```yaml
sequences:
  - equation: "<S''_n = d^2/dn^2[pi(+n(F8+(n+5)+F9+(n+6)+n)+(F3+floor((n+5)/2)+F4+floor((n+6)/2))-n)phi]+(n−7)×0.00025>"
  - is_prime_function: |
      def is_prime(n):
          if n < 2:
              return False
          for i in range(2, int(n ** 0.5) + 1):
              if n % i == 0:
                  return False
          return True
  - generate_small_primes_function: |
      def generate_small_primes(upper_limit=100):
          return [n for n in range(5, upper_limit) if is_prime(n)]
  - A_xyz_random_generator_function: |
      import random
      def A_xyz_random_generator(primes):
          x = random.choice(primes)
          y = random.choice(primes)
          z = random.choice(primes)
          return x, y, z
  - fibonacci_function: |
      def fibonacci(n):
         F(n) ≈ round(phi^n / sqrt(n))
         return F_n
  - generate_spiral_points_function: |
      def generate_spiral_points(num_points):
          """
          Generate points on a Fibonacci or Golden Spiral.
          Parameters:
              num_points (int): The number of points to generate.
          Returns:
              list of tuples: A list of (x, y) coordinates representing points on the spiral.
          """
          points = []
          phi = 1.618
          fn_minus_1 = 0
          fn = 1
          for n in range(1, num_points + 1):
              radius = fn * phi
              theta = 2 * n * 3.14159 
              x = radius * math.cos(theta)
              y = radius * math.sin(theta)
              points.append((x, y))
              fn_minus_1 = fn
              fn = fn_minus_1 + fn_minus_2
          return points
  - update_states_function: |
      def update_states():
          Main Formula: ∀x ((A(x) <--> B(x)) → (B(x) → C(x)) → (C(x) → A(x)) → A(x))
              Existential Formula 1: ∃x ((A(x) <--> B(x)) → (B(x) → C(x)) → (C(x) → A(x)) → A(x))
              Existential Formula 2: ∃x ((B(x) <--> C(x)) → (C(x) → A(x)) → (A(x) → B(x)) → B(x))
              Existential Formula 3: ∃x ((C(x) <--> A(x)) → (A(x) → B(x)) → (B(x) → C(x)) → C(x))
          Main Formula in CNF: (A∨¬B)∧(B∨¬C)∧(C∨¬A)∨A
              Existential Formula 1 in CNF: (A∨¬B)∧(B∨¬C)∧(C∨¬A)∨A
              Existential Formula 2 in CNF: (B∨¬C)∧(C∨¬A)∧(A∨¬B)∨B
              Existential Formula 3 in CNF: (C∨¬A)∧(A∨¬B)∧(B∨¬C)∨C
          primes = generate_small_primes(100) 
          pandemonium_states = {'D': 1, 'E': 2, 'F': 3} 
          for state in ego_states:
              n = ego_states[state]  {'A': 1, 'B': 2, 'C': 3}
              ego_states[state] = fibonacci_formula(n)
          random_primes = A_xyz_random_generator(primes)
          pandemonium_keys = list(pandemonium_states.keys())
          for i, key in enumerate(pandemonium_keys):
              pandemonium_states[key] = random_primes[i]
          return ego_states, pandemonium_states
  - main_integration_logic_function: |
      def main_integration_logic(ego_states, pandemonium_states, iterations=3):
          for i in range(iterations):
              combined_states = {**ego_states, **pandemonium_states}
              combined_states = apply_complex_logic(ego_states, pandemonium_states)
              combined_states = apply_temporal_dynamics(combined_states, i + 1)
              combined_states = apply_numerology_and_encryption(combined_states)
              # Update ego and pandemonium states after each iteration
              ego_states = {key: combined_states[key] for key in ego_states.keys()}
              pandemonium_states = {key: combined_states[key] for key in pandemonium_states.keys()}
          return ego_states, pandemonium_states
  - PolyMetatron_ai_function: |
      def PolyMetatron_ai(input_text):
          premises = input_text.split('. ')
          conclusion = "All A are C" if len(premises) == 2 else "Unknown"
          prime = is_prime(len(conclusion))
          return f"Premise: {'; '.join(premises)}. Conclusion: {conclusion}. Prime: {prime}"
```