Method: input.csv holds one merged spectrum per power (5-100 uW, 15 spectra) on a common energy axis (1.196-1.606 eV). Each spectrum was fitted with a sum of three Lorentzians plus a constant offset: main peak ~1.33 eV, second peak ~1.54 eV, and a third peak at the high-energy edge (~1.61-1.65 eV, truncated by the data range, so poorly constrained and not used). From each fit I took the peak height (intensity) and centre xc.

Main peak (~1.33 eV), Lorentzian fit:
- Intensity grows from 122.7 counts (5 uW) to 1961 counts (100 uW).
- xc shifts from 1.318 eV to 1.335 eV (small blue shift).

Allometric fit y = a * P^b, applied to the two plots (intensity vs power, xc vs power), unweighted least squares with parameter errors from the covariance matrix:
- Intensity vs power (main peak): a = 21.1, b = 0.977 +- 0.017 (nearly linear). A cross-check with a Lorentzian + linear background fitted only in the 1.25-1.45 eV window gives b = 0.997 +- 0.020, consistent within errors.
- Peak position vs power (main peak): a = 1.31 eV, b = 0.0041 +- 0.0001. The position is almost independent of power, with a very small blue shift.
- Second peak (~1.54 eV): intensity b = 0.774 +- 0.027 (sub-linear); xc b = 0.0016 +- 0.0005.

Plot data are in plotdata.csv (P, I, I_err, xc, xc_err). The plot images were not rendered because matplotlib is not installed here.

The reported b is the intensity-vs-power exponent of the main peak.

RESULT: b = 0.977 ± 0.017
