`g2FromLoops`

definition

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module: IndisputableMonolith.RecogSpec.BridgeDerivation
domain: RecogSpec
line: 48 · github
papers citing: none yet

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IndisputableMonolith.RecogSpec.BridgeDerivation on GitHub at line 48.

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formal source

  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

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