1/f Noise as a Macroscopic Signature of Recursive Time in Topological Space-Networks

The ubiquitous presence of 1/f noise (flicker noise) across electronic systems, biological processes, and astrophysical radiation remains one of the most stubborn anomalies in modern physics. Because classical physics treats time as a linear series of independent Markovian events, it cannot adequately explain how systems "remember" distant past states in such a scale-invariant manner. In this paper, we apply the Entropic-Resistance model, which describes spacetime as a discrete, algorithmically expanding graph, and time as a recursive relaxation process. We demonstrate that 1/f electronic noise is not a thermodynamic defect, but the natural tension-decay of the mediating topological network. Due to the mechanism of recursive time, the size of local topological knots (Volume Deficits) and their relaxation times are inversely proportional, generating the 1/f spectrum purely from geometric constraints. This framework bridges quantum network topology and macroscopic information theory, offering new perspectives for neuromorphic computing and AI hardware design.