From Local Gauge Consistency to Global Representation Closure Electric Charge Complementarity and the Conditions for Physical Selection

A mathematical investigation of anomaly constraints, global representation structure, neutrality anchors, and the independence requirements for closure-based charge selection. Why do the proton and electron possess equal and opposite electric charges, and what would be required to derive the individual charge assignments rather than assume them? This manuscript investigates the distinction between local gauge consistency, global representation admissibility, and unique physical selection. It examines a Standard Model matter extension with right-handed Dirac neutrinos, using explicit anomaly, interaction, representation, and operator constraints as mathematical controls for the Unified Coherence Closure Framework. Within the stated matter and interaction assumptions, the locally anomaly-compatible electromagnetic assignments retain a deformation along baryon number minus lepton number. Fixed compact global gauge-group choices restrict that freedom to discrete charge lattices but do not generally eliminate it. The subsequent constructions examine categorical reconstruction, flavor connectivity, Majorana restrictions, vacuum stabilizers, unified representations, triality, color dimension, Gauss-law sectors, and local gauge-invariant operators. Counterexamples identify the information these conditions leave undetermined. A principal conditional result combines two individually insufficient restrictions. In the specified one-Higgs, one-generation Dirac-neutrino family, descent to the fixed conventional quotient restricts the deformation parameter to multiples of three. Existence of a derivative-free, fully gauge-invariant fermionic polynomial containing exactly one lepton doublet and otherwise only the Higgs doublet and its conjugate restricts it to zero or minus one. Their intersection selects zero. A further common-kernel calculation shows that faithful effective gauge action alone retains infinitely many nonconventional assignments. The manuscript therefore supplies conditional selection mechanisms and explicit tests of insufficiency. It does not yet derive the required selecting premises independently from primitive closure. Its foundational target is a noncircular account of why the relevant representation structure, local operator class, and physical matter identity must occur together. Selection of an assignment and protection of its exactness are separate explanatory obligations. Keywords: electric charge quantization; proton–electron complementarity; gauge anomalies; global gauge structure; representation theory; neutrality; closure mathematics; UCCF.