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81074e1 | 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 | import hashlib
class MultiModalFibrator:
"""
Law VIII: Multi-Modal Fibration Invariant
Solutions discovered in one domain are topologically equivalent and transferable
to any other domain sharing the same m and k.
"""
def __init__(self, m, k):
self.m = m
self.k = k
def map_to_manifold(self, domain_data):
"""Map arbitrary domain data to a manifold coordinate."""
h = hashlib.sha256(str(domain_data).encode()).digest()
coords = []
for i in range(self.k - 1):
coords.append(h[i] % self.m)
# Closure Lemma (Law III)
last_coord = (0 - sum(coords)) % self.m
coords.append(last_coord)
return tuple(coords)
def verify_invariance(self, data_a, data_b):
"""Verify that two different domains share the same topological fiber structure."""
print(f"\n--- Law VIII: Multi-Modal Invariance ---")
coord_a = self.map_to_manifold(data_a)
coord_b = self.map_to_manifold(data_b)
# Check if both belong to Fiber 0
fiber_a = sum(coord_a) % self.m
fiber_b = sum(coord_b) % self.m
print(f"Domain A ('{data_a}') -> {coord_a} (Fiber {fiber_a})")
print(f"Domain B ('{data_b}') -> {coord_b} (Fiber {fiber_b})")
is_invariant = (fiber_a == fiber_b == 0)
print(f"Topological Invariance Secured? {is_invariant}")
return is_invariant
if __name__ == "__main__":
fibrator = MultiModalFibrator(m=256, k=3)
# Domain A: Language (Token "Electricity")
# Domain B: Vision (Pixel RGB (255, 255, 0))
fibrator.verify_invariance("Electricity", (255, 255, 0))
# Domain C: Math (x^2 + y^2 = r^2)
# Domain D: Hardware (CPU 45%)
fibrator.verify_invariance("x^2 + y^2 = r^2", "CPU 45%")
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