reverseTick
plain-language theorem explainer
The time-reversal map on the discrete 8-phase cycle sends each phase p to (7 - p) mod 8. Researchers deriving CPT invariance from ledger symmetries in Recognition Science cite this construction when building the T operator. The definition is a direct arithmetic operation on the finite phase set.
Claim. The time-reversal map on phases is defined by $T(p) := (7 - p) mod 8$ for each phase $p$ in the eight-element cycle.
background
In Recognition Science the phase space is the eight-element set indexing one octave cycle, introduced in the EightTick hypothesis as the discrete time structure underlying ledger entries. The module derives CPT invariance from the ledger's double-entry symmetry, where time reversal corresponds to running the cycle backward while charge conjugation and parity arise from J-cost duality and spatial isotropy. Upstream results define the phase space identically as the 8-tick cycle in both ChurchTuringPhysicsStructure and EightTick.
proof idea
The definition is a direct arithmetic construction: subtract the phase index from 7 and reduce modulo 8, with the Nat.mod_lt witness ensuring the result lies in Fin 8.
why it matters
This map supplies the concrete T operator for the CPT construction in the module, which proves that the full CPT combination is an involution and preserves ledger balance. It instantiates the eight-tick octave (T7) that forces three spatial dimensions and supports the claim that CPT remains conserved even when individual C or P symmetries are broken. The definition feeds applyT and the downstream involution and balance theorems.
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