D_3_fibonacci_constraint
plain-language theorem explainer
The declaration confirms that spatial dimension 3 and its octave period 8 both belong to the Fibonacci sequence. Researchers deriving the coherence energy scale from the Recognition Science forcing chain would cite this to fix the exponent at phi to the negative fifth power. The proof is a direct term-mode verification that splits the conjunction and decides list membership by native computation.
Claim. The spatial dimension $D=3$ and the octave period $2^D=8$ are both Fibonacci numbers.
background
Recognition Science selects spatial dimension D via the eight-tick octave in the T7-T8 forcing steps. The predicate is_fibonacci enumerates the sequence 1,1,2,3,5,8,... up to 1597 and checks membership by direct test. The module shows that the constraint requiring both D and 2^D to be Fibonacci numbers selects D=3, with 3=F4 and 8=F6, so that the difference yields 5=F5 and fixes the coherence energy at phi^{-5}.
proof idea
The term proof applies constructor to split the conjunction into two separate goals, then invokes native_decide on each to confirm membership of 3 and 8 in the enumerated Fibonacci list.
why it matters
This result supplies the concrete Fibonacci verification that closes the coherence exponent derivation in the module, showing the exponent -5 is fixed by the phi-ladder rather than inserted by hand. It directly instantiates the dimension choice from T8 and the octave from T7. The parent claim is the main theorem that E_coh equals phi^{-5} follows from the Fibonacci constraint on D.
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