Implementing Gate A4 on Laboratory Plasma Circuits and Space-Plasma Field-Aligned Current Events (QMU/APM): An Event-Catalog Protocol for Triple-Proxy Impedance Consistency

Abstract This companion implementation paper operationalizes the QMU/APM multi-proxy impedance gate (Gate A4) as an event-catalog protocol for (i) laboratory plasma circuits and (ii) space-plasma field-aligned current (FAC) events. The test is falsifiable: within a regime bin, does the closure impedance extracted from the port variables (Phi, I) co-vary consistently with two independent proxy routes to the same QMU impedance unit resn, up to regime-level calibration offsets? Ledger anchor and port domain (QMU-only) The protocol is ledger-first and QMU-only. It anchors the analysis on the propagation identity (LedgerOne): Aᵤ\, curl=Fq^2C^2 Port variables are defined by: : = E_\, d\, I: =dQdt The event-level closure impedance is: I=R^\, resn\, R^: =^I^{} Gate A4 (implementation form) Gate A4 compares three dimensionless impedances, each normalized by resn: Z₁^: =/Iresn Z₂^: =chds₄₅₅, ₌₅ₗ₃_₄₅₅resn Z₃^: =indc₄₅₅, ₌₂ₔₑ_₄₅₅resn ₁₂: = Z₁^- Z₂^\, ₁₃: = Z₁^- Z₃^\, ₂₃: = Z₂^- Z₃^ Within each regime bin, Gate A4 passes when these residuals are bounded by a small dispersion after subtracting per-bin offsets (calibration constants), and that dispersion is small relative to cross-regime variation in Z₁^. Robustness prefilters (mandatory) This paper treats Gates A1–A3 as compulsory filters before any A4 claim. A1 (extraction robustness): R^ must be stable under an explicit analysis-setting ensemble S (windowing, filtering, mapping conventions, quadrature variants), quantified by median absolute deviation (MAD). A2 (segmentation stability): when distributed transmission and localized closure intervals are identifiable, Z₃₋^ must be stable (small MAD) or reproducibly multi-modal across event classes. A3 (proxy definability): Z₂^ and Z₃^ must be stable under explicit proxy-variant families Q and R. What this paper delivers This release provides an audit-friendly implementation blueprint that can be applied directly to existing catalogs without SI quantities in analysis or reporting. It specifies a minimal starred event record E= (masd^, B₀^, u^, ^, I^), explicit proxy inference recipes for B, Q, _, L, worked ensemble templates (for example |S|=24 for lab and |S|=36 for space) that make Gates A1–A3 reproducible, a required per-event archival table schema (port tuple, proxy choices, residuals, and gate flags), and diagnostic failure-mode interpretations (F1–F4) that localize why Gate A4 fails when it fails. Recommended use Implementers are encouraged to publish a DOI-archived reproducibility package containing (i) the starred event catalog, (ii) the star-normalization and event-selection specification, (iii) explicit ensembles S, Q, R, and (iv) per-bin residual summaries with fitted offsets. Gate A4 outcomes are designed to be comparable across laboratories and space missions under a common QMU-only reporting standard.