theorem
proved
term proof
misaligned_ticks_per_cycle
show as:
view Lean formalization →
formal statement (Lean)
81theorem misaligned_ticks_per_cycle :
82 ∀ k : ℕ, ∀ j : ℕ, 1 ≤ j → j ≤ 359 →
83 (360 * k + j) % 360 ≠ 0 := by
proof body
Term-mode proof.
84 intro k j hj1 hj2
85 omega
86
87/-- **THEOREM (Perpetual Complexity)**: The combination of Ω_Λ > 0 and
88 gcd(8,45) = 1 guarantees perpetual local complexity generation.
89
90 The H-theorem drives F_R → 0 globally. But coprimality ensures that
91 at every non-360-aligned tick, some voxels have misaligned cadences.
92 These voxels have positive J-cost (structured excitations). Since the
93 expansion (Ω_Λ > 0) creates new lattice at every epoch, new
94 synchronization mismatches are perpetually generated.
95
96 The universe cannot reach thermal equilibrium because global phase
97 synchronization would require simultaneous alignment of periods 8 and
98 45, which never happens (coprime). -/