Method: input.csv holds 15 spectra (5-100 uW) on a common energy axis (1.196-1.606 eV), so they were used as one merged table. Each spectrum shows a main peak near 1.33 eV, a broad feature near 1.54 eV and a rising edge at the 1.6 eV window limit. The main peak was fitted with a Lorentzian plus constant offset, y = c + A/(1+((x-xc)/w)^2), over 1.22-1.46 eV (scipy curve_fit). Fits in 1.25-1.43 eV, and with an added linear background, gave consistent results.

Lorentzian results (peak height A in counts, xc in eV): A rises from ~113 (5 uW) to ~1964 (100 uW); xc shifts slightly from 1.3193 to 1.3357 eV; width (HWHM) ~0.031 eV, constant.

Plots: matplotlib is not installed here, so no image was rendered; the plotted data (A, dA, xc, dxc, HWHM per power) are in r.npy and the allometric fits are given below (plot.py reproduces both plots where matplotlib exists).

Allometric fits (y = a * P^b, unweighted least squares, parameter errors from the covariance matrix):
- Peak intensity vs power: a = 18.0 ± 1.4, b = 1.012 ± 0.019 (essentially linear). A fit weighted by the Lorentzian-fit errors gives b = 0.967 ± 0.003; alternative windows give b between 0.97 and 1.02.
- Peak position vs power: a = 1.312 ± 0.0005 eV, b = 0.0040 ± 0.0001 (nearly flat, small blue shift).

The headline exponent is the intensity one.

RESULT: b = 1.012 ± 0.019
