Systematic Proof on Necessity and Uniqueness of Original Steady-State Topology System Based on Triple Coaxial Biconic Configuration, 1→5→11 Dimensional Evolution Sequence, Prime Topology Reference Points and 55 Global Steady-State Datum Points Combined with 12:11 Universal Gauge Invariance

Most current studies in fundamental physics, higher-dimensional field theories, differential geometry and elementary number theory are established upon predefined spatial structures, fixed dimensional frameworks and preset discrete basic units. Such research paradigms cannot deduce the inherent necessity and exclusive existence of cosmic original topological structures strictly from first principles. This paper abandons all artificial presuppositions, and adopts steady-state physical constraints, the principle of least action, topological nesting laws, primitive element combination logic based on topological degree-of-freedom completeness, algebraic topological bijection isomorphism, hierarchical geometric datum point statistics and quantitative exclusive counter-evidence methods. By introducing 12:11 universal gauge invariance as one of the fundamental steady-state axioms, two independent demonstration systems with different logical paths are constructed to accomplish systematic verification of all core structural characteristics. This research rigorously verifies that the exclusive optimal original geometric configuration is the 45° triple coaxial biconic structure. Via topological fusion of original existential primitives and complete field evolution domains together with redundant dimension elimination rules, the unique dimensional evolution sequence is confirmed as 1→5→11. By establishing strict bijection isomorphism between irreducible properties of prime numbers and independent anchoring characteristics of topological nodes, it is proven that the spatial arrangement of prime topology reference points is an inevitable self-organized distribution pattern that naturally evolves toward global optimal steady states within high-dimensional original topological spaces. Following unified central orthogonal projection criteria, hierarchical classification statistics and structural failure quantitative verification confirm that the total quantity of globally self-consistent steady-state reference points is uniquely fixed at 55. All theoretical deductions reach complete global logical closure under the constraint of 12:11 universal gauge invariance, achieving unified consistency verification covering microscopic topological units and large-scale cosmic structures. All derivation processes maintain complete logical integrity, closed mathematical reasoning and sufficient exclusive validity, free from circular reasoning, subjective speculation and premature conclusion setting. Serving as the core axiomatic foundational paper of the PFUSRC theoretical system, this study consolidates the most fundamental theoretical groundwork. All subsequent extended theoretical explorations, field coupling deductions and interdisciplinary academic applications can directly cite the finalized core conclusions without repeated demonstrations on original topological principles.