An Integrable Weyl Effective Model for Collective PE-NE Dynamics: Canonical Constraints, a Kinetic Floor, and Conditional Galactic Tests

We examine a two-scalar effective model motivated by a collective expanding-contracting spacetime interpretation. An integrable Weyl connection is identified with the Levi-Civita connection of the matter metric, while its curvature is contracted with a specified representative metric. This action choice produces a positive canonical kinetic floor \epsilon = 6\alpha^2 for the asymmetry field. We derive the metric and scalar equations, the exact velocity Hessian on a spacelike-gradient branch, and the ADM constraint algebra. On the open branch where the Hessian is positive, the gravitational-scalar sector has two tensor and two scalar local degrees of freedom; its static zero-gradient velocity Hessian also has a positive limiting value if \alpha \ne 0. The square-root gradient invariant is not a twice differentiable function of the invariant at its null boundary; consequently neither global Dirac rank nor regular time-dependent crossing at that boundary follows from the open-branch calculation. A static asymptotic analysis shows that the kinetic floor changes the scalar force from approximately 1/r to 1/r^2 sufficiently far from a finite source. Eight previously assembled candidate galactic residuals are reported as unverified exploratory inputs rather than independently reproduced fits. Profiles, frame-consistent source reconstruction and full numerical replication remain necessary to test the proposed mechanism. The framework makes no claim that a global zero-Hamiltonian condition follows from its local action.