Ledger-One Longitudinal Closure from SiC Raman LOPC: DSF+MCR Resolving-Power Protocol and Literature Reanalysis

This paper upgrades silicon-carbide (SiC) Raman longitudinal-optical–phonon–plasmon–coupled (LOPC) metrology from empirical regression to a falsifiable closure test in Quantum Measurement Units (QMU). The practical motivation is straightforward: in multilayer wafers and finite depth-of-field measurements, bulk spectra are mixtures of physically distinct layers, so “carrier density from LOPC” workflows can lose physical identifiability and drift into purely statistical calibration. The paper’s core step is to express Raman observables in a dimensionless QMU normalization anchored by the Ledger One propagation identity. Let $k$ be the Raman wavenumber shift (inverse length). Define the dimensionless spectral coordinate$$\Omega := \lambda_C\,k,$$where $\lambda_C$ is the electron Compton wavelength. This removes all unit conventions from the observable and makes closure statements purely geometric. Ledger closure check (Ledger One). The Aether Rotational Self-Identity is presented in the standardized form:$$A_u\cdot \mathrm{curl} = {F_q}^2\,{\lambda_C}^2,$$where $A_u$ is the Aether unit, $\mathrm{curl}$ is the QMU torsion primitive, and $F_q$ is the quantum frequency scale (photon speed divided by $\lambda_C$). Using the propagation anchor$$F_q\,\lambda_C = c,$$Ledger One becomes$$A_u\cdot \mathrm{curl} = c^2.$$With Maxwell’s correspondence$$c^2=\frac{1}{\mu_0\varepsilon_0},$$Ledger One is interpreted as a QMU decomposition of the electromagnetic propagation constant into rotational (via $A_u$) and torsional (via $\mathrm{curl}$) geometries. Two closure targets are defined for SiC LOPC data: 1) Spectrum-only closure (no external carrier data). From the LOPC feature(s), extract a QMU-normalized plasmon scale $\Omega_p^2$ via a standard LOPC inversion written entirely in $\Omega$-coordinates, and form a linewidth-normalized quotient$$\Xi_{\Omega} := \frac{\Omega_p^2}{\gamma},$$where $\gamma$ is a dimensionless linewidth coordinate built from the same spectral axis (e.g., $\gamma=\lambda_C\,\Gamma$ for an extracted FWHM $\Gamma$). For a single physical layer under stable scattering physics, $\Xi_{\Omega}$ should be approximately invariant under depth scan and optical configuration (within uncertainty). Mixed spectra generally violate this invariance. 2) Transport-coupled closure (unitless resistivity proxy). When a unitless resistivity coordinate $\rho^*$ is available (e.g., a normalized resistivity map), define a coupled invariant$$\Xi_{\rho} := \rho^*\,\Omega_p^2\,g(\gamma),$$where $g(\gamma)$ is chosen so that the invariant is dimensionless and isolates scattering contributions into a single factor. The falsifiable prediction is not “better regression,” but rather the existence (or absence) of a depth-stable closure coordinate once the spectrum has been physically unmixed. Definitive resolving-power experiment (DSF + MCR). The paper specifies a decisive test that data-holders can run immediately: - Acquire a Dual Spatial Filtration (DSF) depth stack $X(z,\Omega)$ over the LOPC window.- Apply multivariate curve resolution (MCR-ALS) with physically appropriate constraints (nonnegativity on spectra and depth weights; optional unimodality/contiguity of depth profiles).- Compute closure coordinates on (i) the raw bulk spectra at each depth, and (ii) each recovered component spectrum. The resolving-power claim is binary and falsifiable:- Bulk mixed spectra should generally fail closure as $z$ varies.- MCR component spectra corresponding to physical layers should satisfy closure within uncertainty (i.e., the variance of $\Xi_{\Omega}$ or $\Xi_{\rho}$ collapses sharply when evaluated on components rather than on the bulk mixture). Where raw spectral matrices are unavailable, the paper provides a feature-space proxy closure approach based on published LOPC deconvolution outputs (peak positions, widths, and ratio-normalized heights), enabling partial validation and making the call for open (or at least shareable) depth-stack matrices explicit. Data request to the community. This work is structured so that any SiC Raman lab (or wafer vendor) can supply a minimal dataset sufficient to settle the closure question: a DSF depth stack (even a narrow spectral window around the LOPC features), plus any independent layer anchor (optional but helpful) such as SIMS/Hall/C–V profiles. The paper provides the full analysis recipe and the exact closure plots that would constitute confirmation or falsification. References (DOI/URL)- QADI Community DOI Guide (Zenodo): https://doi.org/10.5281/zenodo.17479314- Cal\`a et al., ``Resistivity mapping of SiC wafers by quantified Raman spectroscopy'' (PCCP, 2025): https://doi.org/10.1039/D4CP04545A Supplementary info PDFs: https://www.rsc.org/suppdata/d4/cp/d4cp04545a/d4cp04545a1.pdf https://www.rsc.org/suppdata/d4/cp/d4cp04545a/d4cp04545a2.pdf- JASCO ``Raman Spectroscopy: Application eBook'' (corporate PDF): https://jascoinc.com/wp-content/uploads/2022/11/RamanApplicationEBook_US-sm.pdf