IndisputableMonolith.RecogSpec.BridgeDerivation

   1import Mathlib
   2import IndisputableMonolith.RecogSpec.RSBridge
   3import IndisputableMonolith.RecogSpec.ObservablePayloads
   4import IndisputableMonolith.Constants
   5
   6/-!
   7# Bridge Derivation
   8
   9Derives the canonical mixing-angle payload `CkmMixingAngles` and g-2 from
  10`RSBridge` geometry.
  11
  12## Canonical semantics
  13
  14  mixingAngles = { vus := V_us, vcb := V_cb, vub := V_ub }
  15
  16These are CKM mixing elements derived from bridge cycle/geometry:
  17- V_us from golden projection φ^{-3} with radiative correction
  18- V_cb from edge-dual geometry 1/24
  19- V_ub from fine-structure coupling α/2
  20
  21## g-2
  22
  23  g2FromLoops B φ = 1 / φ^{B.loopOrder}
  24
  25The loop order is a structural integer on the bridge (default 5),
  26giving g-2 = 1/φ^5 for the canonical bridge.
  27-/
  28
  29namespace IndisputableMonolith
  30namespace RecogSpec
  31
  32open Constants
  33
  34noncomputable section
  35
  36variable {L : RSLedger}
  37
  38/-- Mixing angles derived from bridge cycle/geometry structure. -/
  39def mixingFromCycles (B : RSBridge L) (φ : ℝ) : CkmMixingAngles :=
  40  ⟨ V_us_from_bridge B φ,
  41    V_cb_real B,
  42    V_ub_from_bridge B ⟩
  43
  44/-- g-2 muon derived from bridge loop structure.
  45
  46The bridge carries a structural `loopOrder` (default 5).
  47g-2 = 1/φ^{loopOrder} for the canonical bridge. -/
  48def g2FromLoops (B : RSBridge L) (φ : ℝ) : ℝ :=
  49  1 / (φ ^ B.loopOrder)
  50
  51/-- For the canonical bridge, V_cb = 1/24. -/
  52theorem mixingFromCycles_Vcb_canonical (B : RSBridge L) (hB : B.edgeDual = 24) :
  53    V_cb_from_bridge B = 1 / 24 := by
  54  simp [V_cb_from_bridge, hB]
  55
  56/-- Canonical bridge g-2 equals 1/φ^5. -/
  57theorem g2FromLoops_canonical (B : RSBridge L) (φ : ℝ)
  58    (hLoop : B.loopOrder = 5) :
  59    g2FromLoops B φ = 1 / (φ ^ 5) := by
  60  simp only [g2FromLoops, hLoop]
  61
  62/-- The canonical bridge yields g-2 = 1/φ^5. -/
  63theorem canonical_g2FromLoops (φ : ℝ) :
  64    g2FromLoops (canonicalRSBridge L) φ = 1 / (φ ^ 5) := by
  65  simp [g2FromLoops, canonicalRSBridge]
  66
  67end
  68
  69end RecogSpec
  70end IndisputableMonolith
  71