The file has one workbook (`Book1`) with the energy axis in column A and 15 merged per-power spectra (columns 1–15: 5 µW → 100 µW). Suggested fit window is 1.23–1.45 eV.

Per the mandatory pipeline, I must despike before any fit. Doing that now.



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

## Pipeline executed
1. **Spectra per power (merged):** `Book1` already holds 15 merged spectra, one column each (5 → 100 µW), energy axis 1.196–1.606 eV.
2. **Despike (mandatory before fit):** removed 130 cosmic-ray spikes across all 15 columns, written back.
3. **Lorentzian fit on all 15 spectra** over 1.23–1.45 eV — every column converged (R² = 0.887–0.984, all HIGH tier; median R² = 0.981).
4. Extracted **peak intensity** and **peak position $x_c$** per power, then ran the **allometric fit** $I = a\,P^{b}$ on the intensity panel and modeled the $x_c$ panel.

## Per-power results (Lorentzian fit)
| Power (µW) | Intensity (counts) | $x_c$ (eV) |
|---|---|---|
| 5 | 98.8 | 1.3206 |
| 10 | 189.9 | 1.3244 |
| 15 | 267.9 | 1.3264 |
| 20 | 353.8 | 1.3278 |
| 25 | 425.2 | 1.3290 |
| 30 | 516.0 | 1.3300 |
| 35 | 564.8 | 1.3304 |
| 40 | 694.6 | 1.3315 |
| 45 | 738.5 | 1.3318 |
| 50 | 818.3 | 1.3328 |
| 60 | 935.9 | 1.3332 |
| 70 | 1140.4 | 1.3343 |
| 80 | 1264.7 | 1.3345 |
| 90 | 1538.0 | 1.3351 |
| 100 | 1714.6 | 1.3356 |

## Allometric fits
- **Intensity vs power** (left, log–log): $I = a\,P^{b}$ with $a = 16.28 \pm 1.81$, **$b = 1.0048 \pm 0.0261$**, R² = 0.995 → essentially **linear (excitonic)**, no saturation over 5–100 µW.
- **Peak position vs power** (right): $x_c$ **blueshifts** monotonically from 1.3206 eV (5 µW) to 1.3356 eV (100 µW), ≈ 5.0 meV per decade of power.

📥 Full per-column data: [power_fit_results.csv]([file link removed])

RESULT: b = 1.005 ± 0.026