ParityOp
plain-language theorem explainer
ParityOp supplies the parity operator as spatial reflection negating each of the three coordinates in the Recognition Science ledger. QFT researchers assembling CPT invariance from discrete symmetries would reference it to link D=3 isotropy to the double-entry structure. The declaration is a structure definition whose single field remains a placeholder predicate.
Claim. The parity operator satisfies $P(x_i) = -x_i$ for each coordinate index $i$ in the three-dimensional spatial lattice.
background
The module derives CPT invariance from the ledger's double-entry structure in Recognition Science. Parity symmetry arises because the three-dimensional voxel lattice admits reflection, forced by D=3 and isotropy of recognition. Upstream, Time is defined as the real line, providing the scalar field on which coordinate negation acts.
proof idea
One-line structure definition that introduces the negate field as a placeholder predicate over Fin 3 and the reals.
why it matters
It supplies the P component for the CPT theorem targeted at PRL, completing the triad with C from J(x)=J(1/x) and T from the eight-tick cycle. The declaration sits inside the forcing chain step that fixes D=3 and prepares the applyP and p_preserves_cost siblings.
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