Data despiked (130 cosmic-ray spikes removed across 15 power columns). Now running the Lorentzian power-dependence fit — this fits a Lorentzian+slope profile to each power spectrum, extracts peak position (xc) and intensity, builds both panels, and applies the allometric (I = a·P^b) fits.



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

Done. The merged spectra (one column per power, 5→100 µW) were despiked first (130 cosmic-ray spikes removed), then each spectrum was fitted with a Lorentzian+slope profile over 1.23–1.45 eV. All 15 powers converged to the **HIGH** tier (R² = 0.887–0.984, median 0.981).

**Per-power Lorentzian fit results**

| 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 (the two plots)**

- **Intensity vs Power** — $I = a\,P^{b}$: $a = 16.28 \pm 1.81$, **$b = 1.0048 \pm 0.0261$**, R² = 0.995. Essentially linear ($b \approx 1$), consistent with a simple excitonic (radiative) regime with no saturation or bimolecular quenching over this range.
- **Peak position vs Power** — the peak **blue-shifts** monotonically from 1.3206 → 1.3356 eV (Δ ≈ 15 meV across 5→100 µW); the fitted trend is ≈ **5.0 meV per decade** of power (log-linear rise, steepest at low power, flattening at high power).

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

The reported `b` below is the intensity–power allometric exponent (the canonical power-law quantity; the xc panel is a monotonic blue-shift trend rather than a pure power law).

RESULT: b = 1.0048 ± 0.0261