Nonlinear Collapse with a Matched Q-Interaction Sector: Constraint-Satisfying Data and an Exact Future-Trapping Threshold

This preprint couples a matched Q-interaction matter law to Einstein gravity in spherical symmetry. It constructs smooth initial data with a homogeneous closed core and an expanding cosmological exterior and derives the future null expansions in the causal domain of the core. For a specified sphere and conformal-time deadline, the solution yields an exact threshold at initial quadratic energy fraction f = 2/3. The result applies to the stated initial-data family and gives an analytic benchmark for nonlinear collapse.