cognitive_oncology_size
plain-language theorem explainer
The theorem establishes that the product of two 5^3 state spaces equals 15625, giving the cardinality of the joint cognitive-oncology recognition lattice. Cross-domain researchers cite it to anchor the 5^6 point in the product hierarchy and confirm the 14-bit bound. The proof is a direct numerical evaluation via the decide tactic.
Claim. The joint cognitive-oncology state space has cardinality $5^3 times 5^3 = 15625$.
background
The Product Recognition Lattice builds hierarchies of recognition state spaces via products of domain lattices. Cognitive and oncology domains each contribute a 5^3 = 125 state space, so their product yields the 5^6 joint space. The module lists the lattice points 5^2 = 25 through 5^8 = 390625 and imposes the bound 5^6 < 2^14 = 16384. The upstream structure as from ContinuumBridge supplies the simplicial identification (1/2) sum w_ij (epsilon_i - epsilon_j)^2 = (1/kappa) sum delta_h A_h that underlies the lattice construction.
proof idea
The proof is a one-line wrapper that applies the decide tactic to evaluate the concrete numerical equality 125 * 125 = 15625.
why it matters
This supplies the joint_size field inside productRecognitionLatticeCert, which assembles the full lattice certificate including five_cubed, five_to_six, and the two bit-bound lemmas. It realizes the module claim that the combined cognitive-oncology state fits inside 14 bits, anchoring the C23 cross-domain product at the scale of the Recognition framework's information bounds.
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