Prime Diagnostic Explorer
Spectral law analysis revealing the π/2 (90°) phase attractor phenomenon
Primes naturally converge toward 90° phase orientation in spectral space
What is This?
The π/2 Attractor Discovery
The spectral law reveals that prime numbers naturally organize toward a 90° (π/2 radian)phase orientation when analyzed through spectral energy decomposition. This isn't forced—it emerges from the balance between competing energy components.
Key Metrics
- Pattern Strength: Overall coherence in spectral space
- Phase Angle (θ): Orientation in complex plane
- Δθ from 90°: Distance from optimal attractor state
- Energy Balance: Equilibrium between growth and inhibition
- Spectral Clarity: Combined quality metric
Expected Outcome
Primes: θ ≈ 90° (Δθ near 0°), high spectral balance
Composites/Random: θ diverges from 90°, low coherence
Integers: Moderate alignment, mixed patterns
The π/2 Significance
90° represents the balance point where competing energy components achieve optimal equilibrium. This is the natural attractor state—not imposed, but emergent from the underlying spectral structure. Primes uniquely converge to this quadrature state.
Note: As the sweep range increases for prime sequences, the phase angle θ continues to decrease toward 90° (π/2 quadrature), demonstrating the attractor convergence property maintained by the underlying spectral balance.
Analysis Parameters
Sequence will contain ~1085 elements