deltaStructural_alt_D3
plain-language theorem explainer
In three dimensions the structural correction equals three halves. Researchers deriving lepton mass ratios from hypercube geometry cite this verification of the alternative form. The proof is a direct term reduction that unfolds the face and vertex definitions then simplifies the resulting arithmetic expression.
Claim. $Δ(3) = 3 / 2^{3-2} = 3/2$, where $Δ(D)$ is the ratio of the number of faces $F(D)=2D$ to the number of vertices per face $V(D)=2^{D-1}$ in a $D$-dimensional hypercube.
background
The module derives the dimension-dependent correction $Δ(D)=D/2$ from cube geometry without calibration to observed masses. Its goal is to show that $Δ(3)=3/2$ is forced by the framework rather than fitted. The local setting contrasts the $μ→τ$ facet-mediated step with the earlier edge-mediated step, treating vertex count as the discrete analog of solid angle.
proof idea
The term proof unfolds deltaStructural, faceCount, and faceVertexCount, then applies norm_num to reduce the concrete numerical expression at D=3.
why it matters
This verification confirms the rewritten structural formula at D=3, supporting the tau-step correction inside the lepton-generation derivations. It aligns with the Recognition Science selection of D=3 at T8 and the geometric origin of the mass-ladder corrections. The declaration closes a direct check that the facet contribution yields exactly 3/2 without external input.
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