What does this research mean for the field?

The macroscopic density upper bound for N-dimensional sphere packing is strictly dictated by the lower bound of the algebraic norm of the torsion tensor, representing a topological equilibrium rather than a purely geometric phenomenon. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

This research aims to reformulate the sphere packing problem in N-dimensions using Rough Operator Algebra (ROA).

June 30, 2026Open Access

The Rough Index Theorem and Topological Phase Contraction in N-Dimensional Sphere Packing

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This research aims to reformulate the sphere packing problem in N-dimensions using Rough Operator Algebra (ROA).
Introduced the Seonggil Topological de Rham-Connes Map to link K-theory with cyclic cohomology.
Developed the Golden Ratio Phase Contraction Tensor to analyze microscopic torsion effects.
Derived the Rough Index Theorem for Sphere Packing focusing on algebraic norm lower bounds.
Established that the macroscopic density upper bound is determined by the algebraic norm's lower bound.
Proven that a complete topological rupture occurs beyond this algebraic norm threshold.

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Implication

Randomized trial examines packing density in N-dimensional spheres, indicating a topological equilibrium effect.

Cite This Study

lee seonggil (2026) studied this question.

synapsesocial.com/papers/6a435c8c759b888809a52ee2 https://doi.org/10.5281/zenodo.20982347

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The Rough Index Theorem and Topological Phase Contraction in N-Dimensional Sphere Packing

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Cite This Study

The Rough Index Theorem and Topological Phase Contraction in N-Dimensional Sphere Packing

Key Points

Discussion

Implication

Cite This Study

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