![Power Fit]([file link removed])

## Power-dependent Lorentzian analysis (Book1, window 1.23–1.45 eV)

All 15 spectra (5→100 µW) were despiked (130 spikes removed) and fitted with a **Lorentzian profile**. Every column converged to **HIGH tier** (R² = 0.887–0.984, median 0.981; SNR 7.6–24.0). Peak intensity was taken from the wing baseline at $x_c$.

**Per-power extracted values:**

| Power (µW) | Intensity (counts) | $x_c$ (eV) | FWHM (meV) | R² |
|---:|---:|---:|---:|---:|
| 5 | 98.8 | 1.32062 | 62.4 | 0.887 |
| 10 | 189.9 | 1.32437 | 64.4 | 0.950 |
| 15 | 267.9 | 1.32636 | 64.1 | 0.958 |
| 20 | 353.8 | 1.32783 | 62.7 | 0.968 |
| 25 | 425.2 | 1.32905 | 61.7 | 0.973 |
| 30 | 516.0 | 1.32998 | 61.3 | 0.975 |
| 35 | 564.8 | 1.33044 | 60.8 | 0.978 |
| 40 | 694.6 | 1.33152 | 59.3 | 0.981 |
| 45 | 738.5 | 1.33179 | 59.1 | 0.981 |
| 50 | 818.3 | 1.33279 | 59.0 | 0.981 |
| 60 | 935.9 | 1.33317 | 58.0 | 0.982 |
| 70 | 1140.4 | 1.33430 | 57.1 | 0.983 |
| 80 | 1264.7 | 1.33446 | 56.3 | 0.983 |
| 90 | 1538.0 | 1.33509 | 55.3 | 0.984 |
| 100 | 1714.6 | 1.33562 | 54.4 | 0.984 |

**Allometric fit — intensity (left panel, $I = a\cdot P^{\,b}$):**
- $a = 16.28 \pm 1.81$, **$b = 1.0048 \pm 0.0261$**, R² = 0.995
- Interpretation: **~linear (excitonic)** — emission scales proportionally with pump power, indicating free-exciton recombination without measurable trap-filling or saturation over 5–100 µW.

**Allometric/trend fit — peak position (right panel):**
- $x_c$ **blueshifts** monotonically from 1.3206 eV (5 µW) to 1.3356 eV (100 µW), a total shift of ≈ 15 meV (~5 meV/decade), following a saturating power-law curve. This mild blue-shift with rising power is typical of exciton–exciton interactions / band-gap renormalization at higher carrier density.

📥 **Full results:** [power_fit_results.csv]([file link removed])

RESULT: b = 1.005 ± 0.026