gap45
plain-language theorem explainer
The declaration introduces the integer 45 as one generator in the Recognition Science cardinality spectrum. Analysts of cross-domain type sizes cite it when decomposing the listed cardinalities into products and powers of the cube generators {2,3}, config dimension 5, and this gap. It is supplied by direct constant assignment inside the module that assembles witnesses for the structured spectrum.
Claim. Define the gap constant as the natural number $45$ appearing in the Recognition Science cardinality spectrum generated from the cube generators, configuration dimension 5, and this value.
background
The module assembles exemplar witnesses showing that cardinalities of canonical RS domain types form the spectrum {2, 3, 4, 5, 6, 7, 8, 10, 12, 15, 16, 45, 70, 125, 216, 256, 3125, ...}. Each entry decomposes via multiplication, summation, or exponentiation from the primitives {2, 3}, the configDim 5, and the gap constant 45. The local theoretical setting is the structural claim that RS produces a non-random numerical spectrum in which every member admits such a decomposition into RS primitives.
proof idea
Direct definition that assigns the natural number 45.
why it matters
This supplies one of the explicit generators required by the module's structural claim C21 on the RS cardinality spectrum. It supports the demonstration that every listed cardinality decomposes from the cube generators, config dimension 5, and this gap. The definition closes one slot in the enumerated spectrum without invoking the forcing chain or Recognition Composition Law.
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