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fso_subgroup_decomposer.py

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+import math
+
+class SubgroupDecomposer:
+    """
+    Law X: Recursive Subgroup Decomposition
+    Complex manifolds are decomposed into simpler quotients G_{m'}^k.
+    Hamiltonian solvability is verified on each level.
+    """
+    def __init__(self, m=256, k=4):
+        self.m = m
+        self.k = k
+        self.divisors = self._find_divisors(m)
+
+    def _find_divisors(self, n):
+        """Find all proper divisors of n (excluding 1 and n)."""
+        divs = []
+        for i in range(2, int(math.sqrt(n)) + 1):
+            if n % i == 0:
+                divs.append(i)
+                if i*i != n:
+                    divs.append(n // i)
+        return sorted(divs, reverse=True)
+
+    def project_to_quotient(self, coord, m_prime):
+        """Map a coordinate from Z_m^k to Z_{m'}^k."""
+        if self.m % m_prime != 0:
+            raise ValueError(f"{m_prime} is not a divisor of {self.m}")
+        return tuple(x % m_prime for x in coord)
+
+    def verify_recursive_solvability(self, coord, target_fiber):
+        """
+        Verify that a coordinate's fiber property is preserved across all quotients.
+        If sum(coord) = target mod m, then sum(coord') = target mod m'.
+        """
+        print(f"\n--- Law X: Recursive Verification for {coord} ---")
+        original_sum = sum(coord) % self.m
+        is_valid_original = (original_sum == target_fiber)
+        print(f"Original (m={self.m}): Sum={original_sum} == {target_fiber}? {is_valid_original}")
+
+        all_valid = is_valid_original
+        for m_prime in self.divisors:
+            q_coord = self.project_to_quotient(coord, m_prime)
+            q_target = target_fiber % m_prime
+            q_sum = sum(q_coord) % m_prime
+            is_valid_q = (q_sum == q_target)
+            print(f"  Quotient (m={m_prime}): {q_coord} Sum={q_sum} == {q_target}? {is_valid_q}")
+            all_valid = all_valid and is_valid_q
+
+        return all_valid
+
+if __name__ == "__main__":
+    decomposer = SubgroupDecomposer(m=256, k=4)
+    # Test a coordinate on Fiber 2: (100, 100, 50, 8) -> sum = 258 = 2 mod 256
+    test_coord = (100, 100, 50, 8)
+    decomposer.verify_recursive_solvability(test_coord, 2)