applyPT
plain-language theorem explainer
The PT transformation composes parity and time reversal on ledger entries that represent recognition events. Researchers deriving CPT invariance from discrete ledger symmetries cite this when proving mass and lifetime equalities between particles and antiparticles. It is realized as the direct functional composition of the parity and time-reversal maps.
Claim. For a ledger entry $e$ carrying position in three dimensions, tick phase, charge, and nonnegative cost, the PT map is defined by $PT(e) := P(T(e))$, where $P$ negates each spatial coordinate and $T$ inverts the tick.
background
The module derives CPT invariance from the ledger's double-entry structure. Charge conjugation arises from the $J(x)=J(1/x)$ symmetry of the cost function, parity from the isotropy of the three-dimensional voxel lattice, and time reversal from the bidirectional eight-tick cycle. A ledger entry is the structure holding position (Fin 3 to real), tick (Phase), charge (integer), and cost (nonnegative real). Upstream, applyP negates the position coordinates while preserving cost; applyT reverses the tick while preserving cost.
proof idea
One-line wrapper that applies applyP to the result of applyT on the input ledger entry.
why it matters
This definition supplies the PT operator required by the downstream theorems cpt_mass_equality and cpt_lifetime_equality, which establish that CPT invariance forces C-invariance for masses and lifetimes. It completes the discrete symmetry chain in the QFT module, connecting to the eight-tick octave and D=3 spatial isotropy forced by the Recognition Science framework. The parent results close the argument that the combined CPT operator is conserved even when individual symmetries are broken.
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