Causal Phase Compatibility as a Candidate Microscopic Foundation for Emergent Gravity

This working paper proposes the Theory of Gravity by Causal-Update Deficit (TG-DAC) as a constitutive framework for gravitational theories with finite curvature response. The starting point is relational: local clocks, causal transmission and physical evolution are compared through their proper-time structure, while gravity is interpreted as the geometry of constrained causal updating. General relativity is retained as the low-occupation, approximately linear regime. The new postulate is that the realized geometrical response has finite capacity. Introducing a normalized occupation variable s and residual capacity a, with s² + a² = 1, leads to the constitutive relation j = s/√(1−s²). In static spherical symmetry, defining ψ=(1−f)/r² and s=ℓ*²ψ yields an algebraic response law whose exact solution is asymptotically Schwarzschild and approaches a de Sitter core. The associated Ricci and Kretschmann invariants remain finite at the centre, while the first exterior correction appears at order r⁻⁷. The constitutive function selects a binomial sequence for an infinite odd-curvature expansion, suggesting a physical selection principle for non-polynomial quasi-topological gravity. A matrix-valued extension acting on curvature modes is proposed, and it is shown that a curvature tower beginning at cubic order does not modify the quadratic Minkowski action. The general covariant completion, curved-background stability, rotation, collapse and cosmology remain open. TG-DAC is therefore presented as a candidate constitutive principle and research programme, not as an empirically validated replacement for general relativity.