{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7ZHKEWYCJC55HDXN745HR7BIZQ","short_pith_number":"pith:7ZHKEWYC","schema_version":"1.0","canonical_sha256":"fe4ea25b0248bbd38eedff3a78fc28cc10154f190f9b7e5ee9a72d574c1ad419","source":{"kind":"arxiv","id":"1302.6400","version":1},"attestation_state":"computed","paper":{"title":"On the period function of Newtonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.CA","authors_text":"A. Raouf Chouikha, Mohsen Timoumi","submitted_at":"2013-02-26T11:29:06Z","abstract_excerpt":"We study the existence of centers of planar autonomous system of the form\n  $$(S) \\quad \\dot x=y,\\qquad \\dot y = -h(x) - g(x)y - f(x)y^2.$$\n  We are interested in the period function $T$ around a center 0. A sufficient condition for the isochronicity of (S) at 0 is given. Such a condition is also necessary when $f,g,h$ are analytic functions. In that case a characterization of isochronous centers of system (S) is given. Some applications will be derived. In particular, new families of isochronous centers will be described"},"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":"1302.6400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-02-26T11:29:06Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"1bc0789ca7fcc93117cd8a2c0e88e279efee94786f7b2e8201f408ec1543749b","abstract_canon_sha256":"4c29dc2d3a584eba03d6d518d67dc28e5411b6a25552d9e00e1aaae3df090c9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:29.355168Z","signature_b64":"3xvKWdU1mIwiK4/XQR8N03ZuzSc0J72O/0+WLH5UZbZV1bCc8fjIipBruaufnvx0zGNS4SH3fCaxzD88pNafDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe4ea25b0248bbd38eedff3a78fc28cc10154f190f9b7e5ee9a72d574c1ad419","last_reissued_at":"2026-05-18T03:32:29.354647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:29.354647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the period function of Newtonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.CA","authors_text":"A. Raouf Chouikha, Mohsen Timoumi","submitted_at":"2013-02-26T11:29:06Z","abstract_excerpt":"We study the existence of centers of planar autonomous system of the form\n  $$(S) \\quad \\dot x=y,\\qquad \\dot y = -h(x) - g(x)y - f(x)y^2.$$\n  We are interested in the period function $T$ around a center 0. A sufficient condition for the isochronicity of (S) at 0 is given. Such a condition is also necessary when $f,g,h$ are analytic functions. In that case a characterization of isochronous centers of system (S) is given. Some applications will be derived. In particular, new families of isochronous centers will be described"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6400","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":""},"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":"1302.6400","created_at":"2026-05-18T03:32:29.354724+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.6400v1","created_at":"2026-05-18T03:32:29.354724+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6400","created_at":"2026-05-18T03:32:29.354724+00:00"},{"alias_kind":"pith_short_12","alias_value":"7ZHKEWYCJC55","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"7ZHKEWYCJC55HDXN","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"7ZHKEWYC","created_at":"2026-05-18T12:27:38.830355+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/7ZHKEWYCJC55HDXN745HR7BIZQ","json":"https://pith.science/pith/7ZHKEWYCJC55HDXN745HR7BIZQ.json","graph_json":"https://pith.science/api/pith-number/7ZHKEWYCJC55HDXN745HR7BIZQ/graph.json","events_json":"https://pith.science/api/pith-number/7ZHKEWYCJC55HDXN745HR7BIZQ/events.json","paper":"https://pith.science/paper/7ZHKEWYC"},"agent_actions":{"view_html":"https://pith.science/pith/7ZHKEWYCJC55HDXN745HR7BIZQ","download_json":"https://pith.science/pith/7ZHKEWYCJC55HDXN745HR7BIZQ.json","view_paper":"https://pith.science/paper/7ZHKEWYC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.6400&json=true","fetch_graph":"https://pith.science/api/pith-number/7ZHKEWYCJC55HDXN745HR7BIZQ/graph.json","fetch_events":"https://pith.science/api/pith-number/7ZHKEWYCJC55HDXN745HR7BIZQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7ZHKEWYCJC55HDXN745HR7BIZQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7ZHKEWYCJC55HDXN745HR7BIZQ/action/storage_attestation","attest_author":"https://pith.science/pith/7ZHKEWYCJC55HDXN745HR7BIZQ/action/author_attestation","sign_citation":"https://pith.science/pith/7ZHKEWYCJC55HDXN745HR7BIZQ/action/citation_signature","submit_replication":"https://pith.science/pith/7ZHKEWYCJC55HDXN745HR7BIZQ/action/replication_record"}},"created_at":"2026-05-18T03:32:29.354724+00:00","updated_at":"2026-05-18T03:32:29.354724+00:00"}