Supplementary Materials

All Python implementations are available in the accompanying repository. The proof-of-concept script poc_spectral_vs_euclidean.py exactly reproduces the reported results and allows further exploration of different potentials, boundary conditions, and fidelity thresholds. Key parameters: $Λ = 1$ , $κ = 0.15$ , $K = 12 max$ , $N = 800 τ$ , $N = 20,000 paths$ , seed $= 42$ .

poc_spectral_vs_euclidean.py — Main proof-of-concept (this paper)
euclidean_vs_spectral_2.py — Proof-of-concept 2
euclidean_vs_spectral_3.py — Proof-of-concept 3
wavefunction.py — Documented wavefunction class implementing the spectral complexity measure
spectral.py — Comparison of classical, Euclidean, and spectral paths in 3D space

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