{"paper":{"title":"A Framework for Intrinsic Poincar\\'e Sections and Phase-Space Manifold Visualization: A Case Study of the Planar Elastic Pendulum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Florian Steffen G\\\"unther, Rafael Salandin Moraes","submitted_at":"2026-07-30T18:25:22Z","abstract_excerpt":"The global phase-space organization of non-linear Hamiltonian systems is traditionally visualized using Poincar\\'e sections. However, rigid choices of sectioning hyperplanes often introduce geometric distortions and coordinate artifacts that obscure or clip fundamental invariant structures. Here, we present a multi-mapping analysis of the planar elastic pendulum to systematically overcome these visual and structural limitations. We implement a comparative framework utilizing inverted phase-space mappings that resolve the dense packing of invariant curves near chaotic boundaries, uncovering an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28758","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/2607.28758/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"}