D_is_fib_4
plain-language theorem explainer
The theorem states that the spatial dimension D equals the fourth Fibonacci number. Researchers deriving the coherence energy scale from the Fibonacci constraint in Recognition Science cite this when showing D=3 is selected by requiring both D and 2^D to be Fibonacci. The proof is a direct one-line wrapper that unfolds the definition of D and rewrites with the pre-established equality fib 4 = 3.
Claim. The spatial dimension satisfies $D = F_4$, where $F_n$ is the Fibonacci sequence with $F_0 = 1$, $F_1 = 1$, and $F_{n+2} = F_{n+1} + F_n$.
background
In this module D is defined as the natural number 3, the spatial dimension fixed by the T8 step of the unified forcing chain. The Fibonacci sequence appears via the recurrence fib 0 = 1, fib 1 = 1, fib (n+2) = fib n + fib (n+1), with the key auxiliary result fib 4 = 3 already established. The local setting is the derivation that the coherence energy exponent equals -5 because D = F₄ = 3 and the octave 2^D = F₆ = 8 together imply 8 - 3 = 5 = F₅, so E_coh = φ^{-5} is fixed by the Fibonacci-φ structure rather than chosen freely.
proof idea
The proof is a one-line wrapper that unfolds the definition of D and rewrites using the theorem fib_4_eq.
why it matters
This supplies the first conjunct of the parent theorem coherence_exponent_unique, which concludes that the coherence exponent equals 5 and is uniquely determined by the Fibonacci constraint. It completes the module's main claim that E_coh = φ^{-5} follows structurally from D = F₄ and the eight-tick octave, linking T8 dimension forcing to the phi-ladder and RCL identities. No open scaffolding remains here.
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