tier_difference

formal source

 106From nuclear tier n_nuclear and luminosity tier n_photon:
 107  Δn = n_nuclear - n_photon
 108  M/L = φ^{Δn} -/
 109def tier_difference : PhiTier := nuclear_tier_local - luminosity_tier_local
 110
 111theorem tier_difference_value : tier_difference = 1 := by
 112  unfold tier_difference nuclear_tier_local luminosity_tier_local
 113  norm_num
 114
 115/-- The nucleosynthesis-derived M/L -/
 116noncomputable def ml_nucleosynthesis : ℝ := phi_ladder tier_difference
 117
 118theorem ml_nucleosynthesis_eq_phi : ml_nucleosynthesis = φ := by
 119  unfold ml_nucleosynthesis phi_ladder tier_difference
 120  simp [nuclear_tier_local, luminosity_tier_local, zpow_one]
 121
 122/-! ## Eight-Tick Quantization -/
 123
 124/-- Nuclear reactions are quantized by the eight-tick cycle.
 125
 126Each nuclear reaction step:
 1271. Requires 8 ticks for one complete recognition cycle
 1282. Releases energy in units of E_coh × φ^{-r} for some rung r
 1293. Updates the ledger with conserved quantities
 130
 131This forces tier indices to be integers. -/
 132def eight_tick_quantizes_tiers : Prop :=
 133  ∀ (ρ_tier L_tier : PhiTier), ∃ n : ℤ, ρ_tier - L_tier = n
 134
 135theorem tiers_are_quantized : eight_tick_quantizes_tiers := by
 136  intro ρ L
 137  use ρ - L
 138
 139/-! ## Validation Against Observations -/