Functional Resolution Without Eradication: Redefining Success in Adaptive Systems Through Future-Path Constraint

Eradication is still the default definition of “success” across medicine, governance, and adaptive system design: if any residual signal or structure remains, the outcome is treated as failure. In adaptive systems, that zero-logic regularly breaks. It mislabels stable, bounded end-states as unresolved, and it pressures people and institutions toward brittle, high-risk interventions whose main achievement is cosmetic purity rather than durable safety. What we actually observe, again and again, is that many systems settle into non-zero states that persist without re-expansion, regeneration, or a return of harmful dynamics. Residual presence on its own turns out to be a weak predictor of future danger. The real question is not “Is anything left?” but “Can what’s left rebuild the harmful identity of the system?” This paper introduces Functional Resolution Without Eradication (FRE) as a formal criterion that answers that question directly. FRE defines resolution as a property of the future: a system is resolved when there is no admissible future trajectory available that can reconstruct the harmful system identity. In other words, resolution is not measured by present-state magnitude or purity, but by whether harmful futures have been structurally foreclosed. Using a minimal dynamical-systems framing, we define admissible futures, active identity, and reconstructibility, and show why eradication-based criteria are neither necessary nor sufficient for resolution in adaptive systems. A system can be “non-zero” yet resolved if the remaining traces cannot regenerate the dynamics that matter; conversely, a system can look “clean” at a snapshot while still retaining a viable path back to harm. By shifting evaluation from snapshot purity to trajectory structure, FRE dissolves long-standing stalemates in cure science (including durable remission and other stable non-zero outcomes), institutional governance, psychological integration, and ecological resilience. The standard becomes stricter in the way that counts: not the demand for perfect absence, but the demand that harmful return has been made structurally impossible—even if traces remain.