{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:7OJNIDO44BMZSC4YLBLEIRZMMA","short_pith_number":"pith:7OJNIDO4","schema_version":"1.0","canonical_sha256":"fb92d40ddce059990b98585644472c6024eb7b7f56f98226e25d59e35d6270e7","source":{"kind":"arxiv","id":"0908.0031","version":2},"attestation_state":"computed","paper":{"title":"Brake subharmonic solutions of first order Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chong Li, Chungen Liu","submitted_at":"2009-08-01T00:17:02Z","abstract_excerpt":"In this paper, we mainly use the Galerkin approximation method and the iteration inequalities of the $L$-Maslov type index theory to study the properties of brake subharmonic solutions for the first order non-autonomous Hamiltonian systems. We prove that when the positive integers $j$ and $k$ satisfies the certain conditions, there exists a $jT$-periodic nonconstant brake solution $z_{j}$ such that $z_{j}$ and $z_{kj}$ are distinct."},"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":"0908.0031","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-08-01T00:17:02Z","cross_cats_sorted":[],"title_canon_sha256":"f2b5e968630b4e8c37bf0ceb882039702579973c844d7f973dad9084f35fe672","abstract_canon_sha256":"fb49fbeb05cd6caefceb264678828eba60a84aa67e79d08152f1a6f4ab9933a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:12:45.537734Z","signature_b64":"esRNLz453PxYJC1Omg4sCG167BFnO07Gcn5E/CwebrJesiapsumMwdfX/Rm2l/YZkf7AclYC0cW4IrssRQr7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb92d40ddce059990b98585644472c6024eb7b7f56f98226e25d59e35d6270e7","last_reissued_at":"2026-05-18T02:12:45.537108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:12:45.537108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Brake subharmonic solutions of first order Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chong Li, Chungen Liu","submitted_at":"2009-08-01T00:17:02Z","abstract_excerpt":"In this paper, we mainly use the Galerkin approximation method and the iteration inequalities of the $L$-Maslov type index theory to study the properties of brake subharmonic solutions for the first order non-autonomous Hamiltonian systems. We prove that when the positive integers $j$ and $k$ satisfies the certain conditions, there exists a $jT$-periodic nonconstant brake solution $z_{j}$ such that $z_{j}$ and $z_{kj}$ are distinct."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.0031","kind":"arxiv","version":2},"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":"0908.0031","created_at":"2026-05-18T02:12:45.537181+00:00"},{"alias_kind":"arxiv_version","alias_value":"0908.0031v2","created_at":"2026-05-18T02:12:45.537181+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.0031","created_at":"2026-05-18T02:12:45.537181+00:00"},{"alias_kind":"pith_short_12","alias_value":"7OJNIDO44BMZ","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"7OJNIDO44BMZSC4Y","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"7OJNIDO4","created_at":"2026-05-18T12:25:58.837520+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/7OJNIDO44BMZSC4YLBLEIRZMMA","json":"https://pith.science/pith/7OJNIDO44BMZSC4YLBLEIRZMMA.json","graph_json":"https://pith.science/api/pith-number/7OJNIDO44BMZSC4YLBLEIRZMMA/graph.json","events_json":"https://pith.science/api/pith-number/7OJNIDO44BMZSC4YLBLEIRZMMA/events.json","paper":"https://pith.science/paper/7OJNIDO4"},"agent_actions":{"view_html":"https://pith.science/pith/7OJNIDO44BMZSC4YLBLEIRZMMA","download_json":"https://pith.science/pith/7OJNIDO44BMZSC4YLBLEIRZMMA.json","view_paper":"https://pith.science/paper/7OJNIDO4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0908.0031&json=true","fetch_graph":"https://pith.science/api/pith-number/7OJNIDO44BMZSC4YLBLEIRZMMA/graph.json","fetch_events":"https://pith.science/api/pith-number/7OJNIDO44BMZSC4YLBLEIRZMMA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7OJNIDO44BMZSC4YLBLEIRZMMA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7OJNIDO44BMZSC4YLBLEIRZMMA/action/storage_attestation","attest_author":"https://pith.science/pith/7OJNIDO44BMZSC4YLBLEIRZMMA/action/author_attestation","sign_citation":"https://pith.science/pith/7OJNIDO44BMZSC4YLBLEIRZMMA/action/citation_signature","submit_replication":"https://pith.science/pith/7OJNIDO44BMZSC4YLBLEIRZMMA/action/replication_record"}},"created_at":"2026-05-18T02:12:45.537181+00:00","updated_at":"2026-05-18T02:12:45.537181+00:00"}