The Sagittarius system defeats joint fitting: halo shapes matching the stream's 3D track and bifurcation misalign the disk or underpredict its warp, the Law-Majewski triaxial solution is dynamically unstable for disk galaxies, and twenty years of modeling have produced mutually exclusive halos rather than a measurement (Law and Majewski 2010; Deg and Widrow 2013).
The model hands the fit a free-function particle halo, and the system's richness exposes the freedom: each observable selects a different halo, and the union is empty. A parameterization that cannot converge on the Galaxy's best-measured dynamical system is failing structurally, not statistically.
SCT fits the Sagittarius system with the same nearly parameter-free potential it offers every stream: the baryons coherently amplified, Φ_eff(r) = -G × A(r) × M_baryonic(<r)/r, the amplification rising to the fixed point A* = 5.970 at the virial radius (P50, P52). The registered program in Paper 13, From Chaos to Coherent Gravity, is explicit: the multi-wrap stream geometry must be reproduced with the measured baryonic mass model and no NFW parameter fit whatsoever, and the sharpest registered discriminant is quantitative, the cumulative azimuthal wrap spacing after four complete wraps should differ from the ΛCDM apsidal prediction by 24 to 120 degrees, a divergence DESI's stream-tracer catalogs and Gaia astrometry can measure directly.
The disk linkage resolves through the standing-tide reading of the warp sector (recid 123): the Galactic warp is held by the mesh tide strongest where local gravity is weakest (P51), with Sagittarius's crossings exciting the corrugations and phase-space spiral on top of that standing baseline. The model's impossible task, one halo shape serving stream and warp simultaneously, dissolves because the warp was never the halo's job. The stream's near-polar plane carries the usual inheritance signature (P31, P32), sitting in the same debris-field architecture as the satellite planes (recid 130).
Keystone economy: P52 fixes the potential, P51 holds the warp, and the registered 24-to-120-degree window makes the whole sector falsifiable with one measurement.
The kill is registered and numerical: if DESI and Gaia stream-tracer astrometry find the Sagittarius arm positions consistent with the ΛCDM apsidal-angle prediction, no 24-to-120-degree cumulative offset, the A(r) potential fails its sharpest quantitative test. Equally, if the stream's geometry demands an effective mass beyond 5 × 10¹¹ M☉ outside 50 kpc at high significance, the amplified-baryon mass budget breaks directly.