Group isomorphism is a fully mature, universally accepted, and rigorously validated mathematical framework that strips away superficial symbols, nomenclature, and representational differences to reveal the essential, invariant algebraic structure underlying any formal system. By imposing bijection and operation‑preserving mapping, group isomorphism rigorously identifies structural equivalence between systems that may appear distinct in outward form. This paper employs the well‑established theory of group isomorphism as an authoritative mathematical foundation to rigorously justify, verify, and validate the original PFUS Double‑Cone Frustum Unified System V14.0 proposed by the author. This work adheres strictly to the standard academic logical chain: posing core problems – solving core problems – Proving core propositions. First, it identifies six fundamental crises in contemporary physics and cosmology: the lack of a self‑sufficient and closed ontological foundation, pervasive logical non‑closure, the irreconcilable incompatibility between quantum mechanics and general relativity, the elusive nature of dark matter and dark energy, the absence of rigorous proof for cosmic structural uniqueness, and the underutilization of structuralism in unification paradigms. Second, it demonstrates that the PFUS system comprehensively resolves all these dilemmas. Third, using group isomorphism as the core tool, this paper rigorously proves that the PFUS system satisfies strict structural invariance, geometric uniqueness, rigid dimension evolution, high‑dimensional isomorphic projection, and the consistent structural unification of gravity and quantum theory.
Zhenmin Wang (2026) studied this question.