`Az_eq`

proved

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module: IndisputableMonolith.Masses.AnchorDerivation
domain: Masses
line: 62 · github
papers citing: none yet

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IndisputableMonolith.Masses.AnchorDerivation on GitHub at line 62.

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depends on

formal source

  59theorem Epz_eq : Epz = 11 := by
  60  simp [Epz, D, passive_field_edges, cube_edges, active_edges_per_tick]
  61
  62theorem Az_eq : Az = 1 := by
  63  simp [Az, active_edges_per_tick]
  64
  65/-! ## Alternative derivation formulas -/
  66
  67/-- Alternative formula for B_pow. -/
  68def B_pow_alt : Anchor.Sector → ℤ
  69  | .Lepton      => -(2 * Epz)           -- = -(2 × 11) = -22
  70  | .UpQuark     => -Az                   -- = -1
  71  | .DownQuark   => (2 * Etz) - 1         -- = 24 - 1 = 23
  72  | .Electroweak => Az                    -- = 1
  73
  74/-- Alternative formula for r0 (using 8-2 form for lepton). -/
  75def r0_alt : Anchor.Sector → ℤ
  76  | .Lepton      => 4 * Wz - (8 - 2)      -- = 68 - 6 = 62
  77  | .UpQuark     => 2 * Wz + Az           -- = 34 + 1 = 35
  78  | .DownQuark   => Etz - Wz              -- = 12 - 17 = -5
  79  | .Electroweak => 3 * Wz + 4            -- = 51 + 4 = 55
  80
  81/-! ## Verification: Main definitions match alternative formulas -/
  82
  83theorem B_pow_eq_alt (s : Anchor.Sector) : Anchor.B_pow s = B_pow_alt s := by
  84  cases s <;> simp only [Anchor.B_pow, B_pow_alt, Anchor.E_passive, Anchor.E_total,
  85    Anchor.A, passive_field_edges, cube_edges, active_edges_per_tick, D,
  86    Epz, Etz, Az]
  87
  88theorem r0_eq_alt (s : Anchor.Sector) : Anchor.r0 s = r0_alt s := by
  89  cases s <;> simp only [Anchor.r0, r0_alt, Anchor.W, Anchor.E_total, Anchor.A,
  90    wallpaper_groups, cube_edges, active_edges_per_tick, D, Wz, Etz, Az]
  91  all_goals norm_num
  92

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