It is an ontological proposal: matter-events and their causal relations are fundamental, and spacetime geometry is the emergent structure of those relations. The natural comparison class is not modified gravity theories, which alter GR's field equations while preserving its ontology, but programs that attempt to answer what spacetime is. The framework is built on six axioms concerning causal substrate, metric response, local covariance, holographic information scaling, causal saturation, and causal conservation. Combined with four minimal structural assumptions (locality, metric-only vacuum dynamics, second-order field equations, asymptotic flatness), we derive, not assume, that the infrared (IR) dynamics must be Einstein vacuum. The Schwarzschild and Kerr exteriors then follow as uniqueness theorems from boundary conditions. We prove an IR Selection Theorem establishing that the MSCF axioms provide the physical basis for every condition in Lovelock's classification theorem. This converts a mathematical classification ("if these conditions hold, then Einstein's equations") into a physical selection principle ("these conditions hold because spacetime is a causal substrate with these properties"). Every published alternative to Einstein's equations violates at least one condition that MSCF derives from its axioms. We prove that Newton's gravitational constant G is not a fundamental constant but a material property of the causal substrate, fully characterized by G = c³ℓ²/ℏ where ℓ is the fundamental causal length. Three theorems reduce the entire gravitational sector to one microscopic parameter. A Dimensional Obstruction Theorem establishes that ℓ* is the irreducible empirical content of gravity, playing the same role as lattice spacing in condensed matter physics. We derive the ultraviolet (UV) completion of the theory through a minimal effective action, SMSCF, within the Degenerate Higher-Order Scalar-Tensor (DHOST) class. This action uniquely determines the saturation potential V (χ) = αχ⁴ and derives the modified Friedmann equation H² ∝ ρ (1 - ρ/ρcrit), resolving the Big Bang singularity via a non-singular bounce. We prove the Substrate-Matter Unity Theorem, establishing that gradient stability is provided by matter coupling, and derive the "dressed metric" prescription for cosmological perturbations. The perturbation prescription is critical: earlier formulations using ad hoc scalar perturbation speeds (cₛ² → 0 at the bounce) produced spectra inconsistent with Planck data. The action-derived dressed metric prescription (cₛ² = cₛ, matter²) yields a qualitatively different perturbation equation. We compute the resulting primordial transfer function and confirm that the Planck-scale bounce leaves no detectable imprint on the CMB scalar power spectrum. The cosmological perturbation theory is fully derived with zero free parameters beyond ρcrit and the equation of state w. Scale separation between the Planck-density bounce and CMB wavelengths renders the bounce imprint undetectable in the scalar power spectrum, introducing no tension with Planck data. The primary falsifiable prediction is the gravitational wave echo signature. For black hole interiors, the constitutive response F (x) = 1 - x, applied to the post-horizon folding variable Φ = xg - 1, yields the resistance factor Ω (xg) = 2 - xg and determines xₘax = 2 with no free parameters (Theorem 10. 4). The same constitutive law determines the full interior metric (Theorem 10. 5), from which the Regge-Wheeler equation in the MSCF background gives a concrete, frequency-dependent echo spectrum with no remaining model inputs in the classical regime. The derivation is structurally parallel to the constitutive Friedmann derivation (Theorem 9. 5): the same response law, applied to the appropriate excitation variable in each sector, determines the dynamics uniquely. Extremal Kerr consistency (Proposition 10. 3) provides an independent consistency check. The resulting two-surface interior structure (Horizon and Inversion Barrier) predicts a unique gravitational wave echo signature. We prove the Amplitude Inversion Theorem: the second echo amplitude exceeds the first (A₂ > A₁) if and only if the horizon reflectivity satisfies 0 < R₁ < (3 - √5) /2 ≈ 0. 38, a "smoking gun" signature distinguishing MSCF from standard quantum modifications. Finally, we derive a modification to Hawking radiation from the causal saturation axiom, predicting stable Planck-mass remnants. MSCF thus provides a complete derivation chain from axioms to falsifiable experimental signatures, with the gravitational constant itself characterized as the macroscopic stiffness of the causal substrate.