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import math
class PrimePhysics:
"""
Protocol 13: SPCW Physics Engine.
Implements learned knowledge from Visual Artifacts (Prime Gaps & Frequency).
"""
@staticmethod
def calculate_gaps(primes):
"""
Calculates Prime Gaps G_n = P_{n+1} - P_n.
Returns a list of dictionaries.
"""
gaps = []
for i in range(len(primes) - 1):
p_n = primes[i]
p_next = primes[i+1]
g_n = p_next - p_n
# Metric: Frequency f = (P_n * pi) / G_n
# Avoid division by zero (G_n is always >= 1 for primes > 2)
freq = (p_n * math.pi) / g_n
gaps.append({
"p_n": p_n,
"p_next": p_next,
"g_n": g_n,
"frequency": round(freq, 4)
})
return gaps
@staticmethod
def get_resonance_frequency(node_id, primes_map):
"""
Returns the frequency 'f' for a given Prime Node.
"""
if node_id not in primes_map:
return 0.0 # Composite
# Find index
# This is O(N), for production use precise index map
try:
# Simple scan for prototype
idx = primes_map.index(node_id)
if idx >= len(primes_map) - 1:
return 0.0 # Last prime has no next gap yet
p_n = primes_map[idx]
p_next = primes_map[idx+1]
g_n = p_next - p_n
return (p_n * math.pi) / g_n
except ValueError:
return 0.0
if __name__ == "__main__":
# Test Data
test_primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
gaps = PrimePhysics.calculate_gaps(test_primes)
print(f"{'Pn':<5} | {'Pn+1':<5} | {'Gap':<3} | {'Frequency (Hz)':<15}")
print("-" * 40)
for g in gaps:
print(f"{g['p_n']:<5} | {g['p_next']:<5} | {g['g_n']:<3} | {g['frequency']:<15}")
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