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

## Lorentzian power-dependence analysis (Book1, 1.23–1.45 eV)

All 15 merged spectra (5→100 µW) were despiked (130 cosmic-ray spikes removed) and Lorentzian-fitted. Every column converged to **HIGH** tier (R² = 0.887–0.984, median 0.981; SNR 7.6–24).

**Per-power results**

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

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

**Peak-position panel (right):** xc rises monotonically from 1.3206 → 1.3356 eV (net **blueshift ≈ 15 meV**), a sub-linear trend of ≈ 5 meV/decade of power, overlaid with its fitted curve. FWHM narrows slightly (62 → 54 meV) with power.

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

RESULT: b = 1.0048 ± 0.0261