Curvature Thresholds as Geometric Continuity Minima: The √3 → √2 → φ Sequence in Elastic Systems under Strict Continuity
Abstract (Index version)
This preprint reports a recurring geometric regularity observed in elastic systems constrained by strict continuity and curvature minimization.
Across simulations of deformable loops under overlapping stabilizing fields, three numerical values consistently emerge as preferred configurations: √3, √2, and φ. These values appear as successive geometric regimes rather than isolated coincidences, suggesting a structured ordering of admissible curvature states.
The result is framed as a geometric continuity phenomenon, not a physical constant, and is explicitly dependent on dimensionality and topological constraints.
Within the Oxygen Octave project, this work serves as an external geometric control case, demonstrating that the same numerical sequence arises in non-chemical systems governed purely by continuity and minimization principles.
Falsifiable predictions and simulation details are provided in the full Zenodo preprint.
