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

**Pipeline:** despike (σ=4, 130 spikes removed across 15 spectra) → Lorentzian fit on each of the 15 merged power spectra (window 1.23–1.45 eV) → extracted peak intensity and center per power → allometric fits $I = a\cdot P^{b}$ on both panels.

**Fit quality:** all 15 spectra in the HIGH tier, per-spectrum R² = 0.887–0.984 (median 0.981).

**Intensity vs power (allometric):**
- $I = a\,P^{b}$, $a = 16.28$, **$b = 1.0048 \pm 0.0261$**, R² = 0.995
- $b \approx 1$ → linear (excitonic) regime; no saturation or blinking over 5–100 µW.

**Peak position vs power:**
- Blueshifts monotonically from **xc = 1.3206 eV** (5 µW) to **1.3356 eV** (100 µW), i.e. ≈ 5 meV/decade — consistent with bandgap renormalization / exciton-exciton effects at higher density.

Per-power table (Lorentzian fit):

| Power (µW) | Intensity (counts) | 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 |

📥 Full data: [power_fit_results.csv]([file link removed])

RESULT: b = 1.005 ± 0.026