Convergent Nodes, Bifurcating Failure: Legibility and the Gate in Cooperative Institutions

The failures of cooperative institutions are usually described one breach at a time — a fraud here, a run there, an eroded norm elsewhere — as though each were its own kind of event. Assembling established results from commons governance and the evolution of cooperation into a single architecture, we argue instead that many are expressions of one design: a committed node that converges several inputs and, past a load threshold, does not degrade gracefully but bifurcates into an adaptive branch or a collapse branch. The most-upstream determinant of which branch is taken is not the magnitude of stress but its species — the legibility of a defection, scored at ingestion — which acts as a partition coefficient between a sanction-tractable pathway and a collapse pathway. The geometry of failure is set by node type: a sensor/gating node fails by fold (pivot, with critical slowing), a mechanical/load-bearing node by fracture (snap, with an event cascade), and a dual node — sensor and actuator at once — can be tuned between the two, which makes it the calibration case. The two geometry-relevant determinants organize into a cusp catastrophe. Because these determinants can be read from an institution's own configuration and event stream, the model yields a two-channel, endogenous instrument and a falsifiable kinetic signature — the sign of the change in recovery time — that distinguishes the two failure geometries before either resolves. We offer this as a mechanistic synthesis warranting investigation, not a demonstrated result, and we lead throughout with the tests that would refute it.