Coupled Stellar and Observation-Field Dynamics Common-Source Tests of Strong Lenses, DF2, DF4, and Coupled Evolution

We derive stellar motion, projected mass and structure formation from one objective observation field in Physical–Observation Cosmology. Its metric stress contributes real gravity and enters an inferred dark residual if omitted. The common quadratic action yields coupled collisionless and Schrödinger–Poisson evolution. Independent canonical component dilations have a positive energy Hessian, and the computed spherical responses remain bounded over the reported intervals. Across three calibrated lens cylinders, the unexplained fraction falls from 76.03% to a signed residual of \( -1.84\pm5.90 \) percentage points. For DF2, the stellar prediction is \( 7.77\pm0.64\,\mathrm{km\,s^{-1}} \); the additional-source fit is minimized at zero, although its approximate profile bound permits 57% extra mass inside the stellar half-mass radius. We prove the regional zero-residual criterion and its finite-error extension. Transferring the earlier intrinsic mode to DF4 without fitting its velocity gives \( 8.20\pm0.65\,\mathrm{km\,s^{-1}} \), consistent with \( 7.8^{+2.3}_{-2.0}\,\mathrm{km\,s^{-1}} \). The field increment is below \( 10^{-9}\,\mathrm{km\,s^{-1}} \), so this agreement tests the stellar-dominated limit. Expanding linear and nonlinear calculations then generate spatial structure from specified occupation and initial transport. A 4% periodic seed at 10 Mpc develops ordinary and field crest densities of 4.089 and 3.918 times their respective means, with new force harmonics fixed by the evolved source. Applying the environment to C0302 exposes its limits. The formal fixed-tracer monopole response is far below the required velocity change, and the unchanged infinite stellar tail develops negative remote pressure in the 10 Mpc environment. A self-consistent isolated-source refit improves the velocity residuals but requires an equivalent external column fraction of 0.433; the evolved profiles supply at most 0.00201 along a specified 10 Mpc path. The dwarf apertures require no detected independent dark component. C0302 still requires a resolved environmental and stellar-boundary solution before the same field can satisfy all of its constraints.