Bohm Transport Closure in QMU/APM: Interferometric Phase, Plasma Cross-Field Diffusion, and Sheath Boundary Gates

Bohm Transport Closure in QMU/APM: Interferometric Phase, Plasma Cross-Field Diffusion, and Sheath Boundary Gates This paper isolates two experimentally anchored pillars in David Bohm’s program—(i) magnetic-flux–driven interferometric phase (Aharonov--Bohm) and (ii) anomalous cross-field plasma transport (Bohm diffusion)—and reformulates both ledger-first in Quantum Measurement Units (QMU) within the Aether Physics Model (APM). What is done (QMU-native) The development is fully QMU-native (no $\hbar$ and no SI constants), using only the ledger primitives $\{m_e,\lambda_C,F_q,{e_\mathrm{emax}}^{2}\}$ and QMU-derived working units: $\mathrm{temp}={\lambda_C}^{2}{F_q}^{2}$ $\mathrm{enrg}=m_e\,\mathrm{temp}=m_e{\lambda_C}^{2}{F_q}^{2}$ $\mathrm{swep}={\lambda_C}^{2}F_q$ $\mathrm{chrg}\equiv {e_\mathrm{emax}}^{2}$ (magnetic square-charge primitive) $\mathrm{mfxd}=m_eF_q/\mathrm{chrg}$ $\mathrm{mflx}=m_e{\lambda_C}^{2}F_q/\mathrm{chrg}$ $\mathrm{cond}=1/\mathrm{mflx}$ Key closures (the spine) (1) Flux--phase law (Aharonov--Bohm, QMU form). The interferometric phase sensitivity closes to a QMU flux quantum:\[\Delta\phi \;=\; 2\pi\,\frac{\Phi}{\mathrm{mflx}},\qquad\mathrm{mflx}=\frac{\mathrm{angm}}{\mathrm{chrg}},\qquad\mathrm{angm}=m_e{\lambda_C}^{2}F_q.\] (2) Bohm diffusion as a fixed fraction of the quantum sweep. Cross-field diffusion is expressed as a fraction of the universal sweep:\[D_{\mathrm{B}} \;=\; \frac{\Xi_{\mathrm{B}}}{16}\,\mathrm{swep},\qquad\mathrm{swep}={\lambda_C}^{2}F_q,\]where $\Xi_{\mathrm{B}}$ is a dimensionless boundary/closure coefficient that packages sheath gates, wall coupling, rotation, and fluctuation-driven decorrelation. (3) Electrostatic--magnetic channel conversion and the $\pi\alpha/2$ factor. The electrostatic square-charge $e^{2}$ and magnetic square-charge $\mathrm{chrg}$ satisfy\[e^{2}=8\pi\alpha\,\mathrm{chrg},\qquad\frac{\pi\alpha}{2}=\frac{e^{2}}{16\,\mathrm{chrg}}.\]This frames $\pi\alpha/2$ as a charge-channel holonomy signature that can appear when sheath/boundary physics selects electrostatic bookkeeping relative to the bulk magnetic-charge transport ledger. Boundary gates and falsifiability The paper separates ledger universality (the sweep sets the only transport dimension) from boundary specificity (sheath/wall physics sets $\Xi_{\mathrm{B}}$ and may select a charge-channel normalization). A compact appendix provides a two-observable ``toy illustration'' with decidable failure modes, separating: Pure boundary gate: transport changes while the flux--phase slope remains invariant. Charge-channel swap: a correlated interferometric signature must appear alongside the transport rewrite. Experimental program (directly testable) Three proposed experiments connect interferometry to edge transport closure: E1: extract the flux--phase slope from fringe shifts while toggling sheath coupling. E2: measure cross-field diffusion and report the dimensionless $\mathcal{D}=D/\mathrm{swep}$ to infer $\Xi_{\mathrm{B}}$ across boundary settings. E3: extract a sheath gate coefficient from boundary phase-gradient diagnostics and compare against $\Xi_{\mathrm{B}}$. Intended use. This release provides a compact QMU-native scaffold for plasma experimentalists and modelers to (i) normalize cross-field transport to a universal QMU scale and (ii) test whether boundary-conditioned transport prefers magnetic or electrostatic charge bookkeeping via a two-observable gate (interferometric slope versus transport closure).