D
plain-language theorem explainer
D is defined as the integer 3, which Recognition Science selects as the unique spatial dimension satisfying the Fibonacci constraint that both D and 2^D are Fibonacci numbers. A physicist deriving mass ladders or coherence energies cites this when fixing the exponent in E_coh = phi^{-5}. The assignment is a direct constant definition that instantiates the T8 step of the forcing chain.
Claim. Let $D$ denote the spatial dimension. Then $D = 3$.
background
The Coherence Exponent module shows that the Fibonacci constraint (both D and 2^D Fibonacci) uniquely fixes D = 3 = F_4 and 2^D = 8 = F_6. The identity 8 - 3 = 5 = F_5 then sets the coherence energy exponent to -5, so E_coh = phi^{-5}. Upstream, octave is defined as the ratio 2 in MusicalScale and as 8 * tick in Constants, supplying the eight-tick period that links to T7 and T8 in the forcing chain.
proof idea
The declaration is a direct definition D := 3 with no further computation. It simply records the integer value required by the T8 dimension-forcing result.
why it matters
This definition supplies the concrete value of D that the module's main theorem uses to prove the coherence exponent equals -5. It completes the T8 step of the T0-T8 forcing chain that derives three spatial dimensions from the Recognition Composition Law and the phi fixed point. The result feeds the phi-ladder mass formula and the alpha band bounds.
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