deltaStructural_eq_half_D3
plain-language theorem explainer
The structural correction for the tau lepton generation step equals 3/2 when spatial dimension is fixed at three. Lepton mass derivations on the Recognition Science phi-ladder cite this to fix the facet-mediated term without empirical fitting. The proof is a one-line wrapper applying the general deltaStructural_D3 result to the D = 3 case.
Claim. In three spatial dimensions the structural correction for the tau step satisfies $Δ_{struct}(3) = 3/2$.
background
Recognition Science derives the dimension-dependent correction Δ(D) = D/2 from cube geometry without calibration to observed masses. The function deltaStructural encodes the facet-vertex ratio: F = 2D faces each contribute 1/V where V = 2^{D-1} is the discrete vertex count per facet, so Δ(D) = F/V. The module contrasts this facet-mediated μ→τ step with the edge-mediated e→μ step that uses the continuous solid angle 4π. Upstream results include the voxel definition as the fundamental length quantum and the Physical structure requiring positive c, ħ, G in RS-native units.
proof idea
The proof is a one-line wrapper that applies the general deltaStructural_D3 theorem directly to the D = 3 case.
why it matters
This theorem specializes the general structural delta to D = 3, confirming Δ(3) = 3/2 as required by the tau step derivation. It supports the module claim that the correction follows from face geometry without calibration and aligns with the forced D = 3 in the unified forcing chain (T8). No downstream uses appear yet.
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