IndisputableMonolith.Verification.EMAlphaCert

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Constants.Alpha
   4import IndisputableMonolith.Constants.GapWeight
   5import IndisputableMonolith.Numerics.Interval.AlphaBounds
   6
   7/-!
   8# EM Fine-Structure Constant (α_EM) Construction Certificate
   9
  10This certificate records the VALUE of the assembled EM coupling expression. It is
  11NOT a derivation of the measured infrared constant `α⁻¹(0) = 137.035999`.
  12
  13What this certificate establishes (all four conjuncts are true Lean facts):
  14  α⁻¹ = α_seed · exp(−f_gap / α_seed),  with α_seed = 44π,  f_gap = w8·ln(φ),
  15  and the resulting expression lies in `(137.030, 137.039)`.
  16
  17## Honest status (2026-06-19 alpha audit, READ THIS)
  18
  19The exponential dressing `g(t)=φ⁻ᵗ` and the spectral weight `w₈` are forced with
  20zero α-input (`AlphaGenesis.CalibrationForcing`, `GapWeight`). The SEED `44π = 4π·11`
  21is NOT a derived coupling: it is an identification that lands ~5.6 ppm from CODATA,
  22and three quarantine verdict modules in `Constants/AlphaGenesis/` settle this:
  23* `U1Normalization`: the gauge-invariant photon DOF on the cube is the cycle rank
  24  `E−V+1 = 5`, not the passive-edge ledger count `11`.
  25* `CurvatureJCostVerdict`: `4π` is a linear Gauss-Bonnet invariant, not a cost; the
  26  genuine quadratic J-cost of the cube curvature is `π² ≈ 9.87`, not `4π·11`.
  27* `MeasurementVerdict` / `ScaleIdentification`: the first-order value is excluded by
  28  measurement (> 30000σ above CODATA) and sits above the Thomson ceiling at every scale.
  29
  30Net: RS forces the photon channel, the closure normalization `4π`, an `O(4π)`
  31recognition-scale coupling, and the φ-dressing. The exact infrared value `α⁻¹(0)` is
  32an irreducible boundary condition of the recognition hierarchy in the present
  33formalization. It is OPEN, stored as a negative closure (five routes tested, all closed).
  34Do not read the `(137.030, 137.039)` interval below as a derivation of CODATA; it is
  35the value of the construction, and CODATA happening to fall inside is the ~5.6 ppm
  36near-miss, not a forced equality.
  37-/
  38
  39namespace IndisputableMonolith
  40namespace Verification
  41namespace EMAlpha
  42
  43open IndisputableMonolith.Constants
  44open IndisputableMonolith.Numerics
  45
  46structure EMAlphaCert where
  47  deriving Repr
  48
  49/-- Construction predicate: the four structural facts of the assembled α expression.
  50"verified" here means these four facts hold; it does NOT mean the measured `α⁻¹(0)`
  51is derived (that is OPEN; see the honest-status note above and the AlphaGenesis
  52verdict modules).
  53
  541. alpha_seed = 44π            (definitional; an identification, not a forced coupling)
  552. f_gap = w8 * ln(phi)        (forced, zero α-input)
  563. alphaInv = alpha_seed * exp(-f_gap / alpha_seed)   (the φ-dressing assembly)
  574. alphaInv lies in (137.030, 137.039)   (value of the construction, NOT a CODATA derivation)
  58-/
  59@[simp] def EMAlphaCert.verified (_c : EMAlphaCert) : Prop :=
  60  -- 1) Seed identification 44π (NOT a derived gauge normalization; cycle rank is 5, see U1Normalization)
  61  (alpha_seed = 44 * Real.pi) ∧
  62  -- 2) Gap term forced from w8 and phi (zero α-input)
  63  (f_gap = w8_from_eight_tick * Real.log phi) ∧
  64  -- 3) Canonical exponential (φ-dressing) assembly
  65  (alphaInv = alpha_seed * Real.exp (-(f_gap / alpha_seed))) ∧
  66  -- 4) value of the assembled expression; exact α(0)=137.035999 is a boundary condition, OPEN
  67  (137.030 < alphaInv ∧ alphaInv < 137.039)
  68
  69/-- Top-level theorem: the EM alpha certificate verifies. -/
  70@[simp] theorem EMAlphaCert.verified_any (c : EMAlphaCert) :
  71    EMAlphaCert.verified c := by
  72  simp only [verified]
  73  refine ⟨by simp only [alpha_seed]; ring, rfl, rfl, ?_⟩
  74  · -- Range check for alphaInv using theorems from AlphaBounds
  75    constructor
  76    · exact alphaInv_gt
  77    · exact alphaInv_lt
  78
  79end EMAlpha
  80end Verification
  81end IndisputableMonolith
  82