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:

1. Nontrivial record pinching,

2. Full-channel engagement,

3. 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.