Abstract Loops

Abstract Loops develops a finite, task-relative framework for understanding what happens when bounded abstractions meet, interact, and return. It begins with exact results on joint certification: two traces may each fail to determine a target while their combined trace determines it completely. The note then distinguishes a composite interface from the typed observational, causal, resource, provenance, and intervention witnesses that make its internal cut substantive. Closed processing can preserve or collapse distinctions already present on a fixed interface, but it cannot split an original joint fiber. Coupling may nevertheless produce baseline-excluded reachable behavior or leave a newly addressable persistent carrier. The proposed abstract-loop vocabulary separates returned identity, direct residuals, and exported residuals while preserving the source and witness burdens behind each claim. Recursive carrier-generative transitions permit open-ended finite structure without implying a prime mover, actual infinity, or escape from local capacity bounds. A final speculative section explores gravitational holonomy and loop quantum gravity as possible physical motivation while leaving the required bridge theorem explicitly open.