QMU Registration of Gyroscopic Coupling in a Nonspinning Ferromagnet: Public-Trace Reproduction, a Composition Envelope, and a Material-Participation Constraint

Abstract

Ahrens and Vinante recently measured gyroscopic spin-rotation coupling between two librational modes of a nonspinning, superconductively levitated hard-ferromagnet microsphere. The measured coupling provides a direct experimental relation between the magnetic moment $\mu$ and the collective intrinsic angular momentum $S$ associated with the particle magnetization. This study independently reconstructs the central experimental observable from the complete public archive. All five deposited MD5 checksums are verified, and all 315 two-channel traces are analyzed using the correlation model specified in the experimental supplement. Three of the four reconstructed Einstein--de Haas frequencies $f_I$ agree with the published central values to within $0.3%$. Dataset 1, which contains the smallest measured quadrature ratio, reconstructs $17.4%$ above the published central value but remains consistent within $1.24$ combined standard deviations. An inverse-variance fit to the four published material factors gives $g_{\mathrm{mat}}=1.16263\pm0.02578$, corresponding to $\Gamma_{\mathrm{mat}}=g_{\mathrm{mat}}/2=0.58131\pm0.01289$. The size-scaling quantity $f_I R^2/M$ is consistent with a common material factor across the four experimental configurations, with $\chi^2=0.969$ for three degrees of freedom and $p=0.809$ under the stated independence approximation. The experimental result is registered in Quantum Measurement Units using $\mathrm{angm}=h=m_e{\lambda_C}^2F_q$, $\mathrm{magm}={e_\mathrm{emax}}^2{\lambda_C}^2F_q$, $\mathrm{mchg}=m_e/{e_\mathrm{emax}}^2$, and $\mathrm{ccf}={e_\mathrm{emax}}^2/e$. These definitions produce the exact correlations $\mathrm{magm}/\mathrm{angm}=1/\mathrm{mchg}$ and $\mathrm{ccf}\,\mathrm{mchg}=m_e/e$. The resulting dimensionless QMU registration is $\Gamma_{\mathrm{QMU}}=(\mu\,\mathrm{ccf}/\mathrm{magm})/(S/\mathrm{angm})=g/2=(\mu\,\mathrm{ccf}/S)\mathrm{mchg}$. For a spherical particle, the experimental closure becomes $\Gamma_{\mathrm{QMU}}=5M\,\mathrm{ccf}\,\mathrm{mchg}/(4\pi\rho R^2f_I)=5Mm_e/(4\pi\rho R^2f_Ie)$. This expresses the measured gyroscopic coupling as a dimensionless ratio of magnetic moment and angular momentum while preserving an exact bridge to the experimentally reported quantities. Public composition reports for commercial Magnequench MQP-S-11-9-20001 powder are converted from weight percent to atomic percent and evaluated with the deliberately simplified constituent model used in the source study. The resulting composition controls give $g_{\mathrm{ctrl}}=1.3647$--$1.3952$ and $\Gamma_{\mathrm{ctrl}}=0.6823$--$0.6976$. Within this model, agreement with the measured value requires the rare-earth share of modeled angular momentum to increase from approximately $0.48$--$0.50$ to approximately $0.661$. The equivalent transition-metal participation factor is $\beta_{\mathrm{TM}}=0.468$--$0.516$. The QMU identity $\Gamma_{\mathrm{QMU}}=g/2$ is an exact registration of the measured observable rather than an independent material prediction. A predictive Aether Physics Model calculation must determine the species- and phase-resolved magnetic-moment and angular-momentum population sums before comparison with the experiment. The paper therefore defines the numerical target, identifies the principal material-participation constraint, and proposes composition, phase, temperature, particle-metrology, and blind-registration experiments capable of distinguishing competing closures. The deposit includes the complete paper, Overleaf-compatible LaTeX source, publication figures, machine-readable result summaries, composition inputs, claims ledger, figure-regeneration code, and package-validation report.