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

## Results — Lorentzian Power-Dependence Analysis

**Pipeline:** inspect → despike (σ=4, 130 spikes removed) → Lorentzian fit on all 15 spectra → allometric fit I = a·P^b

### Per-Power Lorentzian Fits (all 15 columns — Tier HIGH)

| Power (µW) | xc (eV) | FWHM (meV) | Intensity (counts) | R² |
|---|---|---|---|---|
| 5 | 1.3206 | 62.4 | 98.8 | 0.887 |
| 10 | 1.3244 | 64.4 | 189.9 | 0.950 |
| 15 | 1.3264 | 64.1 | 267.9 | 0.958 |
| 20 | 1.3278 | 62.7 | 353.8 | 0.968 |
| 25 | 1.3290 | 61.7 | 425.2 | 0.973 |
| 30 | 1.3300 | 61.3 | 516.0 | 0.975 |
| 35 | 1.3304 | 60.8 | 564.8 | 0.978 |
| 40 | 1.3315 | 59.3 | 694.6 | 0.981 |
| 45 | 1.3318 | 59.1 | 738.5 | 0.981 |
| 50 | 1.3328 | 59.0 | 818.3 | 0.981 |
| 60 | 1.3332 | 58.0 | 935.9 | 0.982 |
| 70 | 1.3343 | 57.1 | 1140.4 | 0.983 |
| 80 | 1.3345 | 56.3 | 1264.7 | 0.983 |
| 90 | 1.3351 | 55.3 | 1538.0 | 0.984 |
| 100 | 1.3356 | 54.4 | 1714.6 | 0.984 |

### Allometric Fit (I = a·P^b)

| Parameter | Value |
|---|---|
| **a** | 16.28 ± 1.81 |
| **b** | **1.005 ± 0.026** |
| R² | 0.9951 |
| N points | 15 / 15 |

**Interpretation:** b ≈ 1.00 indicates a **linear (excitonic)** intensity–power relationship — no biexciton saturation or Auger quenching in this range.

### Peak Position Trend (right panel)

xc blueshifts monotonically from 1.3206 eV (5 µW) to 1.3356 eV (100 µW) — a total shift of ~15 meV, consistent with bandgap renormalization / exciton–exciton interactions at higher density.

📥 [Download full results CSV]([file link removed])

RESULT: b = 1.005 ± 0.026