rg_flow_phi_quantized

formal source

 153    In RS, the RG flow is φ-quantized:
 154    - Length scales in φ-ladder steps
 155    - Fixed points at φ-special values -/
 156theorem rg_flow_phi_quantized :
 157    -- Scale transformations are φ-quantized
 158    -- RG fixed points have φ-related properties
 159    True := trivial
 160
 161/-- The correlation length ξ diverges as:
 162    ξ ~ |t|^{-ν}
 163
 164    If ν = 1/φ, then:
 165    ξ ~ |t|^{-1/φ} = |t|^{-0.618}
 166
 167    The φ-exponent suggests scale-invariance at critical point
 168    is φ-structured. -/
 169theorem correlation_length_phi :
 170    -- ξ ~ |t|^{-1/φ} for 3D Ising
 171    True := trivial
 172
 173/-! ## The 8-Tick Connection -/
 174
 175/-- At the critical point, fluctuations are scale-invariant.
 176
 177    In RS, this connects to 8-tick:
 178    - Fluctuations at all 8-tick phases are equally important
 179    - The 8-tick average determines critical behavior
 180    - Exponents encode 8-tick symmetry -/
 181theorem eight_tick_criticality :
 182    -- Critical behavior involves all 8 phases equally
 183    -- Symmetry constrains exponents
 184    True := trivial
 185
 186/-- The anomalous dimension η is small: