Gauge Architecture and Gauge Skin in the Standard Model

Abstract

SYM-1 of Symmetry ARC Integrated Role-Occupancy Closure and Locus-Sensitive Gauge Audit This paper separates the load-bearing gauge architecture of the Standard Model from representative gauge operations that function only as gauge skin at a specified locus. It develops an integrated, fixed-target classification of gauge transformations, quotients, transport structures, boundary actions, global-form data, representations, anomalies, BRST cohomology, theta sectors, and related physical responses. The analysis is formulated under the Admissibility–Standing–Reference–Irreversibility kernel. Determinate fields, states, transformations, quotients, records, and admissible continuations already instantiate the conditions required for target identity, comparison, standing-bearing use, lawful transformation, and irreversible fixation. Conventional gauge theory then supplies the target-specific transformation, quotient, boundary, topology, representation, cohomology, and anomaly data used in the classification. The principal closure theorem is evaluated on one integrated SYM-1 Standard Model gauge target rather than on a collection of artificially separated microtargets. The target incorporates: coherent presentation, comparison, and transport; physical reduction and matter response; representation and charge data; perturbative and global anomaly constraints; boundary and asymptotic gauge action; global-form and topology information; large transformations and theta-sector realization; BRST/BV and cohomological structure; proper compact-support gauge operations; cross-realization synchronization. Eleven occupant-independent target roles are fixed before candidate inspection. A target-derived protocol then generates the candidate-locus universe, including atlas-backed objects, target-generated composite packages, atlas-external diagnostics, and genuine presentation-equivalence stress pairs. Every residue-role pair receives a certified positive or negative eligibility result. Pointwise eligibility is not treated as physical realization: all eligible injective preassignments are evaluated against independently computed transport, quotient, representation, anomaly, boundary, topology, theta, BRST, and synchronization constraints. The integrated calculation produces: 11 target roles; 4,608 pointwise eligible injective preassignments; one compatible complete assignment; one lawful assignment orbit under the full invariant-preserving automorphism group. A separate two-chart control target demonstrates that a nontrivial lawful automorphism group can identify multiple assignments as one lawful orbit without erasing genuine physical distinctions. The paper also establishes a locus-sensitive gauge-status discipline. Proper compact-support gauge operations remain quotient-trivial skin at the proper-bulk locus, while boundary, asymptotic, large, topological, theta-sector, and other target-dependent operations may acquire distinct physical or structural status when the relevant standing-bearing locus changes. Gauge fixing is not granted independent physical authority, and anomalies are treated as failures of quantum descent at their appropriate locus rather than as undifferentiated negations of every associated action. The endpoint is complete relative to the frozen integrated SYM-1 target signature and certificate. The theorem is reopened by any missing same-target role, omitted target-relevant object, incomplete presentation quotient, incorrect eligibility edge, missing compatibility condition, absent live residue, second non-equivalent assignment orbit, or overbroad automorphism quotient. Full exhaustion of every symmetry-relevant structure in the Standard Model remains reserved for the later SYM-11 programme. Principal contributions An integrated fixed-target gauge-architecture theorem. A separation of gauge architecture from representative-level gauge skin. Occupant-independent role formation before candidate inspection. Target-generated candidate-locus and residue construction. Complete certified eligibility analysis. Computed joint compatibility across all eligible preassignments. Lawful automorphism and assignment-orbit closure. Locus-sensitive treatment of proper, boundary, large, topological, theta-sector, and BRST-related operations. Typed separation of physical action, quotient structure, diagnostic, obstruction, transport, and redescription. A reproducible audit architecture with explicit falsification routes.