PFUSRC-00 and PFUSRC-002 (New Prime Number Theory) have completed the static topological proof: based on 55 global reference points and prime node distribution, the 45° 11-dimensional triple coaxial bicone is the unique steady-state manifold structure of the universe. These works demonstrate the necessity of topological form but do not establish dynamic stress transmission rules adapted to high-dimensional manifolds. Theoretical contradiction: The upper cone region of the large bicone generates a convergent stress field driven by the cross-sectional area difference ΔA. Stress must be transmitted along the generatrix to the waist to achieve global topological closure. However, primes as discrete topological anchors have inherent numerical gaps. If convergence pressure were borne solely by isolated discrete nodes, high-density regions (galaxy cluster cores, large-scale structure nodes) would exhibit stress singularities and jagged density distributions — contradicting astronomical observations of smooth density profiles. This paper proposes a smooth convergence mechanism for the upper cone as the dynamical completion of the PFUSRC static proof: 1. The two small bicones are 4D helical surfaces (prime net). Primes are no longer isolated anchor points but continuous teeth on the helical surface (density ~1/ln n). As the helical surfaces rotate, the teeth mesh continuously without gaps. This paper provides the embedding map φ: P → S, density matching conditions, and the correspondence between prime gaps gₖ and surface generatrix stretching ds/dk = f (gₖ). 2. 3-5-53 forms an elastic triangle (three-point support). 3 (waist) and 5 (apex) are fixed boundary anchor points; 53 is a high-order internal prime cursor (representative example, not unique). The three points are connected by elastic lines, forming dynamic rigidity. Cursor 53 slides along the generatrix: near 5 (flattened triangle, expansion bias) ; near 3 (stretched triangle, contraction bias). The sliding range is constrained by the 55 reference point generatrix coordinates; deformation magnitude is bounded by the 12/11 damping ratio. 3. Bidirectional closed-loop dynamical transmission: The inner elastic triangle homogenizes longitudinal/radial pressure perturbations; the outer helical surfaces continuously mesh to transmit tangential stress; a reverse return channel from the waist back to the upper cone (elastic recovery + surface rebound + global closure constraint) is added, forming a self-consistent cycle compatible with the PFUSRC-018 "Living Universe" bidirectional evolution axiom. This paper presents complete two-layer coupled dynamical equations, explicitly dependent on the 55 and 12/11 invariants, and derives a testable steady-state solution (waist-to-upper-cone stress ratio ≈ 8. 09). Testable predictions: - Projection of 4D helical surfaces produces helical density modulation with characteristic wavelength λₕelix = (2π Rwaist / tan45°) × (12/11) ^ (±1), detectable via weak gravitational lensing power spectrum phase (Euclid/LSST). - Prime gaps linearly couple to helical meshing phase slips, producing identifiable phase jump sequences in the two-point correlation function of large-scale structure. - The position of cursor 53 couples to spatial fluctuations of the local Hubble parameter, testable via redshift-space distortion. - Ground-based three-point support optical experiments can verify the stress-smoothing effect (distortion suppression ≥70%) as auxiliary validation of cross-scale extension. This paper is the final dynamical piece of PFUSRC-00 and PFUSRC-002 (New Prime Number Theory), advancing the static topological existence proof to a computable, falsifiable dynamical transmission model. The fundamental contradiction between discrete prime anchoring and continuous smooth convergence now has a unified geometric and dynamical interpretation.
Zhenmin Wang (Tue,) studied this question.
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