The Standard Model Gauge Group and One Generation of Matter from a Three-Bit State

A state of three bits has eight values and six elementary facts of the form "coordinate i has value ±." We call them literals. Two literals can hold together exactly when they concern different coordinates, and comparing two literals that hold together costs J(x) = ½(x + 1/x) − 1. Summed over the eight-tick cycle, a closed walk through the eight states that flips one coordinate per step, this cost acts on the six literals with three levels, 0, 4 and 6, of multiplicity 1, 3 and 2: a total, three colour modes and two shape modes. The five modes other than the total are the balanced modes, and the unitary maps of them that preserve the cost form U(3)×U(2). A record lists which balanced modes are posted. When every map has determinant one, which leaves the complete record with all five modes posted unchanged, the group is S(U(3)×U(2)) = (SU(3)×SU(2)×U(1))/ℤ₆, the Standard Model gauge group; with any other number of coordinates the construction does not give it. Hypercharge is the cost of a mode above the average cost. A literal and its opposite never hold together, so the cost cannot enlarge the symmetry to the grand-unified group SU(5). The sixteen records with an even number of modes posted are one generation of matter with a right-handed neutrino. Among charges additive over the five modes, only the hypercharge of the cost cancels every anomaly. The eight-tick cycle has one fast axis, the coordinate that flips four times, and it singles out a direction for the electroweak condensate. The result is a conditional construction of the internal symmetry and representation data of the Standard Model, from six foundation facts, four physical identifications and five premises, each stated plainly where it is used. The weak-to-colour coupling weight and kinetic form, the number of generations, the dynamics that make the Higgs condense, and the identifications themselves remain open. Preprint of the Recognition Physics Research Institute, 49 pages.