color_offset_eq
plain-language theorem explainer
Color offset is shown to equal 4 by direct reduction to the edges-per-face count in three dimensions. Researchers deriving particle baselines in Recognition Science cite this when fixing the quark rung from cube geometry. The proof applies the D=3 edges theorem in one step.
Claim. The color offset, defined as the number of edges per face of the 3-cube, equals $4$.
background
This result sits in the module deriving baseline rung integers from the combinatorics of the 3-cube Q₃ once D=3 is fixed. The color offset is defined as edges_per_face D. Upstream, edges_per_face_at_D3 states: At D = 3: edges per face = 4. The module upgrades several boundary assumptions to derived status, including color offset as B-25 with value 2^(D-1).
proof idea
The proof is a one-line wrapper that applies the edges_per_face_at_D3 theorem directly.
why it matters
This theorem supplies the value 4 for color offset (B-25), matching the quark baseline and feeding the neutrino rung derivation. It closes one entry in the baseline derivations table, confirming all such integers trace to D=3. In the framework it supports the mass formula on the phi-ladder and the eight-tick octave.
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