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

## Pipeline
`inspect → despike (σ=4, 130 spikes removed) → Lorentzian power_fit (1.23–1.45 eV)`

All 15 spectra (5–100 µW) were fitted with a **Lorentzian + slope** profile. Every column converged in the **HIGH** tier (R² = 0.887–0.984, median 0.981), so all points are used.

## Per-power results (Lorentzian fit)

| Power (µW) | Intensity (counts) | x_c (eV) | FWHM (meV) | R² |
|---|---|---|---|---|
| 5 | 98.8 | 1.32062 | 62.4 | 0.887 |
| 10 | 189.9 | 1.32437 | 64.4 | 0.950 |
| 15 | 267.9 | 1.32636 | 64.1 | 0.958 |
| 20 | 353.8 | 1.32783 | 62.7 | 0.968 |
| 25 | 425.2 | 1.32905 | 61.7 | 0.973 |
| 30 | 516.0 | 1.32998 | 61.3 | 0.975 |
| 35 | 564.8 | 1.33044 | 60.8 | 0.978 |
| 40 | 694.6 | 1.33152 | 59.3 | 0.981 |
| 45 | 738.5 | 1.33179 | 59.1 | 0.981 |
| 50 | 818.3 | 1.33279 | 59.0 | 0.981 |
| 60 | 935.9 | 1.33317 | 58.0 | 0.982 |
| 70 | 1140.4 | 1.33430 | 57.1 | 0.983 |
| 80 | 1264.7 | 1.33446 | 56.3 | 0.983 |
| 90 | 1538.0 | 1.33509 | 55.3 | 0.984 |
| 100 | 1714.6 | 1.33562 | 54.4 | 0.984 |

## Allometric fits
- **Intensity vs power** (left panel, log–log): $I = a\,P^{b}$ with $a = 16.28 \pm 1.81$, $b = 1.005 \pm 0.026$, $R^2 = 0.995$. The near-unity exponent indicates **linear (excitonic) scaling** — no saturation or Auger/trap-filling over 5–100 µW.
- **Peak position vs power** (right panel): $x_c$ rises monotonically from 1.3206 → 1.3356 eV, i.e. a **~15 meV blueshift** (~5.0 meV/decade), consistent with band-filling / many-body shift at higher carrier density.

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

RESULT: b = 1.0048 ± 0.0261