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debe354 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | """
Sovereign Shift: θ = 89/2462
The fundamental non-commutativity parameter of the Quantum AP Orchestrator.
"""
import math
THETA_NUM = 89
THETA_DEN = 2462
THETA = THETA_NUM / THETA_DEN
Q = THETA_DEN # Total agents / lateral displacement period
N_ACTIVE = 1024 # Active agent subset
THRESHOLD = N_ACTIVE / 2.0 # Dream Cycle trigger: 512
OMEGA = complex(math.cos(2 * math.pi * THETA), math.sin(2 * math.pi * THETA))
def gcd(a: int, b: int) -> int:
while b:
a, b = b, a % b
return a
def verify():
"""Verify θ = 89/2462 is in lowest terms and 89 is prime."""
assert gcd(THETA_NUM, THETA_DEN) == 1, "Not coprime"
assert THETA_DEN == 2 * 1231, "Factorization mismatch"
assert all(THETA_NUM % d != 0 for d in range(2, THETA_NUM)), "89 not prime"
return True
def weyl_bound() -> float:
"""Weyl estimate for max hallucination magnitude: √(N·log Q)."""
return math.sqrt(N_ACTIVE * math.log(Q))
def snr_db() -> float:
"""Signal-to-noise ratio in dB: 20·log10(N / √(N·log Q))."""
return 20 * math.log10(N_ACTIVE / weyl_bound())
if __name__ == "__main__":
verify()
print(f"θ = {THETA_NUM}/{THETA_DEN} = {THETA:.10f}")
print(f"Q = {Q}, N = {N_ACTIVE}, τ = {THRESHOLD:.0f}")
print(f"ω = exp(2πiθ) = {OMEGA:.6f}")
print(f"Weyl bound: √(N·log Q) = {weyl_bound():.2f} ≈ 89")
print(f"SNR: {snr_db():.2f} dB")
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