down_generation_spacing

formal source

 110             cube_edges, active_edges_per_tick, D, wallpaper_groups]
 111  omega
 112
 113theorem down_generation_spacing :
 114    r_down "s" - r_down "d" = 11 ∧ r_down "b" - r_down "d" = 17 := by
 115  simp only [r_down, tau, Anchor.E_passive, Anchor.W, passive_field_edges,
 116             cube_edges, active_edges_per_tick, D, wallpaper_groups]
 117  omega
 118
 119/-! ## Mass Ratio Predictions (Sector-Internal)
 120
 121Within each sector, the mass ratio between generations is a pure phi-power:
 122  m(gen2) / m(gen1) = φ^{tau(1)} = φ^11 ≈ 199
 123  m(gen3) / m(gen1) = φ^{tau(2)} = φ^17 ≈ 3571
 124
 125These are the same ratios already verified for leptons. -/
 126
 127theorem up_charm_to_up_ratio :
 128    rs_mass_MeV .UpQuark (r_up "c") / rs_mass_MeV .UpQuark (r_up "u") =
 129    Constants.phi ^ (11 : ℕ) := by
 130  simp only [r_up, tau, Anchor.E_passive, Anchor.W, passive_field_edges,
 131             cube_edges, active_edges_per_tick, D, wallpaper_groups]
 132  unfold rs_mass_MeV
 133  simp only [B_pow, r0, Anchor.E_passive, Anchor.W, passive_field_edges,
 134             cube_edges, active_edges_per_tick, D, wallpaper_groups, A]
 135  have hphi := Constants.phi_pos
 136  have hphi_ne : Constants.phi ≠ 0 := ne_of_gt hphi
 137  field_simp
 138  rw [← zpow_natCast, ← zpow_add₀ hphi_ne]
 139  congr 1
 140
 141theorem top_to_up_ratio :
 142    rs_mass_MeV .UpQuark (r_up "t") / rs_mass_MeV .UpQuark (r_up "u") =
 143    Constants.phi ^ (17 : ℕ) := by