D5_fails_sync
plain-language theorem explainer
The declaration shows that the least common multiple of 2 to the fifth power and 45 equals 1440 rather than 360. Researchers tracing dimensional constraints in the Recognition Science forcing chain cite it to exclude D=5 from viable models. The verification is a direct native computation of the arithmetic values.
Claim. The least common multiple of $2^5$ and $45$ is not equal to $360$.
background
The Spectral Emergence module starts from T8 (D=3) in the forcing chain and shows that the binary cube Q3 simultaneously produces the SU(3) x SU(2) x U(1) gauge content, three generations from face-pair counting, and 48 chiral fermion states matching |Aut(Q3)|. The local setting requires that only D=3 satisfies the eight-tick octave synchronization expressed through the lcm condition with 45. Upstream, the UniversalForcingSelfReference structure supplies the MetaRealizationCert that records the structural properties needed for self-reference without extra design choices.
proof idea
The proof is a one-line wrapper that applies native_decide to evaluate the least common multiple directly and confirm the inequality.
why it matters
This result supports the module claim that no alternative dimension works, closing the exhaustive check that only D=3 yields the Standard Model structure and the unique consciousness ground state. It sits downstream of T7 (eight-tick octave) and T8 (D=3) and feeds the parent conclusion that the phi-ladder and gauge content emerge uniquely from Q3. No open scaffolding remains here.
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