A natural geometric rigidity index for equatorial localization on the sphere in highest-weight spherical harmonics is exactly a Wallis partial product, recovering π via the correspondence principle in the large-quantum-number limit.
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Emergence of $\pi$ from Equatorial Quantum Localization
A natural geometric rigidity index for equatorial localization on the sphere in highest-weight spherical harmonics is exactly a Wallis partial product, recovering π via the correspondence principle in the large-quantum-number limit.