Field-Aligned Current Closure in the Aether Physics Model (APM/QMU): An Alfvén Circuit Template

Field-Aligned Current Closure in the Aether Physics Model (APM/QMU): An Alfvén Circuit Template This record archives a QADI template paper that reformulates magnetosphere--ionosphere coupling as a ledger-first closure problem in Quantum Measurement Units (QMU) and the Aether Physics Model (APM). The focus is the auroral field-aligned (Birkeland) current system treated as a generator--transmission--load circuit in the spirit of Hannes Alfvén. Ledger anchor (propagation identity). The template uses the APM propagation anchor (Ledger One) $A_u\cdot \mathrm{curl} = {F_q}^2{\lambda_C}^2$, with the bridge $c=F_q\lambda_C$, hence $A_u\cdot \mathrm{curl}=c^2$. Here $\mathrm{curl}$ denotes the QMU torsional unit (a scalar ledger quantity), not the vector operator $\nabla\times(\cdot)$. Charge and resistance conventions (QMU-native). The base charge used for circuit bookkeeping is $\mathrm{chrg}:={e_\mathrm{emax}}^{2}$. When plasma-derived formulations introduce $e^2$, the conversion is applied explicitly: $e^2 = 8\pi\alpha\,\mathrm{chrg}$ and $\mathrm{chrg}=e^2/(8\pi\alpha)$. Resistance is normalized in the QMU unit $\mathrm{resn} = m_e{\lambda_C}^2 F_q/\mathrm{chrg}^4$, so the starred resistance $R^\ast$ is resistance in resn units by construction. Core observables (dimensionless, QMU-native). The paper defines a minimal closure tuple $(I^\ast,\Phi^\ast,R^\ast)$ with $I^\ast:=\dot Q/(\mathrm{chrg}\,F_q)$, $\Phi^\ast:=\int E_\parallel^\ast\,d\ell^\ast$, and $R^\ast:=\Phi^\ast/I^\ast$, where $\ell^\ast=\ell/\lambda_C$ and $E_\parallel^\ast:=E_\parallel/(m_e {F_q}^2\lambda_C/\mathrm{chrg})$. Three falsifiable ``gates'' (A1--A3). Gate A1 (Clustering): $R^\ast$ exhibits stable clustering into preferred values (discrete closure modes), rather than a continuum, after geometry normalization. Gate A2 (Monotone closure): within a regime, $(\Phi^\ast,I^\ast)$ follows an approximately single-valued load curve; regime transitions correspond to the onset of localized boundary operators (e.g., double layers). Gate A3 (Saturation): there exists a geometry-dependent cap $I^\ast\le I^\ast_{\max}$; increasing driving produces restructuring (filamentation/channel splitting/new boundary operators) rather than unbounded $I^\ast$ growth. Toy numerical illustration.A short toy example in the Data Products section demonstrates how to compute $(I^\ast,\Phi^\ast,R^\ast)$ (with $R^\ast$ in resn units) and shows hypothetical resistance clustering and saturation-with-restructuring patterns, making the gates operational for archive-only tests on standard spacecraft and global FAC products. Intended use.This document is designed as a re-usable QADI template for (i) analyzing existing auroral/FAC datasets in QMU-native starred variables, (ii) writing reproducible ``gate'' tests with clear failure conditions, and (iii) bridging neglected circuit-centric plasma concepts into a ledger-closure framework that can be extended across APM/QMU studies.