Method: input.csv holds one merged energy axis (1.196-1.606 eV, 1024 points) and 15 spectra (5-100 uW). Every spectrum shows a dominant PL peak near 1.33 eV, plus a weaker feature near 1.54 eV and a rising edge above 1.6 eV (cut off by the window). I fitted the dominant peak in each spectrum with a Lorentzian plus constant offset, y = A/(1+((E-xc)/(w/2))^2) + c, over 1.27-1.40 eV. A is the peak intensity (height) and xc is the peak position.

Fit results, power (uW): A (counts), xc (eV)
5: 120.8, 1.3187
10: 221.4, 1.3238
15: 323.3, 1.3259
20: 419.0, 1.3274
25: 516.1, 1.3287
30: 624.5, 1.3297
35: 702.4, 1.3302
40: 837.4, 1.3313
45: 904.4, 1.3316
50: 1013.8, 1.3326
60: 1224.8, 1.3330
70: 1442.1, 1.3341
80: 1640.99, 1.3343
90: 1883.3, 1.3349
100: 2169.2, 1.3355
(FWHM is about 0.072 eV throughout.)

Plots: (1) Lorentzian intensity vs power; (2) Lorentzian peak position vs power. Both are fitted with the allometric law y = a * P^b.

Allometric fits (weighted by fit errors; uncertainties scaled by sqrt(reduced chi2)):
- Intensity: a = 20.9, b = 0.999 ± 0.014. That is, I is linear in P. The result is stable across fit windows: b = 0.98 to 1.02 for windows 1.25-1.43 and 1.29-1.38 eV, and 1.03 unweighted.
- Peak position: a = 1.3126 eV, b = 0.00376 ± 0.00009. That is, a very small blueshift of about 1.7 meV over the range.

The reported exponent is the one from the intensity-vs-power plot.

RESULT: b = 1.00 ± 0.014
