Data: input.csv holds one energy axis (1.196-1.606 eV, 1024 points) and 15 spectra (5-100 uW), already merged. A cosmic-ray spike (col 45 uW, ~1.60 eV) was removed by a robust despike.

Each spectrum has a dominant peak near 1.32-1.335 eV (FWHM ~0.07 eV) and further structure at ~1.54 eV and a peak cut off at the upper edge (~1.61 eV). I fitted every spectrum with a sum of 3 Lorentzians + constant offset, L(x) = I / (1 + ((x - xc)/(w/2))^2), where I is the peak height, and took I and xc of the dominant ~1.32 eV peak. As a cross-check I fitted a single Lorentzian + linear background in a 1.20-1.47 eV window.

Fit results (3-Lorentzian model), power (uW): intensity, xc (eV)
5: 122.7, 1.31804 | 10: 226.6, 1.32315 | 15: 319.3, 1.32522 | 20: 409.9, 1.32686 | 25: 500.7, 1.32813
30: 593.7, 1.32907 | 35: 669.1, 1.32955 | 40: 792.7, 1.33071 | 45: 853.3, 1.33098 | 50: 947.7, 1.33195
60: 1131.6, 1.33241 | 70: 1316.9, 1.33361 | 80: 1490.6, 1.33386 | 90: 1704.4, 1.33457 | 100: 1961.8, 1.33519

Plots (intensity vs power, peak position vs power) each with the allometric fit y = a * P^b (curve_fit):
- Intensity vs power: a = 21.0 +/- 1.5, b = 0.978 +/- 0.017 (window-fit cross-check: b = 1.003 +/- 0.019), i.e. essentially linear.
- Peak position vs power: a = 1.310 +/- 0.0004, b = 0.0042 +/- 0.0001 (a small blue shift, ~1.318 to 1.335 eV).

The uncertainty is the 1-sigma covariance error of the unweighted fit (the error-weighted fit gave chi2_red ~ 58, so the formal fit errors were not trusted for weighting).

RESULT: b = 0.978 ± 0.017
