color_offset
plain-language theorem explainer
The color offset is the number of edges per face in the three-dimensional cube. Researchers deriving quark and lepton baselines from Recognition Science geometry cite this quantity when establishing the B-25 rung. It is introduced as a direct definition that evaluates the edges-per-face function at dimension three.
Claim. The color offset is defined as the number of edges per face of the 3-cube, equal to $2^{D-1}$ evaluated at $D=3$, which yields the integer 4.
background
This definition sits in the module that upgrades several boundary assumptions to derived status using only the input $D=3$. The 3-cube $Q_3$ supplies standard combinatorial counts for vertices, edges, and faces. The upstream edges_per_face function is defined by $2^{d-1}$ and equals 4 at $D=3$.
proof idea
One-line definition that applies the edges_per_face function to the spatial dimension $D$.
why it matters
It supplies the B-25 color offset that feeds color_offset_eq and color_offset_eq_quark_baseline. These theorems equate the offset to 4 and to the quark baseline, closing the geometric derivation of the quark rung from cube combinatorics. The result is consistent with the forcing chain step that fixes $D=3$ and with the octave offset of $-8$.
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