Chiral, Custodial, and Infrared Symmetries

SYM-6 of Symmetry ARC Integrated Limit-Ancestry, Vacuum-Realization, and UV-to-IR Occupancy Closure in the Standard Model SYM-6, Release v3.1.0 This paper develops an integrated target-faithful classification of chiral, custodial, and infrared symmetries in the Standard Model. It connects massless QCD flavor structure, axial anomalies, vacuum realization, Goldstone modes, isospin, hadronic flavor, custodial symmetry, effective-field-theory limits, and heavy-quark symmetry without collapsing classical invariance, quantum anomaly, vacuum realization, explicit deformation, approximation, topology, or renormalization into a single status label. The declared domain contains eighteen atomic records organized across six families. Each record receives an eleven-field normal form and a source-identified evidence certificate. The conventional quantum-field-theoretic layer constructs and classifies: the faithful massless-QCD chiral action and center quotient; nonsinglet and singlet Ward identities; the discrete axial residue and ABJ anomaly; conditional vacuum stabilizers and Goldstone realization; anomaly matching and Wess–Zumino–Witten transport; exact vector-flavor, isospin, and hadronic SU(3)SU(3) limits; chiral spurion counting and controlled deformation order; scalar, gauge-Higgs, and matter-coupled custodial structure; custodial diagnostics and symmetry-breaking ancestry; heavy-field decomposition and the leading HQET expansion; heavy-quark spin/flavor symmetry and current matching; operator-level corrections and heavy-hadron occupancy. The paper maintains a strict distinction between exact symmetries, approximate symmetries, anomalous currents, vacuum-realized symmetries, effective symmetries, transport relations, diagnostics, and target updates. The QCD chiral vacuum witness is registered as a conventional physics input; its existence and numerical value are not derived within this work. Likewise, low-energy constants, Wilson coefficients, hadronic matrix elements, and empirical scale comparisons remain conventional inputs where explicitly stated. AASC is applied only after each physical object and map has been constructed. It governs target identity, admissible comparison, reference-preserving transport, certificate fixation, representative equivalence, multi-cause separation, and primitive-role classification. The integrated closure proves that every declared candidate is decided, every admitted record has a complete source-to-handoff path, normalization is unique up to invariant-preserving redescription, all eighteen slots are covered, and no effective, approximate, anomalous, or vacuum-realized symmetry becomes a new primitive Standard Model carrier solely through infrared utility. The finite certificate contains: 6 symmetry families; 18 atomic records; 40 named results; 20 release gates; 82 independently constructed role burdens; 82 independently constructed QFT residues; 778 evaluated same-target pairs; 1 compatible complete assignment; 1 lawful assignment orbit; 12 successful mutation tests. The result closes the declared SYM-6 flavor, chiral, custodial, and infrared architecture. It exports a custodial packet to SYM-8, an effective-theory and renormalization-group transport packet to SYM-10, and an anomaly/infrared packet to the all-arc capstone. Full global-form, line-operator, monopole, defect, finite-temperature, and generalized-symmetry closure remains outside the present theorem boundary. Principal contributions A unified UV-to-IR symmetry-ancestry framework. Faithful chiral QCD action and quotient classification. Separate treatment of continuous and discrete axial anomalies. Conditional vacuum-stabilizer and Goldstone realization. Anomaly matching and Wess–Zumino–Witten transport. Exact and approximate isospin and hadronic-flavor limits. Chiral spurion and controlled-deformation grading. Scalar, gauge-Higgs, and fermion-coupled custodial hierarchy. Custodial diagnostics and explicit-breaking ancestry. Heavy-quark effective theory and spin/flavor emergence. Operator-level correction grades and current matching. Integrated role-occupancy, normalization, and no-promotion closure. Deterministic executable certificate with reproducibility and mutation audits.