![Power Fit]([file link removed])

Pipeline: merged workbook `Book1` (15 powers, 5–100 µW) → despiked (130 cosmic-ray spikes removed, written back) → **Lorentzian fit on all 15 spectra** (R² = 0.887–0.984, all HIGH tier) → allometric fit.

**Per-power Lorentzian results**

| Power (µW) | Intensity (cnt) | xc (eV) | FWHM (meV) | R² |
|---:|---:|---:|---:|---:|
| 5 | 98.8 | 1.3206 | 62.4 | 0.887 |
| 10 | 189.9 | 1.3244 | 64.4 | 0.950 |
| 15 | 267.9 | 1.3264 | 64.1 | 0.958 |
| 20 | 353.8 | 1.3278 | 62.7 | 0.968 |
| 25 | 425.2 | 1.3290 | 61.7 | 0.973 |
| 30 | 516.0 | 1.3300 | 61.3 | 0.975 |
| 35 | 564.8 | 1.3304 | 60.8 | 0.978 |
| 40 | 694.6 | 1.3315 | 59.3 | 0.981 |
| 45 | 738.5 | 1.3318 | 59.1 | 0.981 |
| 50 | 818.3 | 1.3328 | 59.0 | 0.981 |
| 60 | 935.9 | 1.3332 | 58.0 | 0.982 |
| 70 | 1140.4 | 1.3343 | 57.1 | 0.983 |
| 80 | 1264.7 | 1.3345 | 56.3 | 0.983 |
| 90 | 1538.0 | 1.3351 | 55.3 | 0.984 |
| 100 | 1714.6 | 1.3356 | 54.4 | 0.984 |

**Allometric fit — intensity vs power** ($I = a\cdot P^{b}$, log–log):
- $a = 16.28 \pm 1.81$
- **$b = 1.0048 \pm 0.0261$**, R² = 0.995 → ~linear (excitonic) regime

**Peak position vs power:** monotonic **blueshift** from 1.3206 eV (5 µW) to 1.3356 eV (100 µW), ≈ 5.0 meV/decade. Note: the server models this panel as a smooth trend/curve rather than a separate power-law exponent, since a power-law on the absolute xc is ill-conditioned by the large ~1.32 eV offset; the allometric (power-law) engine applies to the intensity relation, which is the source of the reported $b$.

📥 [power_fit_results.csv]([file link removed])

RESULT: b = 1.0048 ± 0.0261