ten_decomp
plain-language theorem explainer
The equality 10 equals the product of the binary-face generator 2 and the configuration-dimension generator 5 holds in the natural numbers. Cross-domain researchers in Recognition Science cite this to verify that the integer 10 belongs to the spectrum generated by operations on {2, 3, 5}. The proof proceeds by a direct decision procedure that confirms the numerical identity without further lemmas.
Claim. $10 = 2 · 5$ in the natural numbers, with 2 the binary face generator and 5 the configuration dimension generator.
background
The RecognitionGenerators module establishes that spectrum members reduce to polynomials in the generators G = {2, 3, 5}, corresponding to binary face, spatial dimension, and configuration dimension. The decomposition 10 = 2 · 5 is one instance among enumerated spectrum members such as 4 = 2², 6 = 2 · 3, and 12 = 2² · 3. Upstream definitions fix G2 as 2 and G5 as 5.
proof idea
The proof is a one-line wrapper that applies the decide tactic to verify the equality 10 = 2 * 5 directly.
why it matters
This theorem completes the decomposition for 10 in the list of spectrum members enumerated in C21, supporting the structural meta-claim that every integer in the RS cardinality spectrum factors through the primitive generators {2, 3, 5}. It contributes to the cross-domain recognition generators framework.
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