Empirical Evidence for a Coherence Threshold in Na-Cluster Matter-Wave Interferometry: A Δ-Gate Analysis

First empirical test of Axiom A4 (coherence threshold) against raw matter-wave interferometry data. Analysis of 95 interference scans from 170 kDa Na-cluster quantum superposition experiments (Pedalino et al. , Nature 649, 866, 2026; Zenodo dataset 10. 5281/zenodo. 17502163). The Δ-Gate sigmoid is strongly favored over standard smooth exponential onset (Δχ² = 13. 1, p < 0. 01), with fitted gate steepness w = 8. 0 and critical power Pcr = 7. 1 mW. Below Pcr, no measurable quantum visibility is observed. Additional comparison with C₇₀ fullerene thermal decoherence data confirms threshold structure (w = 15. 9), while collisional decoherence shows no threshold — physically consistent with the presence or absence of an energy threshold. Three falsification criteria provided. Part of the Δ-Gate Formalism (DOI: 10. 5281/zenodo. 19103765).