Causal Rate Invariance: The Chain Equation and Its Consequences for Gravity, Vacuum Energy, Black Holes, the Coincidence Problem, and Strong CP

Every observation is the endpoint of a causal chain---a sequence of propagation steps and processing events connecting cause to effect, governed by $T = \sum_i (d_i/C + \tau_i)$, where $C$ is the invariant rate of causal propagation and $\tau_i$ are processing times at intermediate nodes. Five structural axioms (C0--C5) on this equation force complex-valued amplitudes, exponential propagation phases, gauge invariance, and the Born rule as theorems rather than postulates. I show that causal coherence---the requirement that the universe be one coherent causal structure despite the heterogeneity of its nodes---forces $C$ to be a universal invariant, recovering Lorentz structure without postulating it. From this framework I derive: (i)~the arrow of time as the structural asymmetry of the chain equation; (ii)~the holographic principle from chain packing at surfaces; (iii)~black hole entropy and the Hawking temperature from chain counting at event horizons; (iv)~gravity as position-dependent processing overhead in the vacuum chain structure, with the Einstein field equations $G_{\mu\nu} + \Lambda g_{\mu\nu} = (8\pi G/C^4)\,T_{\mu\nu}$ derived from the chain axioms via Lovelock's uniqueness theorem, unifying black holes, Newtonian gravity, and the modified dynamics regime as three limits of the same equation; (v)~vacuum energy density $\rho_\Lambda = H^2/(4\pi G)$, reducing the cosmological constant discrepancy from $10^{122}$ to ${\sim}3\%$ and dissolving the coincidence problem, with a new prediction that the vacuum energy is locally modified by gravitational fields; and (vi)~$\theta_\mathrm{QCD} = 0$ exactly, resolving the Strong CP problem without axions. The cosmological constant $\Lambda = 2H^2/C^2$ is not a free parameter but a derived consequence of the vacuum processing overhead, tracking $H^2$ and evolving with cosmic expansion. Each prediction is parameter-free and consistent with current observational data. The dynamical extension of this framework is presented in a companion paper