Numerical Verification

Numerical Golden Verification Suite

All mathematical nodes and algorithms are verified against NumPy/SciPy reference standards in backend/tests/test_golden.py and backend/tests/test_vibration_golden.py:

• Arithmetic Float64 Error: $|x_{\text{computed}} - x_{\text{reference}}| \le 1.0 \times 10^{-12}$ (Pass)
• FFT / IFFT Reconstruction RMS Error: $RMS \le 1.0 \times 10^{-9}$ (Pass)
• DCT Type II Reconstruction Error: $RMS \le 1.0 \times 10^{-12}$ (Pass)
• Haar Wavelet Reconstruction Error: $RMS \le 1.0 \times 10^{-12}$ (Pass)
• Sensor Calibration Precision: Relative error $\le 0.1%$ (Pass)
• Velocity Integration Precision: Relative error $\le 1.0%$ (Pass)
• Bearing Fault Frequency Precision: Relative error $\le 0.1%$ (Pass)
• Single-Plane Rotor Balancing Precision: Mass error $\le 1.0%$, Angle error $\le 1.0^\circ$ (Pass)