Coupled Oracle Involutions on the Calendar Round: A Free Klein Four-Group and a Z2 x D730 Extension on Z18980

The Calendar Round couples the 260-day Tzolkin and the 365-day Haab' into a cycle of length 18, 980. This preprint proves that the valid Calendar Round state space is the congruence slice CR = (t, h) in Z260 x Z365: t = h mod 5, isomorphic to Z18980, rather than the full direct product. On this corrected state space, coupled lifts of the Dreamspell Antipode and Occult operators generate a freely acting Klein four-group with 4, 745 four-element orbits. Adding the coupled Analog operator gives a non-abelian operator group isomorphic to Z2 x D730, with commutator translation of order 365. The uploaded files include the LaTeX manuscript and an exhaustive Python verification script.