The file contains a single workbook `Book1` with 15 power levels (5–100 µW) already merged into one sheet. Energy axis spans 1.20–1.61 eV; suggested fit window is 1.23–1.45 eV. Proceeding with the full pipeline.

**Step 1 — Despike (mandatory before any fit):**



130 cosmic-ray spikes removed across all 15 columns. Data written back.

**Step 2 — Lorentzian fit + allometric power-law on all spectra:**



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

## Results

**Lorentzian fits — all 15 spectra (5–100 µW) converged at HIGH tier** (R² = 0.887–0.984, median 0.981). No rescue or raw-peak fallbacks needed.

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

### Allometric fit — I = a·P^b

| Parameter | Value |
|---|---|
| **b** | **1.0048 ± 0.0261** |
| a | 16.28 ± 1.81 |
| R² | 0.995 |
| N | 15 |
| Interpretation | ~linear (excitonic regime) |

### Peak-position trend (x_c vs P)

x_c shifts monotonically from **1.3206 eV → 1.3356 eV** (≈ 15 meV total), i.e. a progressive **blueshift** of ~5.0 meV per decade of power — consistent with band-filling / state-filling in the excitonic regime.

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

RESULT: b = 1.0048 ± 0.0261