Method: input.csv holds one energy axis (1.196-1.606 eV) and 15 spectra (5-100 uW). Each spectrum was fitted with a sum of three Lorentzians plus a constant background (the 1.32 eV main peak, a 1.54 eV peak, and a third peak cut off at the 1.6 eV edge of the window). Peak height and xc were taken from the fit for the main peak near 1.32 eV, whose fit is stable.

Main-peak results: the intensity rises from 123 counts at 5 uW to 1934 counts at 100 uW. The position moves from 1.3180 eV to 1.3353 eV. Per-power values are in fit_results.csv; plots are intensity_vs_power.svg and position_vs_power.svg.

Allometric fit y = a * P^b (nonlinear least squares, unweighted):
- Intensity vs power: a = 21.3, b = 0.971 +/- 0.019, so the intensity is close to linear in power. A weighted fit gives b = 0.927 +/- 0.013 and a single-Lorentzian fit in a 1.22-1.43 eV window gives b = 1.001 +/- 0.018, so the systematic spread is about 0.04.
- Peak position vs power: a = 1.310 eV, b = 0.0042 +/- 0.0001, a very weak blue shift.

The reported b is the intensity exponent.

RESULT: b = 0.971 ± 0.019
