Due to the fact that negative energies have no existence in physical reality, the advanced mechanics of purely positive energies should describe gravitational interactions and collisions in monistic terms of extended kinetic energies and their local stresses. Such non-Newtonian mechanics of continuous inertial densities reinforces the Cartesian concept of matter-extension in the metric formalism of Einstein-Grossmann with a supplemental (dark, aether) fraction of bi-vertex mass-energy distributions. Local accelerations or decelerations of mono-vertex material densities in a multi-vertex distribution of complete kinetic energy arise under its constant integral due to nonlocal organization of continuous densities. Such integral conservation of the distributed mass-energy occurs instantaneously throughout the whole continuum of correlated densities and metric stresses despite the time-varying contributions of complementary mono-vertex and bi-vertex fractions. Under the nonlocal organization of purely kinetic (positive) mass-energy, geodesic self-heating and self-cooling of the pulsating space-matter conserve the integral energy in the two-fraction virial theorem for the averaged motion of visible mono-vertexes in the presence of invisible bi-vertex (interference, dark) mass-energy. Metric stresses of such material space are subordinate to nonlocal self-government of continuously distributed kinetic energy, including the relativistic rest-energy of General Relativity. These mutually consistent or correlated stresses in inertial space-time-energy create timelessly coordinated self-accelerations, observed for dense material volumes as distant gravitational pulls. In order to falsify/verify the nonlocal self-organization of adaptive kinetic energy, the monistic mechanics of self-consistent inertial densities and metric stresses can suggest moderate field changes in the temporal redshift, cycles of geodetic falls and takeoffs in pulsating kinetic organizations, and the calculated acceleration of the expanding Metagalaxy in its current phase of geodesic self-cooling.