Book

Prime Multiplication as a Physical Organizing Principle develops a falsifiable framework for asking whether prime multiplicative structure can play a genuine organizing role in physical systems. Beginning from the Prime–Wilson construction, the monograph reformulates arithmetic structure through exact congruence reduction, topological coarse-graining, thermal fixed points, and finite-size scaling. Its central question is deliberately stronger than pattern recognition: when does a mathematically exact prime-structured relation survive coarse-graining, persist under thermal averaging, and produce consequences that remain distinguishable from finite-size or combinatorial artifacts? To address this, the book separates mathematical identities from physical interpretation and builds explicit tests, null limits, and reproducibility criteria around that distinction.The result is not a claim that prime multiplication has already been established as a physical law. Rather, it is a research program designed so that the hypothesis can succeed, fail, or be refined under calculation and experiment. The monograph therefore treats falsifiability not as an afterthought, but as part of the model itself.Situated at the intersection of mathematical physics, number-theoretic structure, complex systems, and computational science, the book offers a compact theoretical foundation together with a roadmap for independent numerical and physical investigation.