PSC-Optimality of the Standard Model in 4D Gauge Theory Space

We analyze the space of 4D renormalizable gauge quantum field theories under five axioms of Perfect Self-Containment (PSC): Reflexive Closure (RC), Structural Stability (NM*), Thermodynamic Viability (TV), Semantic Admissibility (SA), and Presentation Invariance (PI). We prove a Two-Layer PSC Theorem: (i) Layer I (Consistency): The hard PSC axioms narrow admissible gauge topologies to SU(3)\times SU(2)\times U(1) with anomaly-minimal chiral matter and N_\mathrmgen\ge 3; (ii) Layer II (Optimality): PI selects N_\mathrmgen=3 as the unique minimal solution. The result distinguishes what is forced by self-consistency from what is selected by minimality. Layer I forces the admissible gauge topology and anomaly-minimal chiral matter structure within 4D renormalizable gauge theory space under the hard PSC axioms. Layer II then selects N_\mathrmgen=3 via Presentation Invariance and minimality. All results apply within the space of 4D renormalizable gauge quantum field theories with compact gauge groups and chiral matter; gravitational extensions define a distinct problem. This overview presents the core NEMS theorem engine and selected applications; stronger domain-specific derivation and ontological synthesis claims belong to separate release surfaces with their own premise bundles and formal artifacts. Trust boundary. Claims are conditional on the PSC axiom package within \TSpace (4D renormalizable gauge QFT, no gravity); NEMS semantic classification and machine-checked spines are cited only as cross-suite context via nems-lean . See .