Despiked 130 cosmic-ray spikes across all 15 columns; cleaned data written back. Main exciton peak sits near ~1.32 eV, captured by the suggested range [1.23, 1.45]. Now running the Lorentzian power-dependence fit (cascade, intensity + peak-position extraction, allometric I = a·P^b).



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

**Pipeline:** merged data (15 power columns, 5→100 µW) → despike (130 cosmic-ray spikes removed, σ=4) → Lorentzian fit on every spectrum over 1.23–1.45 eV → intensity & peak-position extraction → allometric fit.

**Lorentzian fits (per power):** all 15 converged, R² = 0.887–0.984 (median 0.981), all HIGH-tier. SNR 7.6–24.0.

| Power (µW) | xc (eV) | FWHM (meV) | Intensity (counts) |
|---|---|---|---|
| 5 | 1.3206 | 62.4 | 98.8 |
| 25 | 1.3290 | 61.7 | 425.2 |
| 50 | 1.3328 | 59.0 | 818.3 |
| 75 | 1.3343 | 57.1 | 1140.4 |
| 100 | 1.3356 | 54.4 | 1714.6 |

**Peak position (xc) vs power:** monotonic **blueshift** from 1.3206 eV (5 µW) to 1.3356 eV (100 µW) — total shift ≈ **+15 meV**, ≈ 5.0 meV/decade. Fitted curve overlaid on the right panel.

**Intensity vs power — allometric fit** $I = a\cdot P^{b}$:
- $a = 16.28 \pm 1.81$
- $b = 1.0048 \pm 0.0261$
- $R^2 = 0.995$ (15 points) → **~linear (excitonic)** regime; no saturation or bimolecular-quenching sub-linear behavior across 5–100 µW.

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

RESULT: b = 1.0048 ± 0.0261