The Self-Consistency Extremum Principle: From a Single Meta-Principle to the Emergence of the Standard Model and General Relativity

Modern fundamental physics rests on three mutually incompatible axiomatic systems—quantum mechanics, gauge field theory, and general relativity. This paper proposes a unified framework derived from a single meta-principle: what is not self-consistent cannot exist; what is self-consistent exists according to its degree of self-consistency. From this, we derive the mathematical realization—unique within the Deligne categorical framework (Appendix A) —as a comparator network on a finite directed 2-complex, whose partition function is uniquely governed by the Self-Consistency Extremum Principle (SCEP). Without any additional assumptions, SCEP yields: (1) low-energy unitarization as a necessary consequence of extremizing the action; (2) homogeneous fiber geometry G/H emerging from comparator invertibility; (3) Einstein gravity and Yang-Mills gauge fields emerging simultaneously in the cell-refinement limit; (4) the structural form of the Born rule—from reference-frame-independent transition amplitudes; (5) Standard Model fermion quantum numbers from geometric quantization of the fiber; (6) SU (3) ×SU (2) ×U (1) as the unique anomaly-free compact Lie group; (7) three generations from the joint constraint of KO-dimension = 6 and spectral minimization; (8) a new fiber-phase gauge field κ_μ with three-phase unification. The structural form of all dynamical laws is uniquely fixed; numerical values of Standard Model parameters remain undetermined. The appendices provide the anomaly cancellation computation, KO-dimension derivation, Higgs potential sign analysis, Standard Model fermion spectrum computation, nonlinear Schur lemma, and the category-theoretic proof that the comparator network is the unique possible realization of the meta-principle.