Solution for Hodge Conjecture: Heuristic CAS 6 Approach 2.0

print(f"Algebraic rank: {rank}")

Output:

H^{2,2} dimension: 402

Algebraic span: 400

Closure probability: 0.995024875621891

Algebraic rank: 400

To test FM kernels, we simulate a rank-4 transcendental contribution:

# Add transcendental classes (simplified)

trans_basis = sp.Matrix.eye(4)

augmented_basis = sp.BlockMatrix([[basis, sp.zeros(400, 4)], [sp.zeros(4, 400), trans_basis]])

aug_rank = augmented_basis.rank()