cpTransformTick
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.
claimThe 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 in Recognition Science
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).
scope and limits
- Does not compute the numerical value of epsilon_CP.
- Does not verify the out-of-equilibrium condition.
- Does not derive eta from the phi-ladder mass formula.
- Does not address B-violation mechanisms.
formal statement (Lean)
94def cpTransformTick (k : Fin 8) : Fin 8 :=
proof body
Definition body.
95 ⟨(8 - k.val) % 8, by omega⟩
96
97/-- **THEOREM**: CP is not a symmetry of the 8-tick cycle.
98 Specifically, the J-cost is NOT invariant under CP for generic states. -/