The file is a single merged workbook (`Book1`) with 15 power columns (5–100 µW) and energy axis in eV. No Si/reference folder exists, so no background subtraction is needed. Suggested x-range is [1.23, 1.45] eV.

Per protocol, I'll despike first (mandatory before any fit), then run the Lorentzian power-dependence fit.



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

## Lorentzian Power-Dependence Analysis

All 15 spectra (5–100 µW) were despiked (130 cosmic-ray spikes removed) and fitted with a **Lorentzian** profile over 1.23–1.45 eV. Every column converged at HIGH quality (R² = 0.887–0.984, median 0.981); all 15 points entered both panels.

**Per-power extracted quantities** (from the Lorentzian fits):

| P (µW) | Intensity (counts) | x_c (eV) | FWHM (meV) |
|---|---|---|---|
| 5 | 98.8 | 1.3206 | 62.4 |
| 10 | 189.9 | 1.3244 | 64.4 |
| 20 | 353.8 | 1.3278 | 62.7 |
| 30 | 516.0 | 1.3300 | 61.3 |
| 50 | 818.3 | 1.3328 | 59.0 |
| 70 | 1140.4 | 1.3343 | 57.1 |
| 100 | 1714.6 | 1.3356 | 54.4 |

*(full table in the CSV)*

**Left panel — Allometric intensity fit** $I = a\,P^{b}$:
- $a = 16.28 \pm 1.81$
- **$b = 1.0048 \pm 0.0261$**, R² = 0.995 → essentially **linear** (excitonic regime; no saturation or bi-exciton quenching up to 100 µW).

**Right panel — Peak position x_c(P):**
- x_c shifts from 1.3206 eV (5 µW) to 1.3356 eV (100 µW) — a monotonic **blueshift of ~15 meV** (~5.0 meV/decade) as power rises, consistent with band filling / state filling rather than thermal broadening (FWHM actually narrows slightly).

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

RESULT: b = 1.0048 ± 0.0261