four_is_2sq
plain-language theorem explainer
The equality 4 = 2 squared holds in the natural numbers. Researchers examining the Recognition Science cardinality spectrum cite it as one of the small-cube generators that seed the structured set {2, 3, 4, 5, ...}. The verification is a direct decision procedure that confirms the arithmetic identity with no auxiliary lemmas.
Claim. In the natural numbers, $4 = 2^2$.
background
The CrossDomain.CardinalitySpectrum module assembles witnesses for the RS cardinality spectrum, whose members arise by multiplication, summation, or exponentiation from the cube-generators {2, 3}, the configuration dimension 5, and gap45. The module documentation states that every listed cardinality admits such a decomposition into RS primitives, yielding a non-random numerical spectrum. The present declaration supplies the explicit witness for the entry 4.
proof idea
The proof is a one-line term that applies the decide tactic to the arithmetic equality.
why it matters
The declaration fills the C21 structural claim by exhibiting 4 as 2 squared, confirming that spectrum values decompose into the primitive generators {2, 3}. It supports the module's assertion that RS produces a structured rather than arbitrary set of cardinalities. No downstream theorems depend on it in the current graph.
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