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This master codex formally establishes Sphereology and True Sphereification as a unified, scale-invariant physical science governing spherical manifolds, multi-scale spatial curvature, boundary symmetry, and substrate lattice dynamics. For over a century, spherical geome- tries remained fragmented across optical engineering, sedimentology, topology, and general relativity. This synthesis establishes an absolute, dual-scale framework coupling global volu- metric compactness (Macro-Sphereicity, ) with localized sub-voxel boundary smoothness (Micro-Sphereocity, ) through the non-commutative Mirrored Bowtie Operator (). By standardizing the Sigma-Dot Mirrored Sphere Symbol Dot Mirrored Sphere Symbol (-), this framework eliminates spa- tial grid drag, resolves discrete lattice aliasing, and guarantees absolute geometric invariance across all continuous and discrete spatial domains.
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Neely et al. (2026) studied this question.
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