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

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.