D_sq_times_cube
plain-language theorem explainer
The arithmetic identity 5 squared times 2 cubed equals 200 supplies one concrete entry in the cross-pattern matrix of Recognition Science patterns. Researchers verifying the wave-64 meta-theorem on non-degenerate cross-products would cite this result to confirm the D-pair times cube period product. The proof reduces to a single decide tactic call that computes the equality directly.
Claim. $5^{2} 2^{3} = 200$ (D-pair times cube period).
background
The Cross-Pattern Matrix module establishes a structural meta-claim for the Wave-64 cross-domain meta-theorem. Five RS patterns (D=5, 2³=8, J(1)=0, φ-ladder, gap-45/cube-faces) form a non-degenerate matrix of cross-products, with each pair producing a distinct integer or relation. The table lists entries such as 25 = D² for cognitive pair states, 40 = D · 2³ for attention space, and 360 = 2³ · 45 for full turn.
proof idea
The proof is a one-line wrapper that invokes the decide tactic to confirm the numerical equality by direct computation.
why it matters
This theorem supplies one concrete entry in the cross-pattern matrix for the Wave-64 meta-theorem. It contributes to the verification that the five RS patterns produce distinct relations, aligning with the Recognition Science framework's emphasis on integer products from pattern combinations. No open questions are directly addressed here, as the result is fully proved.
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