IndisputableMonolith.Constants.AlphaGenesis.LoopCertificate

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Constants.Alpha
   4import IndisputableMonolith.Constants.AlphaDerivation
   5import IndisputableMonolith.Constants.AlphaGenesis.ResummationForcing
   6import IndisputableMonolith.Constants.AlphaGenesis.PatternForcing
   7import IndisputableMonolith.Foundation.MeasureForcing
   8import IndisputableMonolith.Numerics.Interval.AlphaBounds
   9
  10/-!
  11# Alpha Genesis M3: The EM Recognition Loop and the Genesis Certificate
  12
  13**THE OBJECT.** α⁻¹ is defined forward, as a property of a physical process,
  14before any comparison with measurement:
  15
  16* **Channel budget** — the EM recognition loop spreads one active edge
  17  transition over the passive dressing field of the voxel. The budget is
  18  `Ω(∂Q₃) × E_passive = 4π × 11`: the discrete Gauss-Bonnet total curvature
  19  of the voxel boundary times the passive edge count. Both factors are cube
  20  theorems (`AlphaDerivation.gauss_bonnet_Q3`, `passive_edges_at_D3`); the
  21  cube is the D = 3 voxel and D = 3 is forced (T8).
  22* **Spectral load per channel** — the gap weight w₈ (the Parseval-normalized
  23  DFT-8 projection of the forced φ-pattern; M2) distributed over the channel
  24  budget, in rung units.
  25* **Dressing** — the unique factorizing recognition weight (T9 forced
  26  measure; M1) evaluated at the spectral load.
  27
  28`alphaInvGenesis := channelBudget · contWeight(spectralLoad)` and the theorem
  29`alphaInvGenesis_eq_alphaInv` proves this forward object coincides with the
  30certified pipeline value. The proved band `(137.030, 137.039)` transfers.
  31
  32## Status of the four discrete choices (the no-fit proposition)
  33
  34| Choice | Status after Alpha Genesis |
  35|---|---|
  36| (i) resummation form (E) vs (A) | FORCED (M1: `response_forced`; (A) excluded by `no_additive_response`) |
  37| (ii) canonical φ-pattern | FORCED (M2: `pattern_forced` from T6 self-similarity on the T7 carrier) |
  38| (iii) cube reading of the seed | STRUCTURAL (Gauss-Bonnet + passive-edge theorems on the D=3 voxel; the remaining input is the channel-budget reading itself, named below) |
  39| (iv) D = 3 | FORCED upstream (T8) |
  40
  41The honest remaining input is the **channel-budget bridge**: the reading
  42"inverse coupling = angular budget × passive channels." It is a physical
  43identification (BRIDGE), not a fit: both numbers are cube theorems and no
  44continuous freedom exists. It is named here exactly once, as
  45`ChannelBudgetBridge`.
  46
  47STATUS: THEOREM for all numbered clauses; BRIDGE for the channel-budget
  48reading. No CODATA reference anywhere in this file.
  49-/
  50
  51namespace IndisputableMonolith
  52namespace Constants
  53namespace AlphaGenesis
  54
  55noncomputable section
  56
  57open Constants.AlphaDerivation
  58
  59/-- **The channel budget** of the EM recognition loop: the total angular
  60budget of the voxel boundary spread over the passive dressing edges.
  61`Ω(∂Q₃) × E_passive`, both factors cube theorems. -/
  62def channelBudget : ℝ := AlphaDerivation.geometric_seed
  63
  64/-- The channel budget evaluates to `4π·11` (Gauss-Bonnet × passive edges). -/
  65theorem channelBudget_eq : channelBudget = 4 * Real.pi * 11 :=
  66  AlphaDerivation.geometric_seed_eq
  67
  68/-- The channel budget is the certified pipeline seed. -/
  69theorem channelBudget_eq_alpha_seed : channelBudget = Constants.alpha_seed := by
  70  rw [channelBudget_eq]
  71  simp [Constants.alpha_seed]
  72
  73/-- The channel budget is positive. -/
  74theorem channelBudget_pos : 0 < channelBudget := by
  75  rw [channelBudget_eq]
  76  positivity
  77
  78/-- **The spectral load per channel**: the gap weight w₈ (projection of the
  79forced φ-pattern; M2) per unit of channel budget, in rung units. -/
  80def spectralLoad : ℝ := Constants.w8_from_eight_tick / channelBudget
  81
  82/-- The spectral load is positive. -/
  83theorem spectralLoad_pos : 0 < spectralLoad :=
  84  div_pos Constants.w8_pos channelBudget_pos
  85
  86/-- **THE FORWARD DEFINITION.** α⁻¹ as a property of the EM recognition
  87loop: channel budget attenuated by the T9 forced measure at the spectral
  88load. Defined with no reference to the legacy pipeline or to measurement. -/
  89def alphaInvGenesis : ℝ :=
  90  channelBudget * Foundation.MeasureForcing.contWeight spectralLoad
  91
  92/-- **THE GENESIS IDENTITY.** The forward object coincides with the
  93certified pipeline value: `alphaInvGenesis = alphaInv`. The legacy formula
  94is the display of the forward derivation, exactly as the `RSBridge.rung`
  95table is the display of the mass-derivation program. -/
  96theorem alphaInvGenesis_eq_alphaInv : alphaInvGenesis = Constants.alphaInv := by
  97  unfold alphaInvGenesis spectralLoad
  98  rw [channelBudget_eq_alpha_seed]
  99  exact (alphaInv_eq_seed_mul_forced_weight).symm
 100
 101/-- The proved band transfers to the forward object:
 102`137.030 < alphaInvGenesis < 137.039`. -/
 103theorem alphaInvGenesis_band :
 104    (137.030 : ℝ) < alphaInvGenesis ∧ alphaInvGenesis < (137.039 : ℝ) := by
 105  rw [alphaInvGenesis_eq_alphaInv]
 106  exact ⟨Numerics.alphaInv_gt, Numerics.alphaInv_lt⟩
 107
 108/-- **The channel-budget bridge** (the one named physical input): the
 109inverse EM coupling at leading order is the angular budget of the voxel
 110boundary spread over the passive dressing channels. This is a BRIDGE-grade
 111identification: both numbers are cube theorems, no continuous freedom
 112exists, and the same `11` is consumed by Ω_Λ = 11/16, the η_B arithmetic,
 113and the lepton torsion ladder (cross-application rigidity). -/
 114structure ChannelBudgetBridge where
 115  /-- The seed reading: inverse coupling budget = solid angle × passive channels. -/
 116  seed_reading :
 117    channelBudget = AlphaDerivation.solid_angle_Q3 * (AlphaDerivation.passive_field_edges AlphaDerivation.D : ℝ)
 118
 119/-- The bridge is realized by the cube theorems (non-vacuity). -/
 120def channelBudgetBridge : ChannelBudgetBridge where
 121  seed_reading := AlphaDerivation.alpha_seed_structural
 122
 123/-- **THE ALPHA GENESIS CERTIFICATE.** Bundles the forward derivation:
 124
 1251. channel budget = 4π·11 via Gauss-Bonnet × passive edges (cube theorems);
 1262. the pattern is forced: every admissible ladder is `φᵗ` (M2);
 1273. the spectral envelope is the forced measure (M2);
 1284. the dressing response is forced to `exp(−ε)`; the additive display is
 129   excluded (M1);
 1305. the forward object equals the certified pipeline value;
 1316. the proved band `(137.030, 137.039)` holds for the forward object.
 132
 133No clause references measurement. -/
 134structure AlphaGenesisCert where
 135  deriving Inhabited
 136
 137@[simp] def AlphaGenesisCert.verified (_c : AlphaGenesisCert) : Prop :=
 138  -- 1. seed structure
 139  (channelBudget = 4 * Real.pi * 11) ∧
 140  -- 2. pattern forced
 141  (∀ (L : EightTickLadder) (n : ℕ), L.u n = Constants.phi ^ n) ∧
 142  -- 3. envelope is the forced measure
 143  (∀ k : Fin 8, ¬ k.val = 0 →
 144    GapWeight.geometricWeight k =
 145      (Real.sin ((k.val : ℝ) * Real.pi / 8)) ^ 2 *
 146        Foundation.MeasureForcing.latticeWeight k.val) ∧
 147  -- 4. response forced; additive excluded
 148  (∀ (R : DressingResponse) (ε : ℝ), R.g ε = Real.exp (-ε)) ∧
 149  (∀ R : DressingResponse, R.g ≠ fun ε => 1 - ε) ∧
 150  -- 5. forward object = certified pipeline
 151  (alphaInvGenesis = Constants.alphaInv) ∧
 152  -- 6. proved band
 153  ((137.030 : ℝ) < alphaInvGenesis ∧ alphaInvGenesis < (137.039 : ℝ))
 154
 155theorem AlphaGenesisCert.verified_any (c : AlphaGenesisCert) :
 156    AlphaGenesisCert.verified c := by
 157  refine ⟨channelBudget_eq, ?_, ?_, ?_, ?_, alphaInvGenesis_eq_alphaInv, alphaInvGenesis_band⟩
 158  · intro L n
 159    exact L.pattern_forced n
 160  · exact geometricWeight_eq_sin_mul_forced_measure
 161  · intro R ε
 162    exact R.response_forced ε
 163  · intro R
 164    exact R.no_additive_response
 165
 166end
 167
 168end AlphaGenesis
 169end Constants
 170end IndisputableMonolith
 171