Thermoresonant Structural Registration in Photoexcited Tellurium: A QMU Reconstruction of the Dynamic Magneto-Chiral Compatibility Spectrum

A public time-domain terahertz-emission dataset for photoexcited chiral tellurium contains discrete oscillatory modes whose amplitudes grow or decay according to magnetic-field orientation and temperature. This paper reconstructs the deposited oscillator parameters in Quantum Measurement Units and tests whether the transverse amplified spectrum exhibits a direct correspondence with the geometry of trigonal tellurium. The deposited fitting convention is $$E_n(t)=C_n\cos(2\pi f_n t+\phi_n)\exp(-2\pi\gamma_n t),$$ so that $\gamma_n0$ denotes decay. The QMU thermal identity is $$\mathrm{temp}=\mathrm{area}\,\mathrm{rson},$$ with $$\mathrm{area}={\lambda_C}^2,$$ $$\mathrm{rson}=F_q^2,$$ and $$\mathrm{temp}={\lambda_C}^2{F_q}^2=c^2,$$ A measured temperature fraction and resonant frequency therefore define an effective thermoresonant cross-section length, $$L_n(T)=\lambda_C\dfrac{\sqrt{T/\mathrm{temp}}}{f_n/\mathrm{freq}},$$ where $\mathrm{freq}=F_q$. This quantity is an effective resonant projection of thermal area into a one-dimensional comparison scale. It is not interpreted as literal thermal expansion of a crystal bond. The transverse-temperature analysis uses modes 4--6 exactly as identified in the deposited MATLAB analysis. These modes are labeled the low, core, and high branches. Seven tellurium structural dimensions are specified before the assignment search: $$\mathcal L_{\mathrm{Te}}=\left\{r_h,\dfrac{c}{3},\dfrac{a}{2},d_{\mathrm{intra}},d_{\mathrm{inter}},a,c\right\}.$$ The resulting finite assignment problem contains $$7\times6\times5=210$$ ordered mappings of three measured branches onto three distinct structural dimensions. For an ordered assignment, the registration ratio is $$\mathcal R_{n,s}(T)=\dfrac{L_n(T)}{L_s},$$ and the collective logarithmic registration error is $$\mathcal E_{\mathrm{reg}}(T;\Phi)=\sqrt{\dfrac{1}{3}\sum_{n=1}^{3}\left[\ln\mathcal R_{n,s(n)}(T)\right]^2}.$$ A bounded structural-registration fidelity is also defined by $$\mathcal F_{\mathrm{reg}}=\exp(-\mathcal E_{\mathrm{reg}}).$$ At the deposited temperature corresponding to $42\,\mathrm{K}$ in the SI bridge, the three transverse branches have frequencies $$f_{\mathrm{low}}=0.326099\,\mathrm{THz},$$ $$f_{\mathrm{core}}=0.391682\,\mathrm{THz},$$ and $$f_{\mathrm{high}}=0.509383\,\mathrm{THz}.$$ Their effective thermoresonant cross-section lengths are $$L_{\mathrm{low}}=0.342274\,\mathrm{nm},$$ $$L_{\mathrm{core}}=0.284964\,\mathrm{nm},$$ and $$L_{\mathrm{high}}=0.219119\,\mathrm{nm}.$$ The unique minimum-error assignment is $$L_{\mathrm{low}}\leftrightarrow d_{\mathrm{inter}},$$ $$L_{\mathrm{core}}\leftrightarrow d_{\mathrm{intra}},$$ and $$L_{\mathrm{high}}\leftrightarrow a/2.$$ The individual fractional mismatches are approximately $$-2.07\%,$$ $$+0.52\%,$$ and $$-1.68\%.$$ The collective result is $$\mathcal E_{\mathrm{reg}}=0.015791,$$ corresponding to a root-mean-square fractional mismatch of $$1.5646\%$$ and a structural-registration fidelity of $$\mathcal F_{\mathrm{reg}}=0.98433.$$ The next-best ordered assignment has $$\mathcal E_{\mathrm{reg}}=0.060864,$$ which is approximately $3.86$ times larger than the optimum error. A separate scale-independent test compares measured frequency ratios with inverse structural-length ratios: $$\dfrac{f_i}{f_j}\approx\dfrac{L_j}{L_i}.$$ This test cancels the Kelvin-to-$\mathrm{temp}$ conversion factor, $\lambda_C$, and $F_q$. The low/core and high/core residuals are approximately $2.64\%$ and $2.23\%$, respectively. The three measured modes independently imply structural-match temperatures of approximately $$43.79\,\mathrm{K},$$ $$41.57\,\mathrm{K},$$ and $$43.45\,\mathrm{K},$$ giving $$T_{\mathrm{reg}}=42.9347\pm1.1951\,\mathrm{K}.$$ The same structural assignment is not optimal at the deposited temperatures of $12$, $80$, $120$, $160$, or $200\,\mathrm{K}$. The verified result is therefore a localized thermoresonant compatibility window rather than a permanent identity of the three branches. A deterministic sensitivity analysis perturbs all three deposited frequencies independently and recalculates all 210 assignments. The optimum assignment remains unchanged for bounded frequency perturbations below approximately $$\Delta f_{\mathrm{rob}}\approx0.02247\,\mathrm{THz}=22.47\,\mathrm{GHz}.$$ The first competing assignment replaces the high-branch association $a/2$ with the axial rise $c/3$. This robustness radius measures deterministic assignment stability and is not an experimental confidence interval. The verified numerical result, geometric assignment, and Aether Physics Model interpretation are kept distinct. The numerical result is the unique minimum-error assignment within the predefined search space. The geometric result is the simultaneous registration of three measured branches with three dimensions of trigonal tellurium. The APM interpretation is that this localized assignment represents a thermoresonant compatibility window in which three resonant pathways register simultaneously with the stable crystal geometry. The paper predicts branch-specific frequency shifts under pressure and strain, $$\dfrac{\Delta f_n}{f_n}\approx-\dfrac{\Delta L_s}{L_s},$$ the opening of low and high branches during a continuous magnetic-angle scan, reversal of the field-odd emitted orientation in the opposite tellurium enantiomorph, and a more finely resolved registration minimum in a dense temperature scan between approximately $35$ and $50\,\mathrm{K}$. The accompanying reproducibility package contains the deposited oscillator parameters used in the analysis, all derived QMU tables, the exhaustive 210-assignment comparison, frequency-ratio tests, deterministic perturbation analysis, figures, metadata, and Python reproduction scripts.