On the Fixed-Frequency Distribution of Envelope Surface Closure Points Along the Core Line of a Stable Cylindrical Vortex
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In previous work, the envelope surface was defined as a closed three-dimensional perceptual surface whose fundamental parameters are specified by the rupa-skandha element, whose skeletal structure is constructed by the survey line spiral, and which is shaped into closure by coupling vortex curvature — its form is a long ellipsoid, tapering at both ends and expanding at the equator. This paper addresses the geometric origin of the two closure points: under the premise that the core line has finite cross-section rather than being an infinitesimal singularity, they are the natural consequence of the helical growth rate b being distributed along the core line at a fixed frequency. We prove that, at a given fixed frequency, b varies along the core line from positive to negative: the survey line spiral expands at one end, the anti-survey line spiral contracts at the other, and the zero-crossing point where b=0 corresponds to the equatorial expansion. The two closure points are not externally imposed conditions, but geometric necessities of the standing wave structure on the core line. Physical examples are discussed: the lunar South Pole-Aitken basin, the Earth-Moon vortex system, and the human heart-crown central channel model. These examples are to be understood as structural isomorphisms rather than analogies.



