ml_stellar

formal source

 156def characteristic_tier_scaffold : ℤ := 1
 157
 158/-- The derived stellar M/L ratio in solar units -/
 159noncomputable def ml_stellar : ℝ := φ ^ characteristic_tier_scaffold
 160
 161/-- **THEOREM (PROVED)**: Stellar M/L value is φ. -/
 162theorem ml_stellar_value : ml_stellar = φ := by
 163  unfold ml_stellar characteristic_tier_scaffold
 164  simp only [zpow_one]
 165
 166/-- **CERT(definitional)**: Stellar M/L is a power of φ. -/
 167theorem ml_is_phi_power' (n : ℤ) (Δδ : ℝ) (h : Δδ = n * J_bit) :
 168    ml_from_cost_diff Δδ = φ ^ n := by
 169  simp only [ml_from_cost_diff, J_bit] at *
 170  rw [h]
 171  -- exp(n * log(φ)) = φ^n by definition of zpow for positive reals
 172  have hφ : 0 < φ := Constants.phi_pos
 173  rw [← Real.rpow_intCast φ n]
 174  rw [Real.rpow_def_of_pos hφ]
 175  ring
 176
 177/-- **HYPOTHESIS**: The characteristic mass-to-light ratio for stellar populations is uniquely determined by the eight-tick partition.
 178    STATUS: EMPIRICAL_HYPO
 179    TEST_PROTOCOL: Galactic survey of stellar M/L across different ages and metallicities to verify adherence to φ-ladder rungs.
 180    FALSIFIER: Observation of stable stellar populations with M/L values that consistently deviate from φ^n rungs. -/
 181def H_StellarML : Prop :=
 182  ml_stellar = φ
 183
 184/--- SCAFFOLD: M/L falsifiability check. -/
 185theorem ml_falsifiable (h : H_StellarML) :
 186    ml_stellar ≠ φ → False := by
 187  intro h_neq
 188  exact h_neq h
 189