Paper 57G: VSI–3 — Cross-band Persistence as a Conditional Organizer-Scale Signature A governance-grade persistence test following VSI–1 (stability) and VSI–2 (localization) in PRIMER fields

Paper 57G introduces VSI-3, a governance-grade visibility KPI that measures cross-band persistence in JWST PRIMER catalogs. Each object is assigned a continuous persistence score P∈[0,1]P\in[0,1]P∈[0,1] derived from rank-consistency of short-band flux ordering across F090W, F115W, and F150W. We test whether persistence is conditionally associated with a local-load proxy WWW (foreground neighbor counts in (θ,Δz)(\theta,\Delta z)(θ,Δz) geometry) under deterministic survey-window controls and governed blocked-permutation nulls with centered two-sided p-values. Reporting follows the VSI program posture: WBIN0 is treated as preregistered sensitivity, while WBIN6 is treated as explicit null hardening. At the preregistered organizer-scale operating point (θ,Δz)=(2.0′,0.50)(\theta,\Delta z)=(2.0',0.50)(θ,Δz)=(2.0′,0.50), PRIMER–UDS under WBIN6 is a clean null, constraining universality. In PRIMER–COSMOS, a bounded persistence channel is detectable under WBIN0 with the operating point as the strongest grid cell, while the WBIN6-hardened grid collapses to sub-threshold deviations, consistent with intentional extinguishability under conservative exchangeability. Together with VSI-1 (conditional incidence) and VSI-2 (suppressed dominance), VSI-3 completes a governance-grade discriminator ladder consistent with a field-conditional, organizer-linked visibility channel in which distributed persistence can emerge without peak-dominant concentration. All results are self-producing under a strict artifact contract with a complete run manifest.