The MANTA Sourcing Problem: Relativistic Confined Flow as the Physical Momentum Source of a Toroidal Warp Shell

Abstract The companion control paper (Meyler 2026, hereafter MANTA) established that a positiveenergy toroidal warp shell is governable: full-rank (LARC Rank 5) non-linear controllability, an exact area-holonomy tracking law, and the identification of the plant couplings as constraint Green’s functions, all inside an effective plant whose momentum source Si was taken as given. MANTA named one open link on its critical path: the map from a physical plasma to that source. This paper specifies that link and reduces it to a single, sharply-stated equilibrium problem. We first establish, from the ideal-magnetohydrodynamic (MHD) form of the Arnowitt– Deser–Misner (ADM) momentum density, that the metric shift vector cannot be sourced by static currents ([P], two routes). The Eulerian momentum density Si that drives the shift is proportional to bulk fluid velocity in every term; a magnetostatic plasma has Si ≡ 0 for any current J and field B. The Lorentz force J × B is a force density entering energy-momentum conservation ∇μTμν = 0, not the momentum constraint. Only bulk flow sources the shift. This inverts the naive current-to-shift picture into a two-stage architecture: flow sources the shift; currents establish and hold the flow. We invert the exact 2D poloidal momentum constraint Gt z = 8πSz on the solved MANTA background (Φ = 0.2311, A = 1.6914, N = 0.769) using the correct cylindrical operator — radial in the shift, with no ∂2 z bz term ([P]) — on 141 × 141 finite-difference grids ([N]). For the fixed-width DEC-compliant envelope (λ ≤ 0.14) the required peak bulk flow is subluminal and sub-Alfv´enic, v/c ∈ [0.0608, 0.1303] (18 230–39 060km/s) at n = 1018 m−3, B = 10T (VA = 0.5886c, MA ∈ [0.103, 0.221]). Width re-optimisation (MANTA Theorem 7) extends the standing envelope to 0.50c. The required flow shear over-supplies the sheared-flow-stabilization (SFS) threshold by 11.7×–25.1×, so the sourcing flow is itself strongly stabilizing. Against the best measured confined-plasma flow (∼ 100km/s, 3.3 × 10−4c) the requirement is a factor ∼ 180–390 higher — a regime shift, not a velocity wall, since the controlling ratio is v/VA, not v/c. Stage-2 force balance shows the flow is a 0.2% perturbation on the static shell; charge conservation forces a 62.5% Lorentz / 37.5% thermodynamic split, explaining MANTA’s anisotropic stress; the CGL double-adiabatic invariants drift by ∼ 100% per transit, an honest negative establishing that the sourcing plasma requires a non-ideal closure. The native topology is a high-magnetization, low-density, high-field sheared-flow Z-pinch. No feasibility claim is made in either direction; every load-bearing relation carries an evidentiary tag ([P]/[N]/[E]/[S]).