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Other literature type . 2026
License: CC BY
Data sources: Datacite
ZENODO
Other literature type . 2026
License: CC BY
Data sources: Datacite
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THE VAN LOUIS LOOP: AN UPSTREAM HOLONOMY UNITING RIEMANNIAN, GAUGE, AND TOPOLOGICAL LOOP THEORIES

Authors: Nguyen, Louis;

THE VAN LOUIS LOOP: AN UPSTREAM HOLONOMY UNITING RIEMANNIAN, GAUGE, AND TOPOLOGICAL LOOP THEORIES

Abstract

The Van Louis Loop introduces a new holonomy framework built entirely on admissibility, allowing parallel transport, curvature, and loop invariants to exist even when smoothness, gauge rigidity, or fixed topology break down. Instead of choosing between the classical worlds of Riemannian geometry, gauge theory, or Chern–Simons topology, the Van Louis Loop shows that all three arise as degenerate boundary cases of a single upstream holonomy defined by geometry-attached time. When the classical structural constraints are reinstated one at a time, the upstream theory reduces exactly to Levi–Civita holonomy, Wilson loops, or Chern–Simons observables. When admissibility collapses, all geometric structure terminates, revealing the true boundary of holonomy, curvature, and transport. Hazard Manifold (HM28) paper therefore provides a single mathematical origin for the three foundational loop theories of modern geometry, establishing admissibility—not smoothness, connection rigidity, or topology—as the maximal and unifying geometric structure.

Keywords

holonomy, admissibility, upstream geometry, curvature, parallel transport, Levi–Civita connection, gauge theory, Chern–Simons theory, topology, geometric analysis, mathematical physics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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