The Einsteinian Orbital Stability Manifold

This work introduces the Einsteinian Orbital Stability Manifold, a purely geometric framework for understanding orbital debris dynamics and the conditions under which Kessler Syndrome becomes inevitable or impossible. Orbital space is modeled as a stratified interaction manifold in which collisions and fragment generation form a branching process. A single invariant—orbital criticality, defined via the spectral radius of a cell-restricted branching operator—is shown to govern long-term stability. The paper demonstrates that Kessler Syndrome is not an accumulation problem or an engineering failure, but a supercritical phase transition analogous to nuclear criticality or epidemic runaway. Permanent orbital freedom is proven equivalent to maintaining subcritical curvature across all orbital interaction cells. The formulation is entirely non-implementational: no technologies, mitigation methods, policies, or operational procedures are proposed. This manuscript extends the Ainstein sequence of geometric theories (physics, metric structure, quantum theory, curvature, health, energy, resources, and humanities) to near-Earth orbital space, completing the framework by formalizing orbital sustainability as an invariant stability condition.