Wave Coherence as a Computational Primitive: Phase-Encoded Relationship Detection via Harmonic Analysis

A validated mathematical framework using phase encoding on the unit circle and harmonic coherence as a universal relationship detection operator. A single function — cos(n * (θ_a - θ_b)) — detects exact matches, harmonic families, oppositions, fuzzy proximity, and multi-type relationships. Validated across 10 structured tests with reproducible Rust code. Key result: harmonic scan discovers multi-group relationships that require multiple SQL JOINs, with infinite harmonic capacity and geometric invariants that persist across all frequencies.