Causal-Cone Saturation in Sequential Causal Growth: Independence, Clock Suppression, and Record Erasure

Abstract

A causal order fixes a conformal class and hence a maximal local cone, but it does not by itself force a massless gauge field to propagate on that cone. We formulate the difference as a saturation problem, and show first that it is real: within the regular local constitutive class, the structural hypotheses admit a one-parameter family of strictly subcausal photon cones, so the availability of a causal cone does not imply saturation. We then give dynamical mechanisms that remove the freedom. At the level of order, positive finite-support classical sequential growth exponentially suppresses persistent graded sectors whenever the highest coupling has order at least two; and transitive percolation, which lies outside that class, suppresses the wide layers a 3+1 clock requires at rate exp(−Θ(ε⁻⁶)). For quasi-gradings we isolate the regularity the argument needs, and show that without it the conclusion is false. At the level of the photon record, a one-branch phase leaves a single cone-mismatch scalar, and an explicit five-state refresh process erases it once the cumulative mixing depth diverges. The microscopic photon and causal couplings need not become equal: the differential cone disappears because their common source is erased, and the conclusion survives any smooth equivariant coarse-graining rule. A second, non-mixing closure makes the mismatch sector quantum-null under a single unitary boost, with no appeal to decoherence. The picture is conditional but sharp. Universality of limiting speeds is not saturation of the causal bound; and the observable consequence of saturation is already fixed to roughly twenty-three decimals by the absence of vacuum Cherenkov emission from ultra-high-energy cosmic rays.