Flavor Symmetry, Basis Skin, Spurion Structure, and Invariant Normal Form

SYM-5 of Symmetry ARC A Target-Fibered Orbit–Stabilizer–Invariant and Role-Occupancy Closure This paper develops a target-indexed classification of Standard Model flavor structure that keeps distinct six objects often conflated in flavor physics: the zero-Yukawa kinetic flavor action; weak-basis redescription; the stabilizer of a fixed Yukawa or mass-tensor point; spurion covariance; quotient-stable mass, mixing, and CPCP invariants; anomaly and higher-group data. The central mathematical object is the flavor action groupoid YD//GDbasis,\mathcal{Y}_D // G_D^{\mathrm{basis}}, formed separately for the minimal zero-Yukawa Standard Model, generic and singular quark sectors, minimal massless-neutrino and Dirac-neutrino targets, Weinberg/Majorana targets, quark and minimal-lepton Minimal Flavor Violation effective theories, and a higher-flavor interface target. The paper proves that the physical flavor symmetry at a fixed tensor point is the stabilizer of that point, not the complete covariance group. Generic parameter counts are derived from tensor-space dimension, basis-group dimension, and stabilizer dimension. Registered singular strata are recomputed independently rather than inherited from generic CKM or PMNS charts. The analysis provides target-specific treatments of: the maximal zero-Yukawa flavor action and its faithful global qualification; weak-basis transformations and presentation quotients; fixed-point stabilizers and factorization isotropy; generic and singular quark flavor structure; CKM mixing and quark-sector CPCP invariants; massless, Dirac, and Majorana neutrino flavor targets; generalized CPCP conditions; spurion covariance and conditional Minimal Flavor Violation; invariant algebras and completeness at generic and singular strata; rank loss, degeneracy, enhanced stabilizers, and phase survival; higher-flavor and global-form interfaces. Spurions are treated as nondynamical backgrounds that encode symmetry-breaking ancestry and organize effective-operator structure. They are not promoted into primitive physical objects or independent dynamical symmetries. Likewise, bases, matrix entries, chart phases, and labels do not acquire physical authority merely by being recorded. The AASC classification is applied only after the framework-neutral quantum-field-theoretic construction is complete. Target roles and physical residues are generated independently. The finite certificate contains: 9 target fibers; 25 registered results; 12 generic and singular strata; 82 independently constructed role positions; 82 independently constructed QFT residues; 778 evaluated same-target role–residue pairs; 1 compatible complete assignment; 1 lawful assignment orbit; 12 successful mutation tests. The result establishes a unique lawful integrated flavor normal form for the declared SYM-5 target family: ∣OSYM5∣=1.\left|\mathcal{O}_{\mathrm{SYM5}}\right|=1. This closure is relative to the registered sharp-local and effective-field-theory targets, their stated conventions, and their completeness certificates. It does not predict numerical Yukawa data, derive generation cardinality from matrix size, assert Minimal Flavor Violation as a fact of nature, or close the global-form, line-operator, monopole, defect, and generalized-symmetry sectors assigned to SYM-9. Whole-arc symmetry exhaustion remains reserved for SYM-11. Principal contributions A target-fibered Standard Model flavor-symmetry framework. A rigorous separation of flavor action, basis skin, stabilizer, spurion covariance, and physical invariants. Action-groupoid and orbit–stabilizer treatment of flavor structure. Generic and singular quark-sector parameter-count and invariant analysis. Separate massless, Dirac-neutrino, and Majorana flavor targets. Target-specific generalized-CPCP criteria. Spurion no-promotion and conditional MFV theorems. Invariant-completeness discipline across orbit strata. Higher-flavor and global-form interface classification. Independent role and residue construction. Complete finite role-occupancy closure with lawful automorphism quotient. Reproducible audit, mutation testing, and explicit theorem boundaries.