time_dilation_factor

formal source

  73
  74/-- The subjective time dilation factor: 360/37 ≈ 9.73.
  75    Ledger time passes ~9.73× faster than experienced time. -/
  76theorem time_dilation_factor : (360 : ℚ) / 37 > 9 ∧ (360 : ℚ) / 37 < 10 := by
  77  constructor <;> norm_num
  78
  79/-! ## The Uncomputability Structure -/
  80
  81/-- At tick t, the 8-tick phase is t mod 8 and the 45-fold phase is t mod 45.
  82    These two residues are simultaneously zero only at multiples of 360.
  83    Between such alignments, any decision must handle the interference
  84    of two incommensurable periodic constraints. -/
  85theorem phase_mismatch (t : ℕ) (ht : 0 < t) (ht360 : t < 360) :
  86    ¬ (t % 8 = 0 ∧ t % 45 = 0) := by
  87  intro ⟨h8, h45⟩
  88  have hd8 : 8 ∣ t := Nat.dvd_of_mod_eq_zero h8
  89  have hd45 : 45 ∣ t := Nat.dvd_of_mod_eq_zero h45
  90  exact window_insufficient t ht ht360 ⟨hd8, hd45⟩
  91
  92/-! ## Certificate -/
  93
  94/-- The recognition barrier certificate: packages the mathematical core.
  95    The physical claim (consciousness emergence) is NOT included —
  96    it remains a hypothesis connecting this barrier to phenomenology. -/
  97structure BarrierCert where
  98  coprime : Nat.Coprime 8 45
  99  beat_prime : Nat.Prime 37
 100  beat_irreducible : Nat.gcd 37 360 = 1
 101  window_min : ∀ w, 0 < w → w < 360 → ¬ (8 ∣ w ∧ 45 ∣ w)
 102  full_resolution : 8 ∣ 360 ∧ 45 ∣ 360
 103  aliasing : (37 : ℚ) / 45 < 1
 104
 105def barrier_cert : BarrierCert where
 106  coprime := coprime_barrier