Constructing the Standard Model from Minimal NEA Foundations

Natural Evolution of Actuality (NEA) is a constructive theory of physical realization built on two independently lawful abstract principles and a consequential joining operator within a premetric relational world. This manuscript reconstructs a complete mathematical chain supporting Standard Model-type internal gauge symmetries, chiral matter, and collective-mass dynamics—without requiring a universal law to dictate measured couplings or select a unique realized branch. An explicit algebraic branch leads to the exceptional Albert Jordan algebra over the octonions. A complex sub-corner of this algebra supports both positive quantum-state geometry and Lorentzian null-cone spacetime geometry under different transformations. Its nested subalgebra stabilizer reproduces the exact Standard Model gauge group, while the associated exterior algebra generates a sixteen-component, anomaly-free chiral fermion family with the correct relative hypercharges. Allowing a nested Jordan reference frame to vary induces a canonical gauge connection, curvature, and a positive operator with three distinct sector eigenvalues. Quadratic interpolation across this operator accommodates any positive triple of gauge kinetic coefficients—establishing parameter availability rather than numerical prediction—while a single gauge-invariant effective action yields Yang–Mills, matter, scalar, and selected mass dynamics. Finally, the work strengthens its collective-order construction into a global-uniqueness theorem and introduces a two-parameter family yielding a nonzero commutator sensitive to charge-parity (CP) violation. By preserving its quantum–causal structure, record framework, eighteen-entry particle inventory, and anomaly calculations while cleanly separating algebraic identities from empirical claims, the paper delivers a non-lossy, Standard Model-compatible mathematical architecture.