Finite Closure and the Emergence of a Light-Cone Bound in a Generative Framework

We ask whether a finite, direction-independent propagation bound can be obtained from a pre-geometric generative structure rather than imposed as a spacetime postulate. To this end, we work within a strict three-layer architecture: an ontological layer specifying a minimal generative rhythm (f_0) and phase-bearing events; a generative layer formulated as a finite-degree weighted graph endowed with a discrete finite-radius update rule for phases; and a readout layer that introduces a calibration protocol mapping generative counting quantities to physical observables without modifying the underlying dynamics. The central result of this paper is a principle-to-structure implication: requiring finite-step closure decidability for every finite generative attempt implies that the one-step update rule cannot depend on arbitrarily distant degrees of freedom. In other words, unlike traditional approaches that assume locality as a dynamical input, the locality of the update rule follows as a structural necessity. More precisely, closure is formulated with a finite tolerance (ε) determined by the minimal generative rhythm, ensuring that closure detection remains well-defined within finite logical steps. This requirement implies that the generative dynamics must possess a finite influence radius, which in turn yields a discrete light-cone bound on propagation. Consequently, there exists a dimensionless maximal propagation ratio (cgen) between graph distance and logical steps. Under the natural normalization corresponding to the minimal generative unit, (cgen=1). Furthermore, if the update rule is equivariant under the automorphism group of the generative graph, the resulting propagation bound is statistically isotropic, meaning that no preferred direction exists at the generative level. Physical units appear only at the readout layer. A calibration protocol associates one logical step with a minimal temporal unit (1/f_0) and one unit of graph distance with a minimal structural length (_0). The physical speed of light then arises as [c ;=; cgen_0/1/f_0 ;=; f_0 _0 .] In this framework, the light-cone structure is not assumed geometrically but emerges as a structural consequence of finite-step closure consistency, generative locality, and graph-level symmetry. In this sense, the status of the speed of light shifts from a geometric postulate to a structural consequence of generative consistency.