Accidental Symmetry by Operator Dimension: Baryon, Lepton, and Their Remnants

SYM-7 of Symmetry ARC Fixed-Target Closure of Accidental Charge in the Standard Model Symmetry Arc This paper develops a fixed-target classification of accidental baryon and lepton symmetries in the Standard Model, together with their anomaly qualifications, operator-dimension dependence, neutrino-sector deformations, and continuous or finite remnants. Accidental symmetries are treated as consequences of field content, operator support, flavor structure, and quantum sector rather than as primitive laws. The framework keeps four distinct levels separate: symmetry actions on the local algebra; current conservation and anomaly behavior; perturbative selection rules in a specified quantum sector; charge transfer between nontrivial topological sectors. For the minimal renormalizable theory, baryon number and three independent family-lepton phases are derived from exhaustive monomial neutrality. Electroweak topology is represented by the transfer vector (ΔB,ΔLe,ΔLμ,ΔLτ)=(3,1,1,1),(\Delta B,\Delta L_e,\Delta L_\mu,\Delta L_\tau)=(3,1,1,1), leaving B−LB-L and two family differences in the integer null lattice. Distinct neutrino targets separate the massless-neutrino theory, a Dirac-νR\nu_R theory, renormalizable Majorana breaking, and the Weinberg-operator theory. The paper classifies source-qualified operator sectors at dimensions 3, 5, 6, 7, and 9, together with the dimension-18 electroweak topological vertex. Exact charge signatures and violation vectors are computed for twelve registered effect sets. Smith normal form is then used to reduce the resulting violation lattices, map the generators back to elementary physical fields, and remove pre-existing overlaps with color-center and fermion-parity actions. The declared result comprises: 13 registered target schemas; 34 canonical typed scientific results; 7 scientific families; 12 registered effect sets; 31 target-local equivalence classes; 1 cross-target constraint; 1 target-family synthesis; 1 integrated closure result. The two target-distinct effect sets each leave one order-three operator-level occurrence. They are not simultaneous factors of a single target and remain unpromoted until the global-form and discrete-anomaly conditions assigned to SYM-9 are supplied. The resulting ledger distinguishes: accidental symmetry from primitive symmetry; current anomaly from operator-order violation; perturbative conservation from topological charge transfer; continuous breaking from exact discrete gauging; neutrino-target dependence from universal lepton-number claims; local anomaly information from global-form and defect completion; effective remnants from ultraviolet symmetries. The result is exact over the declared field content, operator support, flavor strata, background content, and quantum sectors. It does not infer a symmetry from an observed small rate, equate an allowed operator with a nonzero coefficient, promote local anomaly cancellation to a global gauging theorem, or infer ultraviolet physics from an effective remnant. Global-form completion, line and monopole sectors, discrete anomalies, non-invertible extensions, numerical Wilson-coefficient evolution, and whole-arc exhaustion remain explicit successor burdens. Principal contributions Derivation of accidental baryon and lepton symmetries from the renormalizable Standard Model grammar. Target-indexed classification of BB, LL, B+LB+L, B−LB-L, and family-lepton directions. Separation of current anomaly, perturbative selection rule, and topological transfer. Neutrino-target bifurcation across massless, Dirac, Majorana, and Weinberg sectors. Operator-dimension grading of baryon- and lepton-number violation. Exact charge-signature and violation-lattice construction. Smith normal form reduction with physical generator back-mapping. Classification of continuous and finite accidental remnants. Explicit treatment of electroweak topology and B+LB+L transfer. Fail-closed boundary between local accidental-charge closure and SYM-9/SYM-11 successor problems.