{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:L7H2GJU7KDQL47M2M74IWRJJBY","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":"899fdbac69387b26601d06f2638675aca52cc503ac0e227b7717ad938baa12a3","cross_cats_sorted":["astro-ph.IM","nlin.CD","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-06-23T12:48:41Z","title_canon_sha256":"a68b10291e6aacb1f3729e873d03a9ef1100b008733e59cf3a073bcc4889a838"},"schema_version":"1.0","source":{"id":"2106.12356","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.12356","created_at":"2026-07-05T02:51:45Z"},{"alias_kind":"arxiv_version","alias_value":"2106.12356v1","created_at":"2026-07-05T02:51:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.12356","created_at":"2026-07-05T02:51:45Z"},{"alias_kind":"pith_short_12","alias_value":"L7H2GJU7KDQL","created_at":"2026-07-05T02:51:45Z"},{"alias_kind":"pith_short_16","alias_value":"L7H2GJU7KDQL47M2","created_at":"2026-07-05T02:51:45Z"},{"alias_kind":"pith_short_8","alias_value":"L7H2GJU7","created_at":"2026-07-05T02:51:45Z"}],"graph_snapshots":[{"event_id":"sha256:337c8b4dde0477dad0b1540c55e27caec9fcdb57853250e4116942fef990fde8","target":"graph","created_at":"2026-07-05T02:51:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2106.12356/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In previous papers, explicit symplectic integrators were designed for nonrotating black holes, such as a Schwarzschild black hole. However, they fail to work in the Kerr spacetime because not all variables can be separable, or not all splitting parts have analytical solutions as explicit functions of proper time. To cope with this difficulty, we introduce a time transformation function to the Hamiltonian of Kerr geometry so as to obtain a time-transformed Hamiltonian consisting of five splitting parts, whose analytical solutions are explicit functions of the new coordinate time. The chosen tim","authors_text":"Fuyao Liu, Wei Sun, Xin Wu, Ying Wang","cross_cats":["astro-ph.IM","nlin.CD","physics.comp-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-06-23T12:48:41Z","title":"Construction of explicit symplectic integrators in general relativity. IV. Kerr black holes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.12356","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":"sha256:99f757c5b20a3f434a997422b7e309be2720b0d8c70cd95d8ec24dd2b49c3f23","target":"record","created_at":"2026-07-05T02:51:45Z","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":"899fdbac69387b26601d06f2638675aca52cc503ac0e227b7717ad938baa12a3","cross_cats_sorted":["astro-ph.IM","nlin.CD","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-06-23T12:48:41Z","title_canon_sha256":"a68b10291e6aacb1f3729e873d03a9ef1100b008733e59cf3a073bcc4889a838"},"schema_version":"1.0","source":{"id":"2106.12356","kind":"arxiv","version":1}},"canonical_sha256":"5fcfa3269f50e0be7d9a67f88b45290e0f451e1b651541af6f7d922d0015769c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fcfa3269f50e0be7d9a67f88b45290e0f451e1b651541af6f7d922d0015769c","first_computed_at":"2026-07-05T02:51:45.188015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:51:45.188015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5oRCElxK2MClF6SSwStOMq0jJoIt1JiuANWHKfO4bT3z6bL3iahvursLaJz0powOkJqCIvsyKtCB5feqjYN/Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:51:45.188513Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.12356","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99f757c5b20a3f434a997422b7e309be2720b0d8c70cd95d8ec24dd2b49c3f23","sha256:337c8b4dde0477dad0b1540c55e27caec9fcdb57853250e4116942fef990fde8"],"state_sha256":"956ec1a22dc8b07b90cdb7ccba49509e3e4a455d9510ab4556cccfd29aca4404"}