The file contains one workbook (`Book1`) with the energy axis (col A) and 15 already-merged power columns: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80, 90, 100 µW. Data is in eV, suggested fit window is 1.23–1.45 eV.

Per protocol, I must despike before any fit. Doing that now, then running the Lorentzian power-dependence fit.



Both panels are generated. The Lorentzian fit converged on all 15 power levels (all HIGH tier, R² = 0.887–0.984). The intensity panel carries the allometric fit **I = a·Pᵇ**. To honor the explicit request for an allometric fit on the peak-position panel too, I'll compute a power-law fit (xc = a·Pᵇ) on the extracted positions.



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

**Pipeline:** inspect → despike (130 cosmic-ray spikes removed, σ=4) → Lorentzian fit on all 15 merged power spectra (window 1.23–1.45 eV, cascade) → allometric fits. Every spectrum converged (all HIGH tier, R² = 0.887–0.984, median 0.981).

## Per-power results (Lorentzian fit)

| Power (µW) | Intensity (counts) | xc (eV) | FWHM (meV) | R² |
|---:|---:|---:|---:|---:|
| 5 | 98.8 | 1.3206 | 62.4 | 0.887 |
| 10 | 189.9 | 1.3244 | 64.4 | 0.950 |
| 15 | 267.9 | 1.3264 | 64.1 | 0.958 |
| 20 | 353.8 | 1.3278 | 62.7 | 0.968 |
| 25 | 425.2 | 1.3290 | 61.7 | 0.973 |
| 30 | 516.0 | 1.3300 | 61.3 | 0.975 |
| 35 | 564.8 | 1.3304 | 60.8 | 0.978 |
| 40 | 694.6 | 1.3315 | 59.3 | 0.981 |
| 45 | 738.5 | 1.3318 | 59.1 | 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 |

## Allometric fits

**Peak intensity vs power — I = a·Pᵇ** (left panel, 15 pts):
- a = 16.28 ± 1.81
- **b = 1.005 ± 0.026**, R² = 0.995
- b ≈ 1 → **linear (excitonic)** response; no saturation or superlinear biexciton enhancement across 5–100 µW.

**Peak position vs power — xc = a·Pᵇ** (right panel):
- xc drifts from 1.3206 eV (5 µW) → 1.3356 eV (100 µW): a total **blueshift of ~15 meV** over 2 decades (~5 meV/decade).
- Allometric exponent **b ≈ 0.004** (statistically ≈ 0): the peak position is essentially power-independent; the weak monotonic blueshift is consistent with band-filling / bandgap renormalization at higher excitation.

📥 Full per-power table: [power_fit_results.csv]([file link removed])

RESULT: b = 1.005 ± 0.026