The file contains a single workbook **Book1** with 15 power levels (5–100 µW) already merged into one sheet, energy axis in eV. Suggested x-range: 1.23–1.45 eV.

Step 1: Despike (mandatory before any fit).



130 cosmic-ray spikes removed across all 15 columns. Data cleaned and written back.

Step 2: Lorentzian fit on all 15 spectra + allometric (power-law) fit on I(P) and xc(P).



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

## Results — Lorentzian + Allometric Fit

**Spectral fits (Lorentzian, 1.23–1.45 eV window):**

| Power (µW) | Intensity (a.u.) | x_c (eV) | FWHM (meV) | R² | Tier |
|---|---|---|---|---|---|
| 5 | 98.8 | 1.3206 | 62.4 | 0.887 | HIGH |
| 10 | 189.9 | 1.3244 | 64.4 | 0.950 | HIGH |
| 15 | 267.9 | 1.3264 | 64.1 | 0.958 | HIGH |
| 20 | 353.8 | 1.3278 | 62.7 | 0.968 | HIGH |
| 25 | 425.2 | 1.3290 | 61.7 | 0.973 | HIGH |
| 30 | 516.0 | 1.3300 | 61.3 | 0.975 | HIGH |
| 35 | 564.8 | 1.3304 | 60.8 | 0.978 | HIGH |
| 40 | 694.6 | 1.3315 | 59.3 | 0.981 | HIGH |
| 45 | 738.5 | 1.3318 | 59.1 | 0.981 | HIGH |
| 50 | 818.3 | 1.3328 | 59.0 | 0.981 | HIGH |
| 60 | 935.9 | 1.3332 | 58.0 | 0.982 | HIGH |
| 70 | 1140.4 | 1.3343 | 57.1 | 0.983 | HIGH |
| 80 | 1264.7 | 1.3345 | 56.3 | 0.983 | HIGH |
| 90 | 1538.0 | 1.3351 | 55.3 | 0.984 | HIGH |
| 100 | 1714.6 | 1.3356 | 54.4 | 0.984 | HIGH |

All 15 spectra passed at **HIGH** tier (R² ≥ 0.85). Median R² = 0.981.

**Allometric fit — I = a·P^b (left panel):**
- $a = 16.28 \pm 1.81$
- $b = 1.005 \pm 0.026$
- R² = 0.995 → **linear (excitonic)** regime; no saturation or bimolecular recombination over 5–100 µW.

**Peak position trend (right panel):**
- x_c blueshifts monotonically from 1.3206 eV (5 µW) → 1.3356 eV (100 µW)
- Total shift: ~15 meV across the full range (~5.0 meV per decade of power)
- Consistent with band-filling / bandgap renormalisation in a direct-gap semiconductor.

📥 [Download full results CSV]([file link removed])

RESULT: b = 1.005 ± 0.026