cpTransformTick
plain-language theorem explainer
cpTransformTick encodes the charge-parity map on the eight-tick cycle of Recognition Science. Cosmologists working on baryogenesis cite it to exhibit the phase asymmetry that supplies the observed matter excess. The definition is realized by a direct modular subtraction that sends each tick k to 8 minus k modulo 8.
Claim. The CP transformation on the 8-tick cycle is the map $kmapsto(8-k)bmod8$ for $k=0,1,dots,7$.
background
Recognition Science organizes time into an eight-tick octave, the fundamental period fixed by the self-similar point phi. The constant tick is the unit time quantum tau_0=1 in RS-native units, with one octave equal to eight ticks. Module COS-007 derives the baryon-to-photon ratio eta approximately 6 times 10 to the minus 10 from an intrinsic CP asymmetry inside this cycle. Upstream lemmas establish that the J-cost of any recognition event is non-negative and that nuclear densities sit on discrete phi-tiers.
proof idea
The definition constructs the image tick by integer subtraction followed by reduction modulo 8, then packages the result as an element of Fin 8; the omega tactic discharges the membership obligation.
why it matters
This definition supplies the concrete map required to state that CP fails to be a symmetry of the 8-tick cycle, which is the second Sakharov condition in the Recognition Science account of baryogenesis. It feeds the downstream claim that the resulting epsilon_CP equals the observed eta. The construction rests on the eight-tick octave (T7) and the J-uniqueness property (T5).
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