total_geometric_at_D3
plain-language theorem explainer
The theorem fixes the total geometric content of the 3-cube at 54, obtained by summing vertices, edges, faces, passive edges, and wallpaper groups. Researchers deriving neutrino mass baselines in Recognition Science cite it to anchor the integer offset in the phi-ladder. The proof is a direct native arithmetic evaluation of the summed geometric functions at D = 3.
Claim. At spatial dimension $D=3$, the total geometric content of the 3-cube equals 54, where this content is the sum of the vertex count, edge count, face count, passive field edge count, and wallpaper group count.
background
The module upgrades several boundary assumptions to derived status by extracting integer rungs from the combinatorics of the 3-cube $Q_3$. The definition total_geometric_content(d) adds cube_vertices d, cube_edges d, cube_faces d, passive_field_edges d, and wallpaper_groups; at D=3 these yield the explicit sum 8+12+6+11+17. Upstream rung definitions in RSBridge.Anchor assign integer offsets to fermions, including the neutrino family, while the module doc states that every integer here traces to the single input D=3.
proof idea
The proof is a one-line wrapper that applies native_decide to confirm the arithmetic identity total_geometric_content 3 = 54.
why it matters
This supplies the B-13 neutrino baseline integer -54 used by the downstream theorem neutrino_baseline_eq to set neutrino_baseline_int = -54. It completes the derivation of the neutrino rung from the eight-tick octave and D=3 in the forcing chain, fixing the absolute offset that enters the phi-ladder mass formula for the lightest neutrino.
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