Causality Wave Theory: Wave-Particle Duality, Galaxy Dynamics, and Gravitational Decoherence from Causal Chain Mechanics

Building on the Causal Rate Invariance (CRI) framework (Paper~I), in which every observation is the endpoint of a causal chain with transit time $T = \sum_i (d_i/C + \tau_i)$, I develop Causality Wave Theory (CWT)---the dynamical theory of how causal influence propagates as waves, interacts at nodes, and completes as discrete outcomes. Five structural axioms (C0--C5) on the chain equation force the complex amplitude structure, exponential propagation phases, the Born rule, and the Feynman path integral as consequences rather than imports. CWT identifies: (i)~Feynman diagrams as literal causal chain diagrams, with the path integral emerging as the sum over chain topologies and the Feynman rules derived from sequential composition and gauge structure; (ii)~wave-particle duality as the distinction between in-progress and completed chains; (iii)~quantum measurement as chain completion at a macroscopic node; (iv)~entanglement as a branching chain with a shared origin; (v)~quantum tunneling traversal time $\tau = d/C$ independent of barrier height; (vi)~fermions as processing nodes and bosons as propagation chains, with spin-1/2 forced by the complex amplitude structure under Lorentz symmetry and the spin-statistics theorem derived from exchange topology in $3{+}1$ dimensions; (vii)~the baryonic Tully-Fisher relation with slope exactly~4 from the chain completion threshold $a_0 = CH_0$, with the observed normalization $a_0^\mathrm{obs} \approx CH_0/(2\pi)$ derived from phase averaging of incomplete gravitational cycles and the BTFR itself emerging as a self-consistency fixed-point equation; and (viii)~temperature-dependent gravitational decoherence arising from processing dissipation at gravitational chain nodes. Observational evidence supports each testable prediction.