{"paper":{"title":"Contraction versus Recurrence: An Exponential Separation in Observation-Based Prediction of Deterministic Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Pavel Popovich","submitted_at":"2026-07-16T11:58:44Z","abstract_excerpt":"Given a scalar observable of an ergodic dynamical system with a low-dimensional attractor, two families of methods reconstruct and predict the underlying state: recurrence-based methods (the method of analogues and its descendants), which wait for the trajectory to return to an $\\varepsilon$-neighborhood of a previously observed state, and observer-based methods, which fit a converging state estimator on the delay reconstruction. We formalize and empirically verify an exponential separation between the two: the expected cost of recurrence scales as $\\varepsilon^{-d}$, where $d$ is the pointwis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14885","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.14885/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}