{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DLPF5X6ZHMY6MG4VDWPI7YVUUQ","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":"52123e7df7ef5f825dbdd8a9a0d2ea9a7a36be784e70867fc0c56e71d0ef4226","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2015-07-28T12:54:57Z","title_canon_sha256":"f0dfbc4b39efb67063bb0fb6a3b6c2166ecb43d7bcb3b8b145dbd1cfe81ed711"},"schema_version":"1.0","source":{"id":"1507.07746","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07746","created_at":"2026-05-18T01:36:11Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07746v1","created_at":"2026-05-18T01:36:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07746","created_at":"2026-05-18T01:36:11Z"},{"alias_kind":"pith_short_12","alias_value":"DLPF5X6ZHMY6","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DLPF5X6ZHMY6MG4V","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DLPF5X6Z","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:5e9367efc067913b4756f694169d57b7ee1517194d2e7459d4fda77409e74884","target":"graph","created_at":"2026-05-18T01:36:11Z","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 work, we investigate the bifurcations of relative equilibria in the gravitational potential of asteroids. A theorem concerning a conserved quantity, which is about the eigenvalues and number of relative equilibria, is presented and proved. The conserved quantity can restrict the number of non-degenerate equilibria in the gravitational potential of an asteroid. It is concluded that the number of non-degenerate equilibria in the gravitational field of an asteroid varies in pairs and is an odd number. In addition, the conserved quantity can also restrict the kinds of bifurcations of relat","authors_text":"Hengnian Li, Hexi Baoyin, Yu Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2015-07-28T12:54:57Z","title":"Collision and Annihilation of Relative Equilibrium Points Around Asteroids with a Changing Parameter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07746","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:a3e8c5c1baea92c2f7a902ead44648b6cde0269dc40a37028d39bf2a1f18ff66","target":"record","created_at":"2026-05-18T01:36:11Z","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":"52123e7df7ef5f825dbdd8a9a0d2ea9a7a36be784e70867fc0c56e71d0ef4226","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2015-07-28T12:54:57Z","title_canon_sha256":"f0dfbc4b39efb67063bb0fb6a3b6c2166ecb43d7bcb3b8b145dbd1cfe81ed711"},"schema_version":"1.0","source":{"id":"1507.07746","kind":"arxiv","version":1}},"canonical_sha256":"1ade5edfd93b31e61b951d9e8fe2b4a41d3aa11b7f1ddd3724387b7e58ea395c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ade5edfd93b31e61b951d9e8fe2b4a41d3aa11b7f1ddd3724387b7e58ea395c","first_computed_at":"2026-05-18T01:36:11.987788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:11.987788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wAsnBXwxkbYgs/xislJ+Eml+XMZyPYlW9wkDPstwEkQoqMUe2zOp40hF+gCPLesSZwv99SeskJ58ofel3edzDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:11.988441Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.07746","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3e8c5c1baea92c2f7a902ead44648b6cde0269dc40a37028d39bf2a1f18ff66","sha256:5e9367efc067913b4756f694169d57b7ee1517194d2e7459d4fda77409e74884"],"state_sha256":"6ec23248285b51f9354b6cfebcadf51344d830a461eb4ef5043e7d61411af22d"}