fourColors
plain-language theorem explainer
fourColors supplies the constant 4 as the number of colors required by the Recognition Science derivation of the four color theorem. A mathematician working on the D=3 lattice would cite this value when connecting the spatial dimension to the tight bound via the 2-bit vector space structure. The definition is a direct assignment with no computation or lemmas inside the body.
Claim. The number of colors sufficient to color any planar map so that no adjacent regions share a color is defined to be $4$.
background
The module Mathematics.FourColorTheoremFromRS treats the four color theorem as a direct consequence of the Recognition Science lattice at D=3. Colors are identified with the four elements of the field extension F₂², and the count 4 is required to equal both D+1 and 2². The local setting follows from the forcing chain that fixes D=3 at T8 and the observation that 4 = 2^(D-1) at this dimension.
proof idea
The declaration is a direct definition that assigns the natural number 4. No lemmas are applied and no tactics are used; the body is a simple constant declaration chosen to match the predicted color count from the D=3 structure.
why it matters
This constant anchors the FourColorCert structure, which bundles the three equalities fourColors = spatialDimPlusOne, fourColors = 2^2, and fourColors = f2sq_card. It realizes the T8 landmark that D=3 forces a four-color bound through the recognition lattice and the eight-tick octave. The definition supplies the concrete integer that downstream theorems equate to the framework predictions.
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