123 rw [J_at_phi] 124 -- (√5 - 2)/2 ≈ (2.236 - 2)/2 = 0.118 125 have h_sqrt5_bound : Real.sqrt 5 < 2.24 := by 126 have h5_sq : Real.sqrt 5 ^ 2 = 5 := Real.sq_sqrt (by norm_num : (5 : ℝ) ≥ 0) 127 have h_target : (2.24 : ℝ)^2 > 5 := by norm_num 128 nlinarith [Real.sqrt_nonneg 5, sq_nonneg (Real.sqrt 5)] 129 linarith 130 131/-! ## Connection to Consciousness Threshold -/ 132 133/-- HYPOTHESIS: The consciousness threshold C = 1 emerges from φ-quantization. 134 135 The exact relationship needs derivation. Some possibilities: 136 1. C = 1 is the point where J-cost integration over one octave equals unity 137 2. C = 1 relates to φ^n summing to specific values 138 3. C = 1 is forced by the 8-tick structure interacting with φ 139 140 This is marked as a hypothesis until the derivation is complete. -/
depends on (25)
Lean names referenced from this declaration's body.