TORUS Ladder Dynamics VI: Closure, Topology, and Emergent Relational Modes

This release investigates whether discrete closure scales identified in earlier TORUS Ladder studies behave as stable relational modes under topology changes, perturbations, and compositional extension. Using only conservative structural diagnostics and calibrated null controls, we demonstrate that closure arises exclusively in composite ladders, persists under cyclic topology, recurs under perturbation, and generates higher-order closure modes when extended relationally. These results establish necessary preconditions for future work relating closure behavior to dimensional emergence and physical constants, while making no interpretive claims at this stage. What Zenodo I–V already proved (cumulatively) Release What it actually locked in I Ladder closure exists and is detectable II Closure has structural mechanisms and failure modes III Closure is invariant under many deformations but brittle under specific ones IV Recurrence emerges from order mutation, not tuning V Closure can be discriminated from nulls via calibrated recurrence gates