Pi as Phase Collapse: A Formal Reinterpretation of Infinity Through Binary Superposition

This white paper proposes a new structural interpretation of the number π—not as an infinite decimal, but as the result of harmonic convergence between two binary poles: 0 (potential) and 1 (impulse). We define π as a stable phase collapse state emerging from their superposition. This allows π to be implemented not as a number to approximate, but as a resonance boundary in logic systems, quantum circuits, and field simulations. Mathematically expressed as:πₛ = lim_{ΔΨ→0} ⟨0 ⊕ 1⟩ → φ The paper presents two functional representations of π (π₁ and π₂) as causal and acausal components of curvature dynamics, forming a dual logic system. We propose an experimental framework to detect πₛ as emergent phase-geometry rather than computed quantity. Keywords: pi redefinition, superposition, binary resonance, curvature logic, quantum phase, harmonic attractor