AIM Framework glossary
Joint Stability Condition
Canonical definition
The Joint Stability Condition is , where is the Effective Loop Gain at the fast layer, is the Slow-Layer Loop Gain from the Bayesian Belief dynamics, and is the higher-order remainder of the cross-block coupling between the fast and slow layers, the leading cross-block product being carried by . The condition specifies the threshold below which the joint fast-slow system remains stable, generalising the fast-layer-only condition to the coupled system. The additive decomposition is a leading-order engineering heuristic for weakly coupled loops, with carrying the leading cross-coupling product and the corrections of higher order in the cross-coupling norms; the exact stability criterion is the largest real eigenvalue of the full coupled block-Jacobian (Appendix A, Section A.5.6).
Explanation
The fast valuation loop has its own loop gain. The slow Belief layer has no cycle of its own: its gain is the loop that leaves the Belief Register, runs through the fast valuation layer and returns as Evidence, so the Slow-Layer Loop Gain is already the main coupling between the two layers. What coupling remains beyond that loop is small and is carried as a third term. All three contributions add up, and the total must stay below a critical threshold for the system to remain stable. This means the system can tip into instability even when the fast loop alone would not be supercritical, because the gain the Belief Register adds through the fast layer can push the total over the threshold. The Knowledge Patch reduces the Effective Loop Gain through the I-Override gate, and the Slow-Layer Loop Gain through AIM Vocabulary Acquisition and Epistemic Suspension; no Patch channel acts on the remainder directly, but the remainder is built from the same couplings those channels reduce, and falls with them.
Epistemic status
Framework-Specific Named Result. Source: Appendix A.5.6.