fivePowFive
plain-language theorem explainer
The equality 5 raised to the fifth power equals 3125 is recorded by direct evaluation. Cross-domain researchers cite it when confirming that five-element structures from sensory, emotional, biological, economic, and linguistic domains multiply to a product of cardinality 125. The proof applies a single decision procedure that reduces the exponentiation to an integer identity.
Claim. $5^{5} = 3125$
background
The module formalizes that configuration dimension D equals 5 appears across domains with high frequency. The predicate HasConfigDim5 holds for a type T exactly when its cardinality is 5, and each domain instance (sensory, emotion, biological, economic, linguistic) carries a proof of this cardinality. The local setting includes cross-domain results asserting that any three such five-element types produce a product of size 125 together with equicardinality between pairs.
proof idea
The proof is a one-line wrapper that invokes the decide tactic to evaluate the natural-number expression 5 raised to the fifth power.
why it matters
This equality supplies the arithmetic fact required by configDimUniversalityCert, the definition that aggregates the five-cardinality instances from each domain. It anchors the triple-product construction of size 125 inside the wave-63 universality claim. The result closes the equicardinality step without introducing axioms or external hypotheses.
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