twentyfive_is_Dsq
plain-language theorem explainer
The theorem confirms that 25 equals the square of the configuration dimension in the RS cardinality spectrum. Cross-domain analysts cite this to anchor numerical consistency among spectrum members generated from primitives 2, 3, and 5. The proof is a direct computational verification that unfolds Dconfig to 5 and checks the arithmetic equality.
Claim. $25 = D^2$ where $D$ is the configuration dimension fixed at 5.
background
The CrossDomain.CardinalitySpectrum module assembles a spectrum of cardinalities {2, 3, 4, 5, 6, 7, 8, 10, 12, 15, 16, 45, 70, 125, 216, 256, 3125, ...} by combining small cube-generators with the configDim 5 and gap45. Dconfig is defined as the natural number 5 and serves as the base for powers appearing in the spectrum. Upstream results supply the definition of Dconfig together with gap constructions from Gap45.Derivation and mass-anchor policies that furnish the factor 45 and related terms in the broader list.
proof idea
The proof is a one-line wrapper that applies the decide tactic to the equality after unfolding the definition of Dconfig to 5 and confirming the arithmetic identity.
why it matters
This declaration supplies an explicit witness for 25 as 5 squared inside the RS Cardinality Spectrum module, supporting the claim that every listed cardinality decomposes into RS primitives. It aligns with the module goal of exhibiting a structured rather than random numerical spectrum and connects to framework landmarks such as the configDim 5 and the eight-tick octave. No immediate downstream theorems are recorded, leaving the result as a self-contained numerical check.
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