File structure: single workbook **Book1**, X-axis in eV (col A), 15 power columns (5→100 µW). Data is already merged per-power, so no folder merge needed. Suggested x-range: **[1.23, 1.45]**.

Despiking (mandatory before any fit), then running the Lorentzian + allometric pipeline.



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

## Pipeline completed

**Book1** · 15 merged power spectra (5→100 µW) · X-axis in eV · window **[1.23, 1.45] eV**
Despiked first (130 cosmic-ray spikes removed, σ=4) → **Lorentzian** fit per spectrum → allometric fits.

All 15 columns converged to **HIGH** quality (R² = 0.887–0.984, median 0.981; SNR 7.6–24). No Si reference folder was present, so the residual background is handled by the fit's baseline term.

### Per-power results (Lorentzian fit)

| P (µW) | Intensity (a.u.) | x_c (eV) | FWHM (meV) | R² |
|---|---|---|---|---|
| 5 | 98.8 | 1.3206 | 62.4 | 0.887 |
| 10 | 189.9 | 1.3244 | 64.4 | 0.950 |
| 20 | 353.8 | 1.3278 | 62.7 | 0.968 |
| 30 | 516.0 | 1.3300 | 61.3 | 0.975 |
| 40 | 694.6 | 1.3315 | 59.3 | 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 |

*(full 15-row table in the CSV below)*

### Allometric fits

**Intensity (left panel):** $I = a\cdot P^{b}$
- a = 16.28 ± 1.81
- **b = 1.0048 ± 0.0261**, R² = 0.995 → essentially **linear (excitonic)** scaling; no evidence of bimolecular/biexciton quenching (which would push b toward 2) or saturation.

**Peak position (right panel):** monotonic **blueshift** from 1.3206 eV (5 µW) to 1.3356 eV (100 µW) — a total shift of ≈ **15 meV** (≈ 5 meV/decade), consistent with band filling / many-body renormalization under increasing excitation density.

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

RESULT: b = 1.0048 ± 0.0261