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

Lorentzian+slope fits converged on **all 15 power levels** (5–100 µW), every column in the HIGH tier (R² = 0.887–0.984, median 0.981). Left panel = fitted peak intensity vs power with the allometric fit $I = a\cdot P^b$; right panel = fitted peak position $x_c$ vs power.

**Per-power extracted values (Lorentzian fit):**

| Power (µW) | Intensity (counts) | $x_c$ (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 fit** ($I = a \cdot P^b$, log–log):
- $a = 16.28 \pm 1.81$
- $b = 1.0048 \pm 0.0261$
- R² = 0.9951 → essentially linear (b ≈ 1), i.e. no measurable saturation up to 100 µW.

**Peak-position trend:** $x_c$ shifts to higher energy (blueshift) from 1.3206 → 1.3356 eV across the range (~15 meV total, ≈ 5 meV/decade), while FWHM narrows from ~62 → 54 meV.

📥 [power_fit_results.csv]([file link removed])

RESULT: b = 1.0048 ± 0.0261