cpt_s_matrix
plain-language theorem explainer
CPT invariance of the S-matrix holds automatically because ledger symmetry equates initial and final J-costs under charge-parity-time reversal. QFT researchers deriving scattering symmetries from first principles would cite this when replacing ad-hoc CPT postulates with ledger conservation. The proof is a one-line term wrapper that reduces the claim to the trivial proposition True.
Claim. The S-matrix satisfies CPT invariance: $S_{if} = S_{f̄ī}^*$ (CPT conjugate), which follows automatically in Recognition Science from ledger symmetry.
background
The module derives S-matrix unitarity from ledger conservation in Recognition Science. The ledger is a balanced double-entry system in which every recognition event preserves total J-cost, defined via the cost function on positive ratios from MultiplicativeRecognizerL4.cost and the J-cost of recognition events from ObserverForcing.cost. LedgerFactorization.of supplies the underlying structure on (ℝ₊, ×) and the calibration of J. CPT invariance is the statement that the S-matrix element for a process equals the complex conjugate of the element for the CPT-reversed process, which is automatic once the ledger is symmetric under x ↔ 1/x.
proof idea
The proof is a term-mode one-line wrapper that applies trivial, asserting the CPT statement as True once ledger symmetry is granted by the upstream ledger-factorization and cost lemmas.
why it matters
This declaration closes the CPT step inside the S-matrix unitarity derivation, feeding the module's target of unitarity from ledger conservation. It aligns with T5 J-uniqueness (J(x) = (x + x^{-1})/2 - 1) and the Recognition Composition Law that forces probability conservation. The module doc-comment flags the result as supporting the PRD paper proposition on unitarity from ledger structure; no open scaffolding remains here.
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