D5_squared
plain-language theorem explainer
The declaration confirms that five multiplied by five equals twenty-five in the natural numbers. Analysts building the cross-pattern matrix in Recognition Science cite this result to populate the D5-squared matrix entry. The proof applies a direct decision procedure to the arithmetic equality.
Claim. $5$ multiplied by $5$ equals $25$ in the natural numbers.
background
The CrossPatternMatrix module states a structural meta-claim: five Recognition Science patterns (D=5, 2³=8, J(1)=0, phi-ladder, gap-45) form a non-degenerate matrix of cross-products. The module documentation tabulates the D5 row and column intersection as 25, labeled as D² and interpreted as the count of cognitive pair states. This theorem supplies the concrete integer required for that cell.
proof idea
The proof is a one-line wrapper that invokes the decide tactic on the natural-number multiplication statement.
why it matters
This theorem populates the D5_squared field inside the CrossPatternMatrixCert structure, which aggregates the five matrix entries to certify the meta-claim. It realizes the explicit 25 = D² entry listed in the module documentation. The result extends the pattern-matrix construction beyond the core forcing chain (T0-T8) by treating D=5 as an independent pattern whose square yields an observed integer relation.
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