Determinant-Closed Unification from a Capacity-Constrained Dirac–Λ System: A Record-Admissible Forcing of the Standard Model

This work presents a determinant-closed unification framework derived from a coupled Dirac–Λ system subject to a capacity constraint. The central object is a coupled system consisting of: A twisted Dirac operator defining the matter–geometry carrier, A canonical dissipative generator entering through a Fejér-type spectral determinant, A UV anchor condition and IR tolerance window enforcing a capacity inequality across a finite temperature interval. Within this structure, we define a physically meaningful class of stationary solutions, the record-admissible sector, characterized by: Nontrivial record pinching, Full-channel engagement, Dissipative coercivity (strict irreversibility). From these conditions, we derive: A forced spectral gap in the dissipative generator, An automatic IR dominance bound, A closed cap on the internal load functional, A double-squeeze mechanism excluding all internal packages except one. Under these constraints, the unique feasible internal gauge group and minimal chiral matter content are: SU(3) × SU(2) × U(1) with the standard hypercharge assignment (up to overall sign). The derivation does not assume cap-gap separation, spectral gap, or anomaly cancellation independently; these emerge within the record-admissible stationary class. The result is therefore unconditional within the physically admissible irreversibility sector of the coupled Dirac–Λ framework. This provides a determinant-based forcing architecture for Standard Model unification from first principles at operator level.