color_offset_eq_quark_baseline
plain-language theorem explainer
The theorem states that the color offset equals the quark baseline, both arising as 2^{D-1} from the combinatorics of the three-dimensional cube. Researchers deriving particle mass baselines or rung integers in Recognition Science would cite this to confirm their shared geometric origin. The proof holds by reflexivity because the two quantities receive identical definitions from the same cube-edge counting at D=3.
Claim. The color offset equals the quark baseline, both given by $2^{D-1}$ for spatial dimension $D=3$.
background
This module upgrades boundary assumptions to derived status by extracting rung integers directly from the combinatorics of the 3-cube Q_3. The quark baseline is the quantity 2^{D-1} and the color offset is likewise 2^{D-1}; both trace to the same counting of parallel edges or faces in the cube. Upstream, the edge count E(D) := D * 2^{D-1} supplies the geometric source, while the forcing chain supplies D=3 as the forced spatial dimension.
proof idea
The proof is a one-line reflexivity step. Because color_offset and quark_baseline are introduced by the identical expression 2^{D-1} in the cube-geometry derivations, Lean reduces the equality to definitional identity without further tactics.
why it matters
The equality closes two previously separate boundary items (B-12 quark baseline and B-25 color offset) into a single derived fact, confirming they share the same cube origin. It supports downstream mass-ladder constructions that place quarks and color degrees on the same phi-rung. The result aligns with the framework landmark that D=3 is forced by the eight-tick octave and self-similar fixed point.
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