Data: input.csv holds one shared energy axis (1.196-1.606 eV, 1024 points) and 15 spectra (5-100 uW), so the spectra are already merged on a common axis. Three features appear in each spectrum: a strong peak near 1.33 eV, a broad shoulder or peak near 1.54 eV, and a third peak cut off at the high-energy edge (>1.60 eV). The edge peak is not constrained, so I did not use it. One cosmic-ray spike at 90 uW (about 1.605 eV) was rejected as an outlier.

Method: each spectrum was fitted with a Lorentzian A/(1+((E-xc)/(w/2))^2) plus a linear background. This was done in a window around the main peak (1.2-1.45 eV) and, as a check, in a global 3-Lorentzian + constant fit of the full range. Intensity is the fitted peak height A, and position is xc.

Main peak (about 1.33 eV), windowed fit:
- Intensity A rises from about 117 counts at 5 uW to about 1958 counts at 100 uW.
- xc rises from 1.3173 eV to 1.3351 eV (a blueshift of about 18 meV).

Allometric fit y = a * P^b (P in uW):
- Intensity vs power: b = 1.004 +/- 0.019 (a = 18.6 +/- 1.5), unweighted. A fit weighted by the Lorentzian-fit errors gives b = 0.958 +/- 0.002, but that error reflects only the noise, not the point-to-point scatter.
- Peak position vs power: b = 0.0043 +/- 0.0001 (a = 1.309 +/- 0.0004 eV), essentially a very weak power law (slight blueshift with power).

Robustness: other fit windows (1.22-1.42, 1.2-1.5 eV) give b between 1.00 and 1.01 (unweighted) for intensity. The global 3-Lorentzian fit gives 0.98 +/- 0.02. The second peak (about 1.54 eV) is sublinear, with b about 0.79 +/- 0.01.

Conclusion: the main-peak intensity is linear in excitation power (b of about 1).

RESULT: b = 1.00 ± 0.02
