A Trumpet-Geometry Tesla Resonator to Test the QMU Carrier Mapping

This dataset contains the LaTeX source and supporting materials for a buildable, falsifiable experiment that tests a core prediction of the Quantum Measurement Units (QMU) framework using a tapered “trumpet” Tesla resonator. The apparatus adiabatically transforms base current into top-load voltage, enabling simultaneous, same-device measurements of an electrostatic carrier $q=C_{\text{top}}\,V_{\text{pk}}$ and a magnetic-mode carrier proxy $Q=\kappa\,I_{\text{pk}}$. The central, geometry-independent hypothesis is
\[
Q^{2}=\frac{q^{2}}{8\pi\alpha}
\]
for electrons. A positive result would empirically exhibit the same fixed geometry factor that underlies the QMU channel identity $A_u=16\pi^{2}k_C$, strengthening the case that electrostatic and RMFD channels are two readouts of a single driver.

The paper provides: (i) complete construction specifications for the trumpet secondary (flare law, turn schedule, topload sizing, tolerances), (ii) standard-operating procedures to calibrate $C_{\text{top}}$ via low-power VNA fitting and $\kappa$ via base $B_\phi(r,z)$ mapping, (iii) high-power measurement protocols with a formal “streamer gate” to ensure data are taken in a confinement regime (minimal corona), (iv) an uncertainty budget with explicit propagation to $\alpha_{\text{extracted}}$, and (v) a conventional electromagnetic benchmark based on tapered transmission-line modeling that predicts a geometry-dependent ratio
\[
\frac{\kappa^{2}I_{\text{pk}}^{2}}{C_{\text{top}}^{2}V_{\text{pk}}^{2}}=\mathcal{F}\!\left[\text{geometry, coupling, loss}\right].
\]
Thus, observation of a universal constant $1/(8\pi\alpha)$ across power levels and geometries would falsify the benchmark and support the QMU mapping.

Implications for the original program are made explicit: with $Q^{2}=q^{2}/(8\pi\alpha)$ validated, the QMU ledger links the channel constants and the driver through
\[
A_u=\frac{\text{Gforce}\,{\lambda_C}^{2}}{{e_a}^{2}},\qquad
k_C=\frac{\text{Gforce}\,{\lambda_C}^{2}}{16\pi^{2}{e_a}^{2}},
\]
so $A_u=16\pi^{2}k_C$ and
\[
\text{Gforce}=\frac{16\pi^{2}k_C\,{e_a}^{2}}{{\lambda_C}^{2}}.
\]