QMU Curl as a Magnet Hardness Index: A Ledger-First Analysis of Magnetic Anisotropy Materials

Abstract

The paper applies the Quantum Measurement Units (QMU) ledger and the Aether Physics Model (APM) to a curated set of magnetic anisotropy materials in order to test whether the substrate curl of the aether unit has observable consequences at the materials level. In the APM, the magnetic sector is organized around the Aether-unit curl\[\mathrm{curl}_{\mathrm{APM}} = \frac{{e_\mathrm{emax}}^{2}}{m_{e}\,\lambda_{C}},\]which quantifies torsional stiffness of distributed charge at the geometric scale set by the electron mass $m_{e}$ and Compton wavelength $\lambda_{C}$. Curl enters the canonical aether ledger through\[A_{u}\,\mathrm{curl}_{\mathrm{APM}} = {F_q}^{2}\,{\lambda_C}^{2},\]linking the rotating magnetic field stiffness $A_{u}$ to the intrinsic torsional response ${F_q}^{2}\,{\lambda_C}^{2}$ of the substrate. Starting from legacy anisotropy fields $H_{k}^{\mathrm{legacy}}$ and remanent fields $B_{r}^{\mathrm{legacy}}$, the article uses the charge-conversion factor (CCF) rules for singular-to-distributed charge to construct a QMU curl estimator,\[\mathrm{curl}_{\mathrm{mat}}^{\mathrm{QMU}} = \frac{H_{k}^{\mathrm{QMU}}}{B_{r}^{\mathrm{QMU}}} = \frac{H_{k}^{\mathrm{legacy}}}{B_{r}^{\mathrm{legacy}}}\,\mathrm{ccf}_{e}^{2},\qquad\mathrm{ccf}_{e} = \frac{{e_\mathrm{emax}}^{2}}{e},\]so that the materials-level quantity $\mathrm{curl}_{\mathrm{mat}}^{\mathrm{QMU}}$ is directly comparable to the substrate curl $\mathrm{curl}_{\mathrm{APM}}$ in the ledger. Numerically, the separation between hard and soft magnets already resides in the ratio $H_{k}^{\mathrm{legacy}}/B_{r}^{\mathrm{legacy}}$; the QMU mapping interprets this ratio as a dimensionless fraction of Aether-unit torsional stiffness. Using QMU-only processing on a set of 29 materials with well-formed anisotropy and remanence data, the article finds that nearly all hard magnets occupy a high-curl band, while four amorphous soft magnets lie in a much lower curl band, separated by more than an order of magnitude in\[\frac{\mathrm{curl}_{\mathrm{Hard}}^{\mathrm{QMU}}}{\mathrm{curl}_{\mathrm{Soft,\,core}}^{\mathrm{QMU}}} \approx 56.\]A single soft cubic alloy, Fe$_{0.47}$Co$_{0.53}$, appears as a notable outlier:\[\mathrm{curl}_{\mathrm{mat}}^{\mathrm{QMU}} \approx -9.285\times 10^{-30},\]with a magnitude comparable to hard magnets but opposite sign. The article treats this honestly as an open question: it may signal a measurement or curation issue in the legacy data, or it may indicate a distinct geometric phase of the distributed charge, where the torsion sign is flipped while the magnitude remains hard-like. Within the APM, such behavior is consistent with geometry-driven state transitions in tight regimes, as seen when key ledger ratios move between special values (for example, near $16\pi^{2}$). The study defines a QMU hardness index\[H_{\mathrm{curl}} = \frac{\mathrm{curl}_{\mathrm{mat}}^{\mathrm{QMU}}}{\mathrm{curl}_{\mathrm{APM}}},\]interpreted as a fraction of the aether-unit torsional stiffness. Hard magnets cluster in a narrow band of $H_{\mathrm{curl}}$, soft amorphous magnets lie significantly below this band, and Fe$_{0.47}$Co$_{0.53}$ provides a concrete outlier test of the curl definition. All derivations close in the QMU ledger; no legacy unit systems appear in the main text, and legacy quantities are used only as intermediates for charge-conversion. Beyond reporting this initial pattern, the paper outlines a program of future work: extending the dataset to hundreds of materials, performing QMU-aware measurements of anisotropy and remanence, and scanning families of magnets across geometric thresholds in the APM ledger to search for additional curl sign changes or quantized curl bands. These experiments are fully falsifiable within the QMU framework and provide a direct connection between APM substrate geometry and macroscopically measurable magnetic hardness.