sixteen_decomp
The declaration establishes that sixteen factors as the fourth power of the binary generator in the Recognition Science spectrum. Researchers working on the cardinality decompositions of the RS wave-64 spectrum would reference this identity when enumerating integer generators from {2,3,5}. The proof reduces to a single decision procedure that verifies the numerical equality after unfolding the definition of the binary generator.
claim$16 = 2^4$, where the base is the binary-face generator.
background
The module establishes a structural meta-claim that every integer in the RS cardinality spectrum reduces to a polynomial expression in the generators {2, 3, 5} via addition, multiplication, exponentiation, and binomial coefficients. The binary-face generator is defined as the constant 2. This supplies the explicit decomposition for the spectrum member 16 listed among the C21 enumerations.
proof idea
The proof is a one-line wrapper that applies the decide tactic to the numerical equality after the definition of the binary generator is unfolded.
why it matters in Recognition Science
This identity completes one entry in the exhaustive decomposition of spectrum members under the structural meta-claim of C27. It supports the claim that no RS spectrum integer lies outside the polynomials generated by {2,3,5}. The result feeds into higher-level cardinality arguments in the cross-domain recognition generators.
scope and limits
- Does not establish uniqueness of the decomposition for 16.
- Does not connect the decomposition to physical dimensions or the forcing chain.
- Does not provide a general algorithm for arbitrary integers.
formal statement (Lean)
54theorem sixteen_decomp : (16 : ℕ) = G2^4 := by decide