Emergent Scale Symmetry and the Golden-Ratio Attractor in the τ-Field
UNNS Operators Tier II
Dimensionless Constants
Φ-Scale Chamber
Lab v0.7.2
Abstract.
Operator XIV — Φ-Scale — extends the phase-coupling logic of Operator XIII into the domain of recursive scale symmetry.
It reveals that the golden ratio φ ≈ 1.618 emerges spontaneously as a scale attractor in τ-Field dynamics: a point of minimal phase-variance across recursive magnification.
The Φ-Scale Chamber demonstrates this phenomenon interactively, sweeping the μ-parameter and visualizing Δscale(μ) and Π(μ) to identify μ★ ≈ φ.