deltaStructural_D3
plain-language theorem explainer
The structural dimension correction evaluates to exactly 3/2 when the spatial dimension is fixed at three. Researchers deriving the muon-to-tau lepton step from hypercube geometry would cite this to confirm that the facet correction follows directly from first principles. The proof is a direct unfolding of the face-count and vertex-count definitions followed by arithmetic normalization.
Claim. The dimension-dependent correction satisfies $Δ(3) = 3/2$, where $Δ(D)$ is the ratio of the number of faces $2D$ of a $D$-cube to the number of vertices $2^{D-1}$ on each face.
background
In the Recognition Science treatment of lepton generations the muon-to-tau step is modeled as facet-mediated. The structural correction is defined as $Δ(D) := F(D)/V(D)$, where $F(D) = 2D$ counts the $(D-1)$-faces of a $D$-cube and $V(D) = 2^{D-1}$ counts the vertices of each such face. This ratio supplies the discrete analog of a solid-angle factor without reference to measured masses.
proof idea
The proof is a one-line wrapper that unfolds the definitions of deltaStructural, faceCount and faceVertexCount, then applies norm_num to reduce the arithmetic expression $(2·3)/2^{3-1}$ to $3/2$.
why it matters
This supplies the concrete value required by the parent theorem delta_D3_derived, which equates the structural and axis-additive expressions at $D=3$ and thereby shows that $Δ(3)=3/2$ is forced by cube geometry. It closes the derivation of the tau-step correction in the lepton ladder, consistent with the eight-tick octave and the forcing of $D=3$ in the unified chain. The larger result delta_derived_not_calibrated assembles this equality to assert that no calibration to data is needed.
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