G2
plain-language theorem explainer
G2 assigns the constant 2 to the binary-face generator in the set {2, 3, 5} that produces all Recognition Science spectrum cardinalities via addition, multiplication, exponentiation and binomial coefficients. Cross-domain decompositions cite this base value to reduce members such as 4, 8 and 16 to powers of 2. The definition is a direct constant assignment with no computational steps.
Claim. Let $G_2 = 2$ denote the binary-face generator in the Recognition Science framework.
background
The Recognition Generators module establishes that every integer in the RS cardinality spectrum arises from primitive operations on the set G = {2, 3, 5}, where 2 is the binary face, 3 the spatial dimension, and 5 the configuration dimension. G2 is defined as the constant 2. This choice aligns with the forcing chain landmarks where D = 3 spatial dimensions and the eight-tick octave appear as powers of 2. No upstream lemmas are required since this is a foundational definition.
proof idea
The declaration is a direct definition assigning the value 2 to G2. No lemmas or tactics are applied.
why it matters
G2 serves as the base for multiple decompositions in the module, including four_decomp (4 = G2²), eight_decomp (8 = G2³), and sixteen_decomp. It contributes to the primorial product G2 * G3 * G5 = 30 and the minimal generating set theorem. This anchors the claim that the RS spectrum is generated by {2,3,5} without external primes, consistent with the T7 eight-tick octave and D = 3 dimensions in the UnifiedForcingChain.
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