{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:O5DY6BXST53ESOYLUG5F4VEJ35","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":"f3363636f8c4dda85fc09b4060fe0fe3150d1cfac9c1a36e00d24a87047cc8e2","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2012-07-13T02:14:13Z","title_canon_sha256":"4e445587aebb3034822306fe415d429e4c0c28c48dfa81ece6cfa8aab9fe07f4"},"schema_version":"1.0","source":{"id":"1207.3130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3130","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3130v1","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3130","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"pith_short_12","alias_value":"O5DY6BXST53E","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"O5DY6BXST53ESOYL","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"O5DY6BXS","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:119bc581b04fefff92e9ad4a81cc0567c0ddc2c58c9a52ce65b8b4e0c5d8c3ad","target":"graph","created_at":"2026-05-18T03:51:12Z","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":"Using variational minimizing methods,we prove the existence of an odd symmetric parabolic orbit for the 2-fixed center problems with weak force type homogeneous potentials.","authors_text":"Shiqing Zhang, Ying Lv","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2012-07-13T02:14:13Z","title":"Variational Minimizing Parabolic Orbits for the 2-Fixed Center Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3130","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":"sha256:18407b36a080029928049480851558777866d306c70653ec9e8d8778389eebf9","target":"record","created_at":"2026-05-18T03:51:12Z","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":"f3363636f8c4dda85fc09b4060fe0fe3150d1cfac9c1a36e00d24a87047cc8e2","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2012-07-13T02:14:13Z","title_canon_sha256":"4e445587aebb3034822306fe415d429e4c0c28c48dfa81ece6cfa8aab9fe07f4"},"schema_version":"1.0","source":{"id":"1207.3130","kind":"arxiv","version":1}},"canonical_sha256":"77478f06f29f76493b0ba1ba5e5489df6f4a98e80a4f8509b2fa797f4c95f051","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77478f06f29f76493b0ba1ba5e5489df6f4a98e80a4f8509b2fa797f4c95f051","first_computed_at":"2026-05-18T03:51:12.390579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:12.390579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OJ6lXwtZv0+jgiorurC6jjEpdAM4yzyDam6uVwmJFF2B8Mg0cDDc5FWbPlc3MDCKFema9SnvR2TsWrFr+VP1AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:12.391174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18407b36a080029928049480851558777866d306c70653ec9e8d8778389eebf9","sha256:119bc581b04fefff92e9ad4a81cc0567c0ddc2c58c9a52ce65b8b4e0c5d8c3ad"],"state_sha256":"ccc02dfdadd64eacbc54acb7412895de24a1008f1ea6df07427d1e3669032dd2"}