PFUSRC‑175B: Prime Constraints on Power Exponents and Occam's Razor — The Ontological Negation of the Fourth Power by the Bottom‑Layer Minimal‑Completeness Principle

Abstract

PFUSRC‑175 has established the square power (radial latching) and the cubic power (tangential closed‑loop revolution) as the native power‑coupling channels within the 55 observational grid, and has pointed out that the fourth and higher powers belong to composite derivative structures. The PFUSRC framework advances this judgment in a more elementary manner: the order of a power itself must obey prime‑anchor constraints. The square power has order 2, the cubic power has order 3 — both 2 and 3 are primes, and are topological anchors of the bicone numerical system. The fourth power has order 4; and 4=2 ×2 is composite, a mere self‑replication of the prime 2, not an independent topological node. The dimensional‑evolution path 1 \to 2 \to 3 \to 5 \to 11 defined by PFUSRC‑002 traverses only primes; the composite number 4 does not lie within this evolutionary sequence. The PFUSRC framework extends Occam’s razor at the ontological level: do not multiply degrees of freedom beyond necessity. The bottom‑layer ontological construction must satisfy the constraints of stability, rigor, minimality, and completeness. Prime‑anchor transitions satisfy this criterion: every anchor is an indecomposable minimal unit, every transition introduces a necessary degree of freedom, and no redundancy exists. The fourth‑power iteration of the form (x^{2})^{2} is a repeated nested structure that introduces unnecessary redundancy into the ontological bottom layer; it is a contamination of the ontological layer by projection‑layer arithmetic, and should be excised by Occam’s razor.