Ontology V8.4.3:From Spacetime Granularity to the Complete Action

Building on Ontology V8.4, this paper completes the key transition from a kinematic formula to a dynamical theory and systematically treats ultraviolet completeness and Lorentz violation. The main results are: (1) promoting dx to a scalar field φ=1/dx; (2) writing the kinetic and potential terms of φ; (3) writing the complete action S[g,ψ,D,φ] (with the T4.3 adjustment); (4) performing the ADM decomposition; (5) performing canonical quantization to obtain the Wheeler–DeWitt equation; (6) identifying the problem of time and proposing a dual internal-clock scheme; (7) fully treating the non-minimal f(D) coupling and proving background independence; (8) rewriting the cutoff Λ_eff=φ in a Lorentz-covariant form; (9) computing the loop divergence and showing finiteness under the covariant cutoff; (10) writing the RGE, finding a non-Gaussian fixed point, and showing asymptotic safety; (11) writing the higher-curvature operators and giving the regime of validity; (12) integrating T4 Lorentz violation: soft-violation magnitude estimate, DSR correspondence, EFT operators, and suppression mechanism; (13) clarifying the T1.3 adjustment: adding the D–matter Lorentz-violating coupling, fixing the lower bound on φ, and resolving the φ–matter coupling conflict. This paper makes clear that gravity is non-renormalizable but can be treated as an effective field theory; the covariant cutoff Λ_eff(x)=φ(x) yields finite loops; the ultraviolet is completed by asymptotic safety; Lorentz violation is soft, tiny at low energy, and consistent with experiment. φ has a lower bound φ_P=1/l_P. Keywords: spacetime granularity; scalar field φ; complete action; ADM decomposition; Wheeler–DeWitt equation; problem of time; internal clock; background independence; covariant cutoff; loop divergence; asymptotic safety; non-Gaussian fixed point; higher-curvature operators; effective field theory; Lorentz violation; doubly special relativity