PFUSRC-00: Supplementary Proofs for the Biconical Ontology

This paper is an independent supplementary paper to PFUSRC-00. PFUSRC-00 has rigorously proved from first principles the 45° triple coaxial bicone, the 1→5→11 dimensional evolution sequence, the spatial arrangement of prime topology reference points, the 55 global steady-state datum points, and the 12: 11 universal gauge invariance. Building on this foundation, this paper provides further exclusive arguments and refinements for the four core derivations: (1) 45° Angle: Through inequality analysis showing that vᵣ > vᵦ leads to tearing and vᵣ < vᵦ leads to collapse, combined with Axiom 2 (shear-free deformation) and Axiom 3 (elimination of redundant dimensions), it is proved that vᵣ = vᵦ is the unique steady-state condition, hence θ = 45° is the unique solution. (2) 1→5→11 Dimensional Sequence: It is argued why three 5-dimensional units are required (determined by the triple nested structure), why the eliminated dimension is 4 (dimension of the common subspace), and why the 5-dimensional intermediate state cannot be skipped (local self-sustenance requires it). The sequence is proved to be the unique inevitable evolutionary chain. (3) Necessity of Prime Nodes: The variational derivation of ρ (n) ~ 1/ln n from Axiom 4 is supplemented. The three mechanisms of composite node instability are refined. The stratification into boundary anchor points (small primes 2, 3, 5, 7) and internal flow points (primes ≥ 11) is clarified. (4) 55 Global Datum Points: The symmetry of the inner and outer layers (19=19), the fewer constraints on the middle layer (17), the completeness of the five-fold node classification, and the dual relationship 55 = 5 × 11 with the dimensional sequence are demonstrated. All supplementary arguments are consistent with the original PFUSRC-00 and involve no contradiction. They serve to strengthen and close the original derivations. All conclusions remain falsifiable, with falsification criteria identical to those of PFUSRC-00.