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): $$A_u\,\mathrm{curl}={F_q}^{2}{\lambda_C}^{2}$$ Port variables are defined by: $$\Phi:=\int E_{\parallel}\,d\ell\,\qquad I:=\frac{dQ}{dt}$$ The event-level closure impedance is: $$\frac{\Phi}{I}=R^{\ast}\,\mathrm{resn}\,\qquad R^{\ast}:=\frac{\Phi^{\ast}}{I^{\ast}}$$ Gate A4 (implementation form) Gate A4 compares three dimensionless impedances, each normalized by resn: $$Z_1^{\ast}:=\frac{\Phi/I}{\mathrm{resn}}$$ $$Z_2^{\ast}:=\frac{\mathrm{chds}_{\mathrm{eff}},\mathrm{mfxd}_{\mathrm{eff}}}{\mathrm{resn}}$$ $$Z_3^{\ast}:=\frac{\mathrm{indc}_{\mathrm{eff}},\mathrm{mcur}_{\mathrm{eff}}}{\mathrm{resn}}$$ $$\Delta_{12}:=\ln Z_1^{\ast}-\ln Z_2^{\ast}\,\quad \Delta_{13}:=\ln Z_1^{\ast}-\ln Z_3^{\ast}\,\quad \Delta_{23}:=\ln Z_2^{\ast}-\ln Z_3^{\ast}$$ 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 $\ln Z_1^{\ast}$. Robustness prefilters (mandatory) This paper treats Gates A1–A3 as compulsory filters before any A4 claim. A1 (extraction robustness): $R^{\ast}$ must be stable under an explicit analysis-setting ensemble $\mathcal{S}$ (windowing, filtering, mapping conventions, quadrature variants), quantified by median absolute deviation (MAD). A2 (segmentation stability): when distributed transmission and localized closure intervals are identifiable, $Z_{\mathrm{DL}}^{\ast}$ must be stable (small MAD) or reproducibly multi-modal across event classes. A3 (proxy definability): $Z_2^{\ast}$ and $Z_3^{\ast}$ must be stable under explicit proxy-variant families $\mathcal{Q}$ and $\mathcal{R}$. 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 $\mathcal{E}=(\mathrm{masd}^{\ast},B_0^{\ast},u^{\ast},\Phi^{\ast},I^{\ast})$, explicit proxy inference recipes for $\beta_B,\beta_Q,\beta_\omega,\beta_L$, worked ensemble templates (for example $|\mathcal{S}|=24$ for lab and $|\mathcal{S}|=36$ 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 $\mathcal{S},\mathcal{Q},\mathcal{R}$, 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.