What does this research mean for the field?

In contracted torsionful α-surface linearity, vector-type torsion is forced-linear, pure tensor torsion is native-display linear, and mixed vector-tensor torsion produces the first selected nonlinear boundary. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This paper aims to classify contracted torsionful α-surface linearity by examining irreducible Riemann-Cartan torsion sectors.

July 4, 2026Open Access

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Irreducible Torsion Sectors and Contracted α-Surface Quadratic Residuals

HSHiroyuki Shioiri

Key Points

This paper aims to classify contracted torsionful α-surface linearity by examining irreducible Riemann-Cartan torsion sectors.
Classifying torsion sectors into representation-allowed, Esposito-selected, and expansion-recovered types.
Analyzing the linearity of vector-type, pure tensor, and mixed vector-tensor torsion.
Vector-type torsion is shown to be forced-linear.
Pure tensor torsion is native-display linear, recovered in the certified comparison layer.
Mixed vector-tensor torsion establishes the first selected nonlinear boundary.

Abstract

This paper classifies contracted torsionful αα-surface linearity by irreducible Riemann-Cartan torsion sector. It separates representation-allowed, Esposito-selected, and expansion-recovered quadratic obstructions, showing that vector-type torsion is forced-linear, pure tensor torsion is native-display linear but recovered in the certified comparison layer, and mixed vector--tensor torsion gives the first selected nonlinear boundary.

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Irreducible Torsion Sectors and Contracted α-Surface Quadratic Residuals

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Abstract

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