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import numpy as np
import sympy
from collections import Counter
from typing import Dict, List, Tuple
class PrimeNetwork:
"""
Represents the Radial Prime Topology as an instantiated graph object.
Used for both visualization and signal routing validation.
"""
def __init__(self, max_integer: int = 1000):
self.max_integer = max_integer
self.positions: Dict[int, Tuple[float, float]] = {}
self.gpf_map: Dict[int, int] = {}
self.prime_counts = Counter()
self.primes: List[int] = []
self.composites: List[int] = []
# Build the network immediately
self._build()
def _get_gpf(self, n: int) -> int:
"""Returns the Greatest Prime Factor."""
if n <= 1: return 1
i = 2
while i * i <= n:
if n % i:
i += 1
else:
n //= i
return n
def _build(self):
"""Constructs the network nodes and edges."""
for n in range(1, self.max_integer + 1):
# Radial position based on Mod 10
angle = np.pi/2 - (2 * np.pi * (n % 10)) / 10 # Clockwise from Top
radius = n
self.positions[n] = (radius * np.cos(angle), radius * np.sin(angle))
if n > 1:
if sympy.isprime(n):
self.primes.append(n)
else:
self.composites.append(n)
gpf = self._get_gpf(n)
self.gpf_map[n] = gpf
self.prime_counts[gpf] += 1
elif n == 1:
self.primes.append(1)
def validate_wave(self, heat_code: int) -> bool:
"""Check if a subset of the wave aligns with valid network topology."""
residue = heat_code % 10
return residue in [1, 3, 7, 9]
# Pre-calc network
SHARED_NETWORK = PrimeNetwork(max_integer=2000)
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