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The note investigates whether the established geometric structures in the 0-Sphere model necessitate the presence of torsion.

March 13, 2026Open Access

Open-Path Spinorial Transport in the 0-Sphere Model and the Status of Torsion: Holonomy Sufficiency and the Possibility of Emergent Semigroup Geometry (Structural Clarification Note)

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The note investigates whether the established geometric structures in the 0-Sphere model necessitate the presence of torsion.
Examine 4π spinorial periodicity and its implications.
Identify mechanisms for generating torsion based on the model's constraints.
Contrast non-symmetric connections with non-trivial holonomy.
4π spinorial periodicity is compatible with torsion-free SU(2) holonomy.
Ordered-path asymmetry is reflected in curvature, not affine connection.
The torsion question depends on whether arc-length is scalar or directionally distinct.

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This note examines geometric structure and torsion in the 0-Sphere model, suggesting implications for emergent geometry.

Satoshi Hanamura (2026) studied this question.

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