applyCPT
plain-language theorem explainer
The applyCPT operation composes charge conjugation, parity reflection, and time reversal on a ledger entry for a recognition event. Researchers deriving CPT invariance in discrete QFT models would reference this construction when establishing that the composite symmetry is conserved. It is implemented as the sequential composition applyC (applyP (applyT e)).
Claim. For a ledger entry $e$ with position vector $x$, tick phase $t$, charge $q$, and cost $c$, the CPT map is defined by $CPT(e) = C(P(T(e)))$, where $C$ sends $q$ to $-q$, $P$ sends $x$ to $-x$, and $T$ reverses the tick phase.
background
The QFT module derives CPT invariance from the ledger's double-entry structure in Recognition Science. A LedgerEntry records a recognition event via a 3D position in Fin 3 to real, a Phase tick, an integer charge, and a non-negative real cost. The three component operators are supplied by sibling definitions: applyC negates charge (realizing J(x) = J(1/x) symmetry), applyP reflects the position vector (using D=3 isotropy), and applyT reverses the tick via reverseTick (using the eight-tick cycle). Upstream cost definitions from MultiplicativeRecognizerL4 and ObserverForcing supply the J-cost that remains invariant under each map.
proof idea
This is a one-line wrapper that applies the three symmetry operators in sequence: first time reversal via applyT, then parity via applyP, then charge conjugation via applyC.
why it matters
The definition supplies the composite CPT operator required by downstream theorems cpt_preserves_cost, cpt_involutive, cpt_mass_equality, and cpt_lifetime_equality. It fills the QFT-005 claim that CPT is always conserved in the ledger model, drawing on the eight-tick octave for time reversal and the J-cost symmetry for charge conjugation. The construction closes the discrete-symmetry scaffolding that feeds into balance preservation and particle-antiparticle mass equality.
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