The Discrete Symmetry Ledger of the Standard Model

SYM-4 of Symmetry ARC C, P, T, CP, Sector-Localized Violation, Invariant Diagnostics, and Normal-Form Closure This paper develops a sector-indexed ledger for the discrete symmetries CC, PP, TT, CPCP, and CPTCPT in the Standard Model. It shows why these symmetries cannot be faithfully represented by a single theory-wide yes/no label: the same named operation may denote an active transformation, a local-field implementation, a passive convention change, a condition on couplings, a theorem consequence, a vacuum stabilizer, a parameter-limit regularity, or an invariant diagnostic. The SYM-4 framework classifies discrete-symmetry status relative to the target sector, interaction channel, field content, parameter region, mass degeneracy, neutrino convention, topological sector, boundary data, operator category, and selected vacuum. It distinguishes: active transformations from passive redescriptions; unitary from antiunitary implementations; exact sector symmetries from parameter-limit symmetries; complex matrix representatives from physical phases; weak-basis and rephasing freedom from quotient-stable invariants; explicit from spontaneous CPCP violation; TT-odd kinematic correlations from direct time-reversal tests; Dirac oscillation CPCP effects from Majorana-phase loci; the QCD θ\theta coordinate from the anomaly-invariant strong-CPCP combination; the one-Higgs-doublet core from extended-scalar target updates; CPT premises, theorem consequences, implementations, and physical actions. The construction uses two independent upstream systems. Standing burdens are generated through controlled target-slot denials and recorded query-loss profiles. Physical candidates are generated separately from quantum-field-theoretic seeds using 45 formula-bearing constructors executed to a fixed point of depth five. Eligibility is operationally tested by restoring each candidate into a denied target hole and rerunning the complete query vector. Compatibility is tested by reassembling every complete eligible occupation and recomputing all local and cross-object equations. The declared SYM-4 certificate contains: 19 closed physical targets; one integrated ledger assembly; 6 explicit frontier or successor records; 147 independently derived role positions; 213 raw physical artifacts; 174 presentation residues; 1,311 evaluated role–residue pairs; 22 complete pointwise-eligible assignments; 23 lawful automorphisms; 20 assignment orbits; 4,762 registered audit tests. Each closed physical target has one lawful normal-form orbit, and the integrated compiler assembly has one corresponding compiler orbit: ∀λ∈Λ4closed,∣N4(λ)∣=1.\forall \lambda\in\Lambda^{\mathrm{closed}}_4,\qquad \left|\mathcal{N}_4(\lambda)\right|=1. The ledger establishes a unique lawful discrete-symmetry normal form modulo witnessed presentation equivalence. Sector projections recompose to the integrated ledger, while new field content, global form, operator order, vacuum data, or extended scalar structure are routed to explicit successor targets. The work does not claim to predict CKM or PMNS parameters, determine the QCD θ\theta angle, solve the strong-CPCP problem, derive baryogenesis, predict electric dipole moments, close extended-Higgs or SMEFT sectors, or complete the faithful global-form and generalized-defect inventories. Those remain explicit downstream burdens. Principal contributions A sector-indexed C/P/T/CP/CPTC/P/T/CP/CPT symmetry ledger. Target-relative classification of discrete actions and violations. Separation of active, passive, unitary, antiunitary, exact, accidental, anomalous, vacuum, and diagnostic status. Basis-invariant treatment of weak-basis transformations, rephasings, degeneracy, and generalized CPCP. A detailed CKM and charged-current CPCP analysis. Strong-CPCP treatment of axial transport, invariant θˉ\bar\theta, topology, and vacuum scope. Distinction between direct TT tests and kinematic TT-odd observables. Sector-sensitive treatment of Dirac and Majorana neutrino CPCP structure. Higgs-carrier, scalar-CPCP, and vacuum-realization classification. Independent burden and physical-object construction. Executable presentation quotients and lawful automorphism computation. A reproducible finite normal-form certificate with explicit falsification routes.