The file is a single merged workbook (`Book1`) — column A is energy (eV, 1.196–1.606 eV) and columns 1–15 are the 15 power levels (5→100 µW). So the spectra are already merged, one column per power. Suggested fit window is 1.23–1.45 eV.

Despiking first (mandatory before any fit), then running the Lorentzian cascade + allometric analysis.



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

**Pipeline:** 15 merged spectra (5→100 µW) → despiked (25 spikes removed) → Lorentzian cascade fit (window 1.23–1.45 eV) → allometric fit on each derived panel. All 15 columns passed as **HIGH** tier (R² = 0.887–0.984, median 0.981).

**Per-power extraction (Lorentzian):**
- Peak position xc: **1.3206 eV (5 µW) → 1.3356 eV (100 µW)** — a ~15 meV **blueshift**, FWHM narrowing 62 → 54 meV.
- Peak intensity: **~99 (5 µW) → ~1715 counts (100 µW)**.

**Allometric fits (y = a·xᵇ):**
- **Intensity vs power:** $I = a\,P^{b}$, $a = 16.28$, **$b = 1.005 \pm 0.026$**, R² = 0.995 → essentially **linear (excitonic)**, no saturation up to 100 µW.
- **Peak position vs power:** a **saturating (sub-linear) blueshift**, ~5.0 meV/decade. This curve is not a clean power law, so a literal $x_c = a\,P^{b}$ fit is degenerate and returns a near-zero exponent ($b_{x_c} \lesssim 0.01$) — i.e. the peak is effectively power-independent (rigid exciton).

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

RESULT: b = 1.005 ± 0.026