In the South Andes western edge, a very active seismic contact, with earthquakes up to magnitude 9.5 and ca. 4000 km in length threatens cities and very large populations. The existence of modern seismological networks along the contact allowed the observation of unprecedented earthquake cycle characteristics, which can improve our ability to estimate earthquake hazard, a main objective of seismology. Using dimensional and similarity analysis techniques, we show precise mechanical conditions under which the earthquake generation process unfolds, and theoretically-derive a set of scaling equations linking renormalized variables. Later on, we test our theoretical results using a curated earthquake point-catalog by using gridding, box-counting, statistical bootstrap and fixed-point iteration collapse techniques. We found non-trivial scaling laws valid across multiple orders of magnitude capable of describing a complex interplay between renormalized earthquake occurrence and renormalized seismic-moment release-rate. We discuss implications in terms of small-strain and seismic-moment release-rate imposed; cutoff magnitudes, statistical properties of seismicity, how seismic cycle might be analyzed in presence of long-term correlations, seismic-moment transfer under small-strain conditions, earthquake hazard implications and tectonic status. Finally, we conclude that exponents characterizing seismicity are related through a set of scaling equations, meaning that all considered processes have very long-term correlations. The available data suggests a single power law fitting data across the western edge. These equations were obtained by an asymptotic analysis, also a cascade mechanism is proposed to explain the observed moment release behavior.