Structural Closure under Weak Self-Gravity: Application of the structural-closure framework to weakly self-gravitating assemblies

This working paper asks a simple physical question: When can weak self-gravity keep a cohesionless contact network closed? A finite assembly of rigid bodies is represented by an embedded graph of frictionless unilateral contacts. The analysis separates four physically distinct questions: whether a contact configuration can be formed, whether it admits instantaneous equilibrium, whether the applied action favours any accessible opening motion, and whether the resulting structure can persist. Linearisation of the active non-penetration constraints defines a contact matrix and a cone of admissible internal motions. A configuration is action-relatively closed when the gravitational and rotational action performs no positive work along any admissible non-rigid motion. Equivalently, the action must be supportable by non-negative, compression-only contact reactions. This dual formulation provides a closure criterion, reaction margins and identifiable thresholds at which individual contacts unload and the active contact graph changes. Analytical and numerical examples involving linear, triangular, tetrahedral and octahedral sphere networks illustrate the distinction between geometrical rigidity, force equilibrium, formation accessibility and structural persistence. The work extends the physical sequence developed in From Free Bodies to Static Structure and From Space-Filling Particles to a Porous Heap from boundary-supported granular systems to isolated, weakly self-gravitating assemblies. Asteroid (101955) Bennu is used as a bounded application example. Its measured gravity and rotation define a weak-gravity action regime, while slopes, contours of fine-material deposits and exposed blocks provide observational constraints on possible local closure geometries. These observations do not determine a unique internal contact network and are not treated as direct evidence of cohesion. The paper develops a first-principles route from initially free fragments to persistent contact networks without introducing tensile bonding or an assumed bulk cohesive strength. Working Paper (Preprint), Version 2.0, September 2026.