{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BLXLOMVIITGA4QHS3TEMGNQYCQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c3a475c68b9c3478e5d5d66d0dde68dc50ce6dc8fbdcae1b1738c17d71a1aa15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-14T13:42:19Z","title_canon_sha256":"a0a0e5791cb1362b91a0f71e0e1562840260fa13179d25c4ed77cdf54cbc1197"},"schema_version":"1.0","source":{"id":"1606.04357","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04357","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04357v1","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04357","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"pith_short_12","alias_value":"BLXLOMVIITGA","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BLXLOMVIITGA4QHS","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BLXLOMVI","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:1151a9fa69c4915ec99222b08ae56d80972128f22e56016b6435b528ff4e1de3","target":"graph","created_at":"2026-05-18T01:12:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper some existence results for the minimal P-symmetric periodic solutions are proved for first order autonomous Hamiltonian systems when the Hamiltonian function is superquadratic, asymptotically linear and subquadratic. These are done by using critical points theory, Galerkin approximation procedure, Maslov $P$-index theory and its iteration inequalities.","authors_text":"Shanshan Tang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-14T13:42:19Z","title":"Minimal $P$-symmetric periodic solutions of nonlinear Hamiltonian systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04357","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:aa086942c56297e8dc1b0b0325f0ce1af00c8050f7a4e2984d6693b8be20602a","target":"record","created_at":"2026-05-18T01:12:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c3a475c68b9c3478e5d5d66d0dde68dc50ce6dc8fbdcae1b1738c17d71a1aa15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-14T13:42:19Z","title_canon_sha256":"a0a0e5791cb1362b91a0f71e0e1562840260fa13179d25c4ed77cdf54cbc1197"},"schema_version":"1.0","source":{"id":"1606.04357","kind":"arxiv","version":1}},"canonical_sha256":"0aeeb732a844cc0e40f2dcc8c33618141b5e2d1be656c381429963a5a56cf5b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0aeeb732a844cc0e40f2dcc8c33618141b5e2d1be656c381429963a5a56cf5b8","first_computed_at":"2026-05-18T01:12:25.713396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:25.713396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+Uw9tPjWqzVriu4NhvExdyT8jNz6xP5KyY31WOlgo3+MttKfxJ/+79HS5DsftwIUpQ4QkUa7kDV+YZ2G6hfeCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:25.713776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.04357","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa086942c56297e8dc1b0b0325f0ce1af00c8050f7a4e2984d6693b8be20602a","sha256:1151a9fa69c4915ec99222b08ae56d80972128f22e56016b6435b528ff4e1de3"],"state_sha256":"ec632562b046be81665f3b176009aa97d07d15b23778b5240312b05ba5bbc59b"}