Emergent Scalar Screening from a Rotational Knot Geometry

We report the emergence of a sharp, invariant critical transition arising purely from a rotational knot geometry, without introducing a fundamental scalar field or explicit microscopic dissipation. Using a large ensemble of loop-level observables generated from a chiral Kerr-like knot construction, we identify a universal screening transition separating pre- and post-critical regimes. When capture rates derived from multiple independent observables are expressed in a collapsed coordinate, the resulting curves collapse onto a single universal profile characterized by a logistic onset with a well-defined location and width. This collapse persists across distinct gate variables, capture definitions, and sector partitions, demonstrating strong invariance with respect to observable choice and parameterization. Permutation and shuffle controls destroy the collapse, confirming that the transition is not a statistical artifact or binning effect. The results indicate that scalar-like screening behavior can emerge as a collective geometric property of rotational knot ensembles, rather than as a fundamental field. These findings motivate further investigation into how matter degrees of freedom may couple to such emergent geometric screening structures.