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def

canonicalRSBridge

definition
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module
IndisputableMonolith.RecogSpec.RSBridge
domain
RecogSpec
line
110 · github
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IndisputableMonolith.RecogSpec.RSBridge on GitHub at line 110.

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 107/-! ## The Canonical RSBridge -/
 108
 109/-- The canonical RS bridge with standard geometric parameters -/
 110noncomputable def canonicalRSBridge (L : RSLedger) : RSBridge L where
 111  toBridge := { dummy := () }
 112  edgeDual := 24
 113  alphaExponent := alphaLock  -- The RS fine structure formula
 114  phiProj := -3
 115  radCoeff := 3/2
 116
 117/-- The canonical bridge has edge dual = 24 -/
 118@[simp] theorem canonicalRSBridge_edgeDual (L : RSLedger) :
 119    (canonicalRSBridge L).edgeDual = 24 := rfl
 120
 121/-- The canonical bridge has alpha from ILG -/
 122@[simp] theorem canonicalRSBridge_alpha (L : RSLedger) :
 123    (canonicalRSBridge L).alphaExponent = alphaLock := rfl
 124
 125/-! ## Canonical Mixing Angle Values -/
 126
 127/-- V_cb = 1/24 for canonical bridge -/
 128theorem canonical_V_cb (L : RSLedger) :
 129    V_cb_from_bridge (canonicalRSBridge L) = 1 / 24 := by
 130  simp [V_cb_from_bridge, canonicalRSBridge]
 131
 132/-- V_ub = alphaLock/2 for canonical bridge -/
 133theorem canonical_V_ub (L : RSLedger) :
 134    V_ub_from_bridge (canonicalRSBridge L) = alphaLock / 2 := by
 135  simp [V_ub_from_bridge, canonicalRSBridge]
 136
 137/-- V_us formula for canonical bridge -/
 138theorem canonical_V_us (L : RSLedger) :
 139    V_us_from_bridge (canonicalRSBridge L) phi =
 140      phi ^ (-3 : ℤ) - (3/2 : ℚ) * alphaLock := by