THE ASYMMETRIC CONNECTOME A Diagnostic Protocol for Detecting Whether Recursion Is Doing Work

Every recursive reasoning system -- a CEGAR loop, an actor-critic training run, an autonomous agent revising its own plan, a research programme revising its own theory -- eventually faces the same unmarked moment: the point at which another cycle stops producing anything and starts merely *occurring*. Nothing in the architecture announces this moment. The system keeps running, keeps generating outputs that look like progress, and keeps consuming the same code path it used when it actually was making progress. The failure is not visible in any single cycle. It is visible only in the relationship between what was generated and what was eliminated, summed over time. This paper is not, at its core, a proposal for a new kind of reasoning architecture. It is a proposal for an *instrument*: a small, domain-general, computable signal -- the Recursive Work Ratio (RWR) -- that can be attached to any generate-then-reduce loop to answer one question on every cycle: IS THIS RECURSION DOING WORK, OR IS IT JUST TURNING? The Asymmetric Connectome is the minimal architectural scaffolding required to make that question askable in a principled way, and the Straight-Line Boundary is the decision rule built on top of the signal once it is available. The novelty here is not in any one component. Falsification, counterexample- guided refinement, and critic-grounded generation are all old ideas, individually. What is new is the SYNTHESIS: pulling the *adjudication structure* out of each tradition (Popper's testability requirement, CEGAR's counterexample loop, actor-critic's independent value function) and recombining them into a single portable measurement that does not require being a research programme, a model checker, or a training run to use. The second piece of novelty is the APPLICATION: once recursion-doing-work is a measurable quantity rather than a judgment call, it can be applied to domains none of the three source traditions were built for -- autonomous agent loops, organizational decision cycles, multi-agent debate, and recursive self- improvement monitoring -- none of which have a native equivalent of "convergence" or "verification," but all of which can be instrumented with RWR. Section 10 demonstrates the instrument on a fully worked numeric trace, showing the exact cycle at which RWR drops to zero and the recursion is correctly flagged as exhausted -- not asserted as exhausted, *measured*.