Topology-Level Containment with Autonomous Withdrawal: Analytic Conditions for Support-Free Multi-Agent Recovery

Cascading disorientation can arise in adaptive multi-agent systems when degraded orientation at one node destabilizes its neighbors through mutual-reference coupling. This paper asks under what conditions recovery can be achieved by reshaping the conditions of interaction - attenuating coupling, rewiring inflow toward recovery-favorable helpers, and temporarily buffering fatigue - without directly rewriting agents' orientation states, and under what conditions such support can afterwards be withdrawn without relapse. This theoretical study separates three obligations. First, an exact deviation recursion gives the sign of attenuation and an exact condition for joint attenuation and receiver-relative bridging. Second, common comparison certificates bound deviation and preserve thresholds under declared service and resource constraints; effective-inflow coordinates make these conditions affine, so convex operational constraints certify restoration paths and affine constraints reduce configuration synthesis to linear feasibility. Third, withdrawal requires safe support, finite joint entry into an exit set, complete restoration, and invariance under unsupported nominal dynamics. Constructive witnesses combine bounded-error approval, support-budget calculations, and node-specific restoration schedules after common entry. Uniformly positive unsupported net load supplies a complementary obstruction to permanent safety after finite support. Note on Version 2.0: these are conditional analytic results, not empirical validation. The simulation-based claims of v1.1 are withdrawn as documented in Section 1.1, and the v1.1 simulation scripts are not part of this version; they remain available in the v1.1 record. The supporting archive carries an exact-arithmetic verification script whose recorded run reports 127 named checks passed and 0 failed, together with a README, verification log, manifest and SHA-256 checksums. Those are selected exact arithmetic checks, not an empirical experiment or verification of every model instance.