IndisputableMonolith.Cosmology.PhiRungLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Cosmology.BaryonAsymmetryExact
   4
   5/-!
   6# The Baryon Rung on the φ-Ladder
   7
   8This module records the baryon-asymmetry rung on the φ-ladder and proves the
   9arithmetic relations it satisfies (factorizations through the 8-tick period and
  10the passive-mode count).
  11
  12## Core Rung
  13
  14| Rung | Value | Meaning | Status |
  15|------|-------|---------|--------|
  16| 44   | φ⁻⁴⁴ | η_B (baryon asymmetry) | THEOREM |
  17
  18## Status: 0 sorry, 0 axiom
  19-/
  20
  21namespace IndisputableMonolith
  22namespace Cosmology
  23namespace PhiRungLadder
  24
  25open Constants
  26open BaryonAsymmetryExact
  27
  28noncomputable section
  29
  30/-! ## Part 1: The Baryon Rung Value -/
  31
  32/-- The baryon asymmetry rung: −44. -/
  33def eta_B_rung_val : ℤ := -44
  34
  35/-- φ⁴⁴ = 1/η_B. -/
  36noncomputable def eta_B_inv_val : ℝ := phi ^ (44 : ℤ)
  37
  38/-- The baryon rung agrees with the value proved in `BaryonAsymmetryExact`. -/
  39theorem eta_B_rung_val_eq : eta_B_rung_val = eta_B_rung := rfl
  40
  41/-! ## Part 2: Rung Arithmetic -/
  42
  43/-- 44 = 4 × 11 (baryon rung = 4 × passive modes). -/
  44theorem baryon_rung_factorization : (44 : ℕ) = 4 * 11 := by norm_num
  45
  46/-- 55 = 44 + 11: the conjectured inflation e-foldings equals the
  47    baryon rung plus the passive mode count. -/
  48theorem N_e_arithmetic : (44 : ℕ) + 11 = 55 := by norm_num
  49
  50/-- 55 = 5 × 11. -/
  51theorem N_e_factorization : (55 : ℕ) = 5 * 11 := by norm_num
  52
  53/-- The "11 times table": 4×11, 5×11, and the gap 5×11 − 4×11 = 11. -/
  54theorem eleven_times_table :
  55    (4 : ℕ) * 11 = 44 ∧
  56    (5 : ℕ) * 11 = 55 ∧
  57    (55 : ℕ) - 44 = 11 := by norm_num
  58
  59/-! ## Part 3: The Certificate -/
  60
  61/-- Baryon-rung certificate: the rung value and its arithmetic structure. -/
  62structure PhiRungLadderCert where
  63  eta_B_rung_neg : eta_B_rung_val = -44
  64  baryon_factor : (44 : ℕ) = 4 * 11
  65  n_e_sum : (44 : ℕ) + 11 = 55
  66  n_e_factor : (55 : ℕ) = 5 * 11
  67
  68/-- **THE BARYON-RUNG THEOREM**: the baryon asymmetry rung (−44) sits on the
  69    φ-ladder with arithmetic encoding the passive-mode count. -/
  70theorem phi_rung_ladder_cert : PhiRungLadderCert where
  71  eta_B_rung_neg := rfl
  72  baryon_factor := by norm_num
  73  n_e_sum := by norm_num
  74  n_e_factor := by norm_num
  75
  76end
  77
  78end PhiRungLadder
  79end Cosmology
  80end IndisputableMonolith
  81