Scale-Mismatch, Lyapunov Stability, and Post-Attractor Decision Regimes
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2026
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| _version_ | 1866901959503511552 |
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| author | Zhan, Dedong |
| author_facet | Zhan, Dedong |
| contents | <p>This paper develops a dynamical-systems account of civilizational stability under conditions of timescale mismatch, weak consensus, and post-attractor transition. The central claim is that many contemporary disagreements in public academic discourse do not arise primarily from opposing positions, insufficient rigor, or lack of information, but from an unmodeled shift in system timescales. Historical and slow-variable models often assume that corrective mechanisms operate faster than amplification processes. When amplification dynamics approach or exceed correction dynamics, inherited stability conclusions lose structural validity while still appearing locally reasonable within their original domains.</p> <p>The paper first formalizes this condition as a Scale-Mismatch Proposition: if a model assumes \tau_{corr} < \tau_{amp}, while the actual system satisfies \tau_{corr} \ge \tau_{amp}, then stability claims derived from historical precedent no longer cover the system’s real trajectories. This explains the emergence of weak consensus: rigorous observers may sense that existing models fail to explain reality, yet no replacement model has fully stabilized.</p> <p>The analysis then reformulates civilizational stability in Lyapunov–Attractor terms. A stable civilizational regime requires a bounded attractor and a Lyapunov function whose derivative remains non-positive along system trajectories. When corrective dynamics can no longer constrain amplification dynamics, the system may preserve transient order while losing Lyapunov stability. This defines the post-attractor regime.</p> <p>Finally, the paper introduces the Synchronous Hard-Decision Proposition and a behavior classification theorem for post-attractor conditions. When hard decisions emerge simultaneously across domains, regions, industries, classes, and institutional branches, this indicates a loss of stable attractor governance rather than individual cognitive failure. In such a regime, behaviors are classified as stability-seeking, over-jump, or structure-preserving. The paper concludes that, after attractor loss, correctness becomes structurally underdetermined, while reversibility, buffering, and multi-path exposure remain meaningful stabilizing principles.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20252581 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Scale-Mismatch, Lyapunov Stability, and Post-Attractor Decision Regimes Zhan, Dedong <p>This paper develops a dynamical-systems account of civilizational stability under conditions of timescale mismatch, weak consensus, and post-attractor transition. The central claim is that many contemporary disagreements in public academic discourse do not arise primarily from opposing positions, insufficient rigor, or lack of information, but from an unmodeled shift in system timescales. Historical and slow-variable models often assume that corrective mechanisms operate faster than amplification processes. When amplification dynamics approach or exceed correction dynamics, inherited stability conclusions lose structural validity while still appearing locally reasonable within their original domains.</p> <p>The paper first formalizes this condition as a Scale-Mismatch Proposition: if a model assumes \tau_{corr} < \tau_{amp}, while the actual system satisfies \tau_{corr} \ge \tau_{amp}, then stability claims derived from historical precedent no longer cover the system’s real trajectories. This explains the emergence of weak consensus: rigorous observers may sense that existing models fail to explain reality, yet no replacement model has fully stabilized.</p> <p>The analysis then reformulates civilizational stability in Lyapunov–Attractor terms. A stable civilizational regime requires a bounded attractor and a Lyapunov function whose derivative remains non-positive along system trajectories. When corrective dynamics can no longer constrain amplification dynamics, the system may preserve transient order while losing Lyapunov stability. This defines the post-attractor regime.</p> <p>Finally, the paper introduces the Synchronous Hard-Decision Proposition and a behavior classification theorem for post-attractor conditions. When hard decisions emerge simultaneously across domains, regions, industries, classes, and institutional branches, this indicates a loss of stable attractor governance rather than individual cognitive failure. In such a regime, behaviors are classified as stability-seeking, over-jump, or structure-preserving. The paper concludes that, after attractor loss, correctness becomes structurally underdetermined, while reversibility, buffering, and multi-path exposure remain meaningful stabilizing principles.</p> |
| title | Scale-Mismatch, Lyapunov Stability, and Post-Attractor Decision Regimes |
| url | https://doi.org/10.5281/zenodo.20252581 |