NFW acceleration conditions exclude six more of 141 SPARC curves at three listed errors with fixed geometry and bounded baryon masses

We add acceleration shape conditions to an exact test of 141 public SPARC rotation curves. Navarro-Frenk-White (NFW) halo acceleration has derivatives with alternating signs. Its divided differences therefore give necessary linear constraints with no halo mass or scale-radius bounds. We add consecutive constraints through orders two, three, and four to the previous spherical cusp class. At three listed speed errors, fixed geometry, and bounded constant baryon masses, the fourth-order exclusion count rises from 16 to 22. Three of the six added cases belong to the fixed 72-galaxy quality subset. A 5 km/s error floor plus allowed distance and inclination changes removes all six additions. The same three prior conflicts remain, including with wider mass bounds or the first retained row removed. We preserve 1,692 new rational score brackets, exact feasible vectors and exclusion weights, public input bytes, source code, and figures. An audit without an optimizer checks all new and 564 prior brackets. Constructed controls and fresh searches also pass. The score is a deterministic interval mismatch, not a statistical significance. Passing these finite conditions does not prove an NFW fit. These results give a useful added test and conditional exclusions; they do not establish a failure of dark matter theory.

SPARC · NFW halos · galaxy rotation curves · halo acceleration · divided differences · complete monotonicity · linear feasibility · exact certificates