What does this research mean for the field?

A proposed geometric framework demonstrates that continuous perturbations in Möbius phase loops discretize into integer holonomy winding through defect formation, with residual phases governed by a sine-Gordon-type equation. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research aims to develop a geometric framework linking continuous perturbations and integer holonomy winding through defect structures.

April 6, 2026Open Access

Neck-Distributed Holonomy and Integer Winding in Möbius Phase Loops

Key Points

This research aims to develop a geometric framework linking continuous perturbations and integer holonomy winding through defect structures.
Proposed geometric framework for analyzing loops and cycles
Utilized sine-Gordon-type equations for system phase behavior
Explored defect formation leading to independent cycles
Examined composite structures and irreducible obstruction modes
Discovered integer matching leads to full independence in cycles
Identified emergence of multi-defect networks
Demonstrated correspondence of obstruction modes to prime structures
Showed natural compatibility with SU(2)/SU(3) gauge field theory

Abstract

We propose a geometric framework in which continuous perturbations are discretised into integer holonomy winding through defect formation. Exponential neck expansion decomposes a single loop into two independent U(1) cycles on a torus, achieving full independence only at integer matching. The residual phase is governed by a sine-Gordon-type equation, driving the system toward Laplacian decoupling. Composite structures emerge as multi-defect networks, while irreducible obstruction modes correspond to primes. The construction admits a natural lift to SU(2)/SU(3) gauge fields via progressive Cartan reduction.

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Authors

Jeong Min Yeon

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Korea Aerospace University

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Neck-Distributed Holonomy and Integer Winding in Möbius Phase Loops

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Abstract

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