OG-II-06 — V — Common-Clock Evolution and Continuum Causality - Shared-clock free evolution and a conditional spin-2 criterion for common continuum cones

We construct a common-clock realization of three specified free regulators on a nonsingular D₆/H₃ cut-and-project carrier: diagonal Maxwell fields, an overlap spinor Hamiltonian and a conforming tensor system for linearized vacuum gravity. All use one spatial metric, one aligned Lorentzian principal form and the same positive Fibonacci time marks. A classification of invariant quadratic forms shows that geometry alone still permits an independent speed ratio in each sector. For the declared aligned dynamics, a shared variable-step midpoint theorem proves compact-time convergence of the reconstructed evolutions on strongly prepared finite-energy data. In the overlap sector, the conserved Hamiltonian charge defines invariant spectral subspaces whose reconstructed projectors converge to the continuum chirality projectors on all L² data. The charge-zero cutoff endpoint disappears on such prepared data; locality of the sharp chiral projection is not assumed. The physical continuum quotients have the same characteristic cone and finite propagation speed. Strong convergence therefore implies vanishing reconstructed norm outside their common expanding support. A direct paired primal–dual sampling argument supplies the Maxwell generator theorem for the original diagonal regulator; a separately defined conforming Maxwell regulator is an alternative. Detailed smooth-data space and time bounds accompany the qualitative limit. Orthogonal-cell moment and constant-flux minimization results establish separate static normalization identities. The common cone is a proved compatibility property of the specified dynamics, with equal principal propagation speeds explicitly selected. A separate conditional theorem shows how an added spin-2 interaction criterion can remove the relative-speed freedom: a specified leading soft residue, Ward decoupling and a connected family of nonzero energy-and-momentum exchanges force equal limiting speeds. Quantitative Ward defects bound speed mismatch and its contribution to free-propagation error. The interacting amplitudes required by this criterion are not constructed by the free regulators.