The Semantic Wavefunction

Every token/concept represented as a complex-valued wave packet:

ψ = (r + i·d) × e^(iθ)

Components

r (Real Amplitude): Information density / semantic "mass"

• Higher for rare, conceptual words
• Lower for common, structural words

d (Imaginary Amplitude): Semantic entropy / volatility

• Higher for polysemous words (multiple meanings)
• Lower for stable, unambiguous terms

θ (Phase Vector): 32-dimensional eigenspace position

• Derived from Graph Laplacian decomposition
• Encodes relational position in semantic hyperspace

Hermitian Resonance

Interaction between concepts via Hermitian inner product:

E_ab = ψ_a · ψ_b†

Real Resonance: (r_a·r_b + d_a·d_b) · cos(θ_a - θ_b)

• Structural alignment, symmetric

Imaginary Flux: (r_a·d_b - r_b·d_a) · sin(θ_a - θ_b)

• Directional information flow, asymmetric
• Captures semantic tension and ambiguity collapse

Related: Graph Laplacian, Spectral Theory, Complex Analysis