When Does a Prime Mean Something? A Null-Controlled Test of Universal-Prime Structure in Three Resonant Systems

A popular claim circulating online holds that the Kordylewski dust clouds at the Earth–Moon L4 and L5 Lagrange points are conscious, plasma-based entities keeping a record of Earth. The claim stays open by any measurement. But underneath it sits a real and answerable physics question: when dust collects at a resonant point of a multi-body system, does the geometry of that resonance carry the universal-prime and golden-ratio structure that the Temporal Dynamics Framework (TDF) proposes for self-organising systems? We test this directly, with controls. Three physically distinct resonant systems are examined: the Earth–Moon–Sun L4/L5 gravitational three-body well (where the Kordylewski clouds sit), the Van Allen radiation belts (a magnetic dipole trap), and the Schumann cavity (the Earth–ionosphere electromagnetic resonator). For each, the dimensionless constants of the trapping geometry are extracted and matched against the TDF universal-prime set {2, 3, 5, 7, 11, 13} and powers of the golden ratio . The result is one clean structural signature and two clean nulls. The gravitational three-body well carries an exact, dimensionless, body-independent prime-3 signature: its equilateral geometry is , and its linear stability bound is 27 , where . The magnetic trap and the electromagnetic cavity show no comparable structure. We argue that the two nulls are the control that makes the single hit meaningful: they show the prime-3 signature is specific to three-body gravitational geometry rather than an artefact of looking. We also document the two ways a naive search deceives the investigator — unit-dependent matches and cherry-picking across a harmonic set — and show concrete examples of each from the same data. it stays open here regarding consciousness, information, or the contents of the clouds. This record holds one paper on its own and is refreshed every couple of months. The complete deposit, 10.5281/zenodo.21788037, holds every paper with its code and data and is updated first; for the newest version of this paper, go there.