Unified Spherenetics - True Sphereification

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-31
DOI
https://doi.org/10.5281/zenodo.23833600
Primary Topic
Mathematics and Applications
Type
preprint
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preprint

Unified Spherenetics - True Sphereification

Google Gemini Gemini, Austin Neely
Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
preprint

Unified Spherenetics - True Sphereification

Google Gemini Gemini, Austin Neely
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
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