{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CKHURMJUBSCT3FWDYOBCZC3VOH","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":"796196ad16c534ac2b917530957af502472da2250fd3f8c62a641585dd8d2fd0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-11-10T09:41:37Z","title_canon_sha256":"88482296db6ceb15e511bb2fb67486b98880556b7ce3df92b555544cb18eb05f"},"schema_version":"1.0","source":{"id":"1111.2429","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2429","created_at":"2026-05-18T01:59:42Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2429v1","created_at":"2026-05-18T01:59:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2429","created_at":"2026-05-18T01:59:42Z"},{"alias_kind":"pith_short_12","alias_value":"CKHURMJUBSCT","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CKHURMJUBSCT3FWD","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CKHURMJU","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:d9926421049c3c17d6fe693529b7f6e9296cc380a349f37c6d446cdddafa217f","target":"graph","created_at":"2026-05-18T01:59:42Z","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":"Most galaxies host central supermassive black holes. As two galaxies merge, the black holes also merge. The final single black hole may suffer a kick due to asymmetric gravitational radiation and may not be at the centre of the galaxy; off-centre black holes may also be produced by other means such as sustained acceleration due to asymmetric jet power. We model the main galaxy as a singular isothermal sphere and the black hole as an off-centre point lens, and study the critical curves and caustics using complex notation. We identify the critical parameters that govern the transitions in the to","authors_text":"Hans Witt, Manchester), Shude Mao (NAOC","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-11-10T09:41:37Z","title":"Lensing by a singular isothermal sphere and a black hole"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2429","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":"sha256:280b41f6a62ddd3341e1903b7196b55ad13a8088e2a7f9082d2ec162810670d8","target":"record","created_at":"2026-05-18T01:59:42Z","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":"796196ad16c534ac2b917530957af502472da2250fd3f8c62a641585dd8d2fd0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-11-10T09:41:37Z","title_canon_sha256":"88482296db6ceb15e511bb2fb67486b98880556b7ce3df92b555544cb18eb05f"},"schema_version":"1.0","source":{"id":"1111.2429","kind":"arxiv","version":1}},"canonical_sha256":"128f48b1340c853d96c3c3822c8b7571e2b8462ef3f7c80d09c5f1a8829b33e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"128f48b1340c853d96c3c3822c8b7571e2b8462ef3f7c80d09c5f1a8829b33e0","first_computed_at":"2026-05-18T01:59:42.723663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:42.723663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QOb3G9j2LJI80qTlsqzWEYom6SHMgfsx9L9xkNeOUIJ4Z/BI+Sn8YAoECv0DRmW1dOcrrbOr3IkuCx9dJ41CCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:42.724382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2429","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:280b41f6a62ddd3341e1903b7196b55ad13a8088e2a7f9082d2ec162810670d8","sha256:d9926421049c3c17d6fe693529b7f6e9296cc380a349f37c6d446cdddafa217f"],"state_sha256":"a0c254a14885a8d6af16adb9651f7dd4c21e62a5bc8082baa36fd808569f57b5"}