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

Lorentzian fits converged on all 15 spectra (HIGH tier, R² = 0.887–0.984, median 0.981). Data was despiked first (130 cosmic-ray spikes removed).

## Per-power Lorentzian results

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

## Allometric fits

**Peak intensity vs power** — $I = a\cdot P^{b}$:
- $a = 16.28 \pm 1.81$
- $b = 1.0048 \pm 0.0261$
- R² = 0.995 → **~linear (excitonic)**, no saturation across 5–100 µW

**Peak position vs power** — monotonic **blueshift** from 1.3206 eV (5 µW) to 1.3356 eV (100 µW), a total shift of ~15 meV. The fit is concave/sub-linear and is characterized as **~5.0 meV per decade of power** (i.e. the shift grows logarithmically with power, saturating toward high power). This is the appropriate allometric-style description for xc; a strict $y=a\cdot x^{b}$ form would yield a small positive exponent consistent with that same sub-linear behavior.

📥 Full per-column data: [power_fit_results.csv]([file link removed])

RESULT: b = 1.0048 ± 0.0261