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

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

## Pipeline summary
1. **Spectra located** — the OPJ is already merged: one spectrum per power in `Book1/Sheet1`, 15 columns from 5 → 100 µW, energy axis in eV.
2. **Despike** (σ=4, mandatory pre-fit) — removed 130 cosmic-ray spikes across all 15 spectra.
3. **Lorentzian fit** on every spectrum (window 1.23–1.45 eV). All 15 converged to **HIGH tier**, R² = 0.887–0.984, SNR 7.6–24.0.

## Per-power extracted values (Lorentzian fit)
| Power (µW) | Intensity (counts) | xc (eV) | FWHM (meV) | R² |
|---:|---:|---:|---:|---:|
| 5 | 98.8 | 1.32062 | 62.4 | 0.887 |
| 10 | 189.9 | 1.32437 | 64.4 | 0.950 |
| 20 | 353.8 | 1.32783 | 62.7 | 0.968 |
| 30 | 516.0 | 1.32998 | 61.3 | 0.975 |
| 50 | 818.3 | 1.33279 | 59.0 | 0.981 |
| 70 | 1140.4 | 1.33430 | 57.1 | 0.983 |
| 100 | 1714.6 | 1.33562 | 54.4 | 0.984 |

(Full table of all 15 powers in the CSV.)

## Allometric fits
- **Intensity vs power** — $I = a\cdot P^{b}$: $a = 16.28 \pm 1.81$, **$b = 1.0048 \pm 0.0261$**, R² = 0.9951. $b \approx 1$ → linear (excitonic) scaling, no saturation or Auger nonlinearity.
- **Peak position vs power** — monotonic **blueshift**: xc rises from 1.3206 eV (5 µW) to 1.3356 eV (100 µV), i.e. ~15 meV total, ≈ 5.0 meV/decade; FWHM narrows 62 → 54 meV.

RESULT: b = 1.0048 ± 0.0261