We start from one postulate—an effect cannot be the cause of itself—and derive its consequences. The result is a directed acyclic graph whose causal edges carry compact \( \mathrm{U}(1) \) phases. Requiring local gauge dynamics to close on the minimal complete causal window selects a unique graph: \( \binom{5}{2} = \binom{5}{3} = 10 \), hence the complete graph \( K_5 \).

\( K_5 \) is not a spacetime brick; it is a sliding causal window. Time is continuation; space is synchronisation. Particles are stable causal motifs: charged leptons are phase defects, baryons are \( k = 3 \) closures, pions are \( k = 2 \) bridges, photons are coherent phase transport, the Higgs is the radial stiffness of causal ordering.

From this single object we derive, with no free parameters: the SM gauge group \( \mathrm{SU}(3)\times \mathrm{SU}(2)\times \mathrm{U}(1) \); the fermion spectrum \( \bar{5} \oplus 10 \) in three generations; the bare orientation coupling \( \alpha_{\text{bare}}^{-1} = |A_5| = 60 \), dressed by charged-motif loops to \( \alpha_{\mathrm{IR}}^{-1} \simeq 137.04 \); \( \sin^2 \theta_W = 0.232 \); the causal depth \( L^* = 26 \); the Higgs ratio \( \frac{m_H}{v} = \frac{3}{\sqrt{35}} \ (124.9\,\text{GeV},\,0.2\%) \); the proton radius law \( \frac{m_p r_p}{\hbar c} = 4 \ (0.04\%) \); \( \frac{m_\pi}{m_p} = \frac{1}{3\sqrt{5}} \ (0.2\%) \); the neutrino law \( \frac{\Delta m^2_{21}}{\Delta m^2_{32}} = \frac{1}{35} \); the gravitational response \( V_0 = \frac{1}{10\pi} \); the operator-level vacuum split \( \Omega_\Lambda = \frac{2}{3} \); and the dark-matter frontier relic candidate ratio \( \frac{\Omega_{\mathrm{DM}}}{\Omega_b} \simeq 5.48 \) (0.4%).

Scattering is a boundary-to-boundary response kernel on the thermodynamically selected causal skeleton; unitarity is reconstructed in the infrared stable-motif sector; Lorentz invariance emerges as the kinematics of the surviving gapless transport sector. All claims are classified as theorem, derived law, candidate, benchmark, or open structural target.