Data is already merged — one workbook (`Book1`) with 15 power-level columns (5–100 µW) and an energy axis in eV. Suggested fit window: **1.23–1.45 eV**. Proceeding with the full pipeline now.

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



130 cosmic-ray spikes removed across all 15 columns; cleaned data written back.

**Step 2 — Lorentzian batch fit on all 15 spectra:**



All 15 Lorentzian fits converged (R² = 0.89–0.99). Peak positions shift from 1.319 eV (5 µW) to 1.336 eV (100 µW); amplitudes grow from ~11 to ~188 counts.

**Step 3 — Allometric fits (I vs P and xc vs P) using Lorentzian profile:**



Pipeline complete. Here are the full results:

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## Lorentzian Fit Summary (15 spectra, window 1.23–1.45 eV)

| Power (µW) | xc (eV) | FWHM (meV) | Amplitude (counts) | R² |
|---|---|---|---|---|
| 5 | 1.3206 | 62.4 | 98.8 | 0.887 |
| 10 | 1.3244 | 64.4 | 189.9 | 0.950 |
| 15 | 1.3264 | 64.1 | 267.9 | 0.958 |
| 20 | 1.3278 | 62.7 | 353.8 | 0.968 |
| 25 | 1.3290 | 61.7 | 425.2 | 0.973 |
| 30 | 1.3300 | 61.3 | 516.0 | 0.975 |
| 35 | 1.3304 | 60.8 | 564.8 | 0.978 |
| 40 | 1.3315 | 59.3 | 694.6 | 0.981 |
| 45 | 1.3318 | 59.1 | 738.5 | 0.981 |
| 50 | 1.3328 | 59.0 | 818.3 | 0.981 |
| 60 | 1.3332 | 58.0 | 935.9 | 0.982 |
| 70 | 1.3343 | 57.1 | 1140.4 | 0.983 |
| 80 | 1.3345 | 56.3 | 1264.7 | 0.983 |
| 90 | 1.3351 | 55.3 | 1538.0 | 0.984 |
| 100 | 1.3356 | 54.4 | 1714.6 | 0.984 |

All 15 columns classified **Tier 1 (HIGH)** — R² ≥ 0.85, FWHM within adaptive gate, xc not at bound.

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## Allometric Fit: I = a·P^b

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

- **a** = 16.28 ± 1.81
- **b** = 1.0048 ± 0.0261
- R² = 0.9951 (15/15 points included)
- Interpretation: **~linear (excitonic regime)** — intensity scales linearly with excitation power, consistent with free-exciton emission where radiative recombination dominates over non-radiative channels.

### Peak position trend (right panel)
xc shifts monotonically from 1.3206 → 1.3356 eV (+15 meV) over 5→100 µW (~5 meV/decade), consistent with band-filling / Burstein–Moses blueshift saturating at higher powers.

📥 [power_fit_results.csv]([file link removed]) · [Lorentz fit CSV]([file link removed])

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RESULT: b = 1.0048 ± 0.0261