Maximal Separated Phase Clocks and Spatial Charges for Cyclic Langton Ants

For a cyclic n-color Langton ant, we classify observables that separate the complete coloring from the head pose and have a constant increment on every update. The coloring statistic is allowed to be arbitrary, rather than assumed additive, local, or spatially periodic. In one invariant heading–checkerboard sector, the largest modulus of a unit-increment clock is 8n when the rule contains odd numbers of both right and left turns, and 4n otherwise. Explicit four-periodic spatial coefficients attain the bound. A coloring statistic shared by both sectors has maximal modulus 4n. For the classical two-color ant this gives a sharp sixteen-phase clock, together with a complete classification of separated cocycles over every abelian coefficient group. For mixed rules we also classify all compactly supported coloring potentials: they are unique finite sums of explicit order-two plaquette charges, with the available face families determined by the two turn-count parities. The proofs use forced additivity, local pose equations, and planar integration. Exact Smith-form audits and independent literal implementations provide reproducible controls. The resulting formulas describe the exact phase information available from separated full-state observations.