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

Done. All 15 power spectra (5–100 µW) were already merged into a single sheet (`Book1`, x-axis in eV). I despiked first (130 cosmic-ray spikes removed, written back), then ran a **Lorentzian** cascade fit (high→low power) on the dominant peak in the 1.23–1.45 eV window, extracting peak intensity and center $x_c$ per power, and fit the allometric law $I = a\,P^{b}$.

**Per-power Lorentzian results** (all 15 points passed the HIGH-quality gate, $R^2 \ge 0.85$; included in both panels):

| P (µW) | Intensity (cnt) | $x_c$ (eV) | FWHM (meV) | $R^2$ |
|---|---|---|---|---|
| 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** ($I = a\,P^{b}$):
- $a = 16.28 \pm 1.81$
- $b = 1.0048 \pm 0.0261$
- $R^2 = 0.995$ (15 points) → **~linear, excitonic regime**

**Peak-position vs power ($x_c$ vs P):** monotonic **blueshift** from 1.3206 eV (5 µW) to 1.3356 eV (100 µW), a total of ~15 meV, i.e. ~5 meV per decade of power. The dependence is weak and near-saturating (not a clean power law), so it is reported as a trend rather than a meaningful exponent — consistent with band-filling/bandgap-renormalization behavior.

📥 Full per-power table: [power_fit_results.csv]([file link removed])

RESULT: b = 1.0048 ± 0.0261