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 Eₙ(t)=Cₙcos(2π fₙ t+φₙ)exp(-2πγₙ t), so that γₙ<0 denotes amplification and γₙ>0 denotes decay. The QMU thermal identity is temp=area\,rson, with area=λC², rson=Fq², and temp=λC²Fq²=c², A measured temperature fraction and resonant frequency therefore define an effective thermoresonant cross-section length, Lₙ(T)=λC√T/tempfₙ/freq, where freq=Fq. 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: LTe=ₕ,c/3,a/2,dᵢₙₜᵣₐ,dᵢₙₜₑᵣ,a,c\. The resulting finite assignment problem contains 7×6×5=210 ordered mappings of three measured branches onto three distinct structural dimensions. For an ordered assignment, the registration ratio is Rn,s(T)=Lₙ(T)/Lₛ, and the collective logarithmic registration error is Ereg(T;Φ)=√1/3∑ₙ₌₁³[ln Rn,s(n)(T)]². A bounded structural-registration fidelity is also defined by Freg=exp(- Ereg). At the deposited temperature corresponding to 42\,K in the SI bridge, the three transverse branches have frequencies flow=0.326099\,THz, fcore=0.391682\,THz, and fhigh=0.509383\,THz. Their effective thermoresonant cross-section lengths are Llow=0.342274\,nm, Lcore=0.284964\,nm, and Lhigh=0.219119\,nm. The unique minimum-error assignment is Llow↔ dᵢₙₜₑᵣ, Lcore↔ dᵢₙₜᵣₐ, and Lhigh↔ a/2. The individual fractional mismatches are approximately $$-2.07%,$$ $$+0.52%,$$ and $$-1.68%.$$ The collective result is Ereg=0.015791, corresponding to a root-mean-square fractional mismatch of $$1.5646%$$ and a structural-registration fidelity of Freg=0.98433. The next-best ordered assignment has Ereg=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: fᵢ/fⱼⱼ/Lᵢ. This test cancels the Kelvin-to-temp conversion factor, λC, and Fq. 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\,K, 41.57\,K, and 43.45\,K, giving Treg=42.9347±1.1951\,K. The same structural assignment is not optimal at the deposited temperatures of $12$, $80$, $120$, $160$, or 200\,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 Δ frob≈0.02247\,THz=22.47\,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, Δ fₙ/fₙ≈-Δ Lₛ/Lₛ, 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\,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.