Invariant Speed in the Scale- Relative SpaceTime

Building on our previous framework, A Scale-Relative Model of SpaceTime, we show how the invariant speed C emerges naturally, rather than being postulated as a fundamental constant. Time arises from monotonic scale flow, and observable spacetime geometry is defined by a scale-filtered convolution of an underlying topological substrate, with finite bandwidth reflecting the limits of observation. Together, these ingredients impose a macroscopic bound on the propagation of physical effects, corresponding to the observed speed C. This mechanism generates Lorentz-like causal structure without assuming a metric, linking temporal ordering, observables, and emergent geometry. At sub-atomic scales in the “quantum desert” fluctuations in topological superpositions can cause scale-dependent variations in C, suggesting potential signatures in early-universe cosmology and high-energy phenomena. The framework provides a minimal, coherent setting for emergent spacetime, causal structure, and invariant propagation speeds, offering insights toward emergent gravity and unified descriptions of fundamental interactions.