{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:VFGNP2JQLAMAEVIGLWJ64XW2S5","short_pith_number":"pith:VFGNP2JQ","schema_version":"1.0","canonical_sha256":"a94cd7e93058180255065d93ee5eda976052fcb34f690cb4b12c68f404a1e01f","source":{"kind":"arxiv","id":"2506.07307","version":1},"attestation_state":"computed","paper":{"title":"Global Centers and Phase Portraits in Generalized Duffing Oscillators: A Comprehensive Study of the Center-Focus Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gabriel Rond\\'on, Nasrin Sadri","submitted_at":"2025-06-08T22:43:09Z","abstract_excerpt":"This work presents a comprehensive study of the generalized Duffing oscillator, a fundamental model in nonlinear dynamics described by the system $$ \\dot{x} = y, \\quad \\dot{y} = -\\alpha y - \\epsilon x^m - \\sigma x, $$ where $\\epsilon \\neq 0$ and $m \\geq 1$. We focus on the topological classification of phase portraits, the characterization of global centers, and the absence of limit cycles for $\\alpha\\neq0$. For the linear case ($m = 1$), we establish necessary and sufficient conditions for the origin to be a global center, showing that this occurs if, and only if, $\\alpha = 0$ and $\\epsilon +"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.07307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-06-08T22:43:09Z","cross_cats_sorted":[],"title_canon_sha256":"b13cb3a3cf2f8838153896020d2b4493856fd551b935f6ece8dd0735abecd352","abstract_canon_sha256":"ab7a7cc5d3ea830cd7a34c219cb1e616c5ce7e0e201611dff98459a9cf5f0637"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:24.817080Z","signature_b64":"iO27+jB9BnVh4hILvp+zimawgP8vTKm+7m+RmCjeUvEOv61pDhY9VSba12xbn4L8zYtgiqVn3prhKjB6VSdiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a94cd7e93058180255065d93ee5eda976052fcb34f690cb4b12c68f404a1e01f","last_reissued_at":"2026-07-05T11:18:24.816634Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:24.816634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Centers and Phase Portraits in Generalized Duffing Oscillators: A Comprehensive Study of the Center-Focus Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gabriel Rond\\'on, Nasrin Sadri","submitted_at":"2025-06-08T22:43:09Z","abstract_excerpt":"This work presents a comprehensive study of the generalized Duffing oscillator, a fundamental model in nonlinear dynamics described by the system $$ \\dot{x} = y, \\quad \\dot{y} = -\\alpha y - \\epsilon x^m - \\sigma x, $$ where $\\epsilon \\neq 0$ and $m \\geq 1$. We focus on the topological classification of phase portraits, the characterization of global centers, and the absence of limit cycles for $\\alpha\\neq0$. For the linear case ($m = 1$), we establish necessary and sufficient conditions for the origin to be a global center, showing that this occurs if, and only if, $\\alpha = 0$ and $\\epsilon +"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07307","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/2506.07307/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.07307","created_at":"2026-07-05T11:18:24.816690+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.07307v1","created_at":"2026-07-05T11:18:24.816690+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07307","created_at":"2026-07-05T11:18:24.816690+00:00"},{"alias_kind":"pith_short_12","alias_value":"VFGNP2JQLAMA","created_at":"2026-07-05T11:18:24.816690+00:00"},{"alias_kind":"pith_short_16","alias_value":"VFGNP2JQLAMAEVIG","created_at":"2026-07-05T11:18:24.816690+00:00"},{"alias_kind":"pith_short_8","alias_value":"VFGNP2JQ","created_at":"2026-07-05T11:18:24.816690+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VFGNP2JQLAMAEVIGLWJ64XW2S5","json":"https://pith.science/pith/VFGNP2JQLAMAEVIGLWJ64XW2S5.json","graph_json":"https://pith.science/api/pith-number/VFGNP2JQLAMAEVIGLWJ64XW2S5/graph.json","events_json":"https://pith.science/api/pith-number/VFGNP2JQLAMAEVIGLWJ64XW2S5/events.json","paper":"https://pith.science/paper/VFGNP2JQ"},"agent_actions":{"view_html":"https://pith.science/pith/VFGNP2JQLAMAEVIGLWJ64XW2S5","download_json":"https://pith.science/pith/VFGNP2JQLAMAEVIGLWJ64XW2S5.json","view_paper":"https://pith.science/paper/VFGNP2JQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.07307&json=true","fetch_graph":"https://pith.science/api/pith-number/VFGNP2JQLAMAEVIGLWJ64XW2S5/graph.json","fetch_events":"https://pith.science/api/pith-number/VFGNP2JQLAMAEVIGLWJ64XW2S5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VFGNP2JQLAMAEVIGLWJ64XW2S5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VFGNP2JQLAMAEVIGLWJ64XW2S5/action/storage_attestation","attest_author":"https://pith.science/pith/VFGNP2JQLAMAEVIGLWJ64XW2S5/action/author_attestation","sign_citation":"https://pith.science/pith/VFGNP2JQLAMAEVIGLWJ64XW2S5/action/citation_signature","submit_replication":"https://pith.science/pith/VFGNP2JQLAMAEVIGLWJ64XW2S5/action/replication_record"}},"created_at":"2026-07-05T11:18:24.816690+00:00","updated_at":"2026-07-05T11:18:24.816690+00:00"}