{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6WQYRHJVVSPRYGHJQBXD7ODBY6","short_pith_number":"pith:6WQYRHJV","canonical_record":{"source":{"id":"1510.08024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-10-27T18:39:53Z","cross_cats_sorted":["math-ph","math.AP","math.DG","math.MP"],"title_canon_sha256":"868b7bf80b0eae051dfe3b056017d3f181f8f1dafaeedc0facab0550eb227ae2","abstract_canon_sha256":"74532da1a71da6b1fda5c77e69de605f8710db73ca00285d6c86129346492787"},"schema_version":"1.0"},"canonical_sha256":"f5a1889d35ac9f1c18e9806e3fb861c7b642eeb7a4ae26a4c196bf2ac0bbc323","source":{"kind":"arxiv","id":"1510.08024","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08024","created_at":"2026-05-18T01:28:44Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08024v1","created_at":"2026-05-18T01:28:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08024","created_at":"2026-05-18T01:28:44Z"},{"alias_kind":"pith_short_12","alias_value":"6WQYRHJVVSPR","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6WQYRHJVVSPRYGHJ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6WQYRHJV","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6WQYRHJVVSPRYGHJQBXD7ODBY6","target":"record","payload":{"canonical_record":{"source":{"id":"1510.08024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-10-27T18:39:53Z","cross_cats_sorted":["math-ph","math.AP","math.DG","math.MP"],"title_canon_sha256":"868b7bf80b0eae051dfe3b056017d3f181f8f1dafaeedc0facab0550eb227ae2","abstract_canon_sha256":"74532da1a71da6b1fda5c77e69de605f8710db73ca00285d6c86129346492787"},"schema_version":"1.0"},"canonical_sha256":"f5a1889d35ac9f1c18e9806e3fb861c7b642eeb7a4ae26a4c196bf2ac0bbc323","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:44.805305Z","signature_b64":"bBXFAI2u+eNXfioxlvl3mv0x+XgTgPVDw7886eF6+/D83n/O0Ti4Nwg56LvwF39QYl+dTlX+oDD8EXECAFxjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5a1889d35ac9f1c18e9806e3fb861c7b642eeb7a4ae26a4c196bf2ac0bbc323","last_reissued_at":"2026-05-18T01:28:44.804742Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:44.804742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.08024","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:28:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B99KfhtaJhqzOAKznKK41qH81OkIRZO1WVSFFW+V+jN0qgnifuTBJ6AdohI6toqpzzGWlKKGY02/ZcWvqJVwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:02:42.379195Z"},"content_sha256":"1914ae512120be17ed0462c14cf591e871c168da3a13e7bb00ca2e6b255d2d0b","schema_version":"1.0","event_id":"sha256:1914ae512120be17ed0462c14cf591e871c168da3a13e7bb00ca2e6b255d2d0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6WQYRHJVVSPRYGHJQBXD7ODBY6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stationary axisymmetric black holes with matter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.DG","math.MP"],"primary_cat":"gr-qc","authors_text":"Otis Chodosh, Yakov Shlapentokh-Rothman","submitted_at":"2015-10-27T18:39:53Z","abstract_excerpt":"We provide a geometric framework for the construction of non-vacuum black holes whose metrics are stationary and axisymmetric. Under suitable assumptions we show that the Einstein equations reduce to an Einstein-harmonic map type system and analyze the compatibility of the resulting equations.\n  This framework will be fundamental to our forthcoming construction of metric-stationary axisymmetric bifurcations of Kerr solving the Einstein--Klein--Gordon system, and as such, we include specializations of all of our formulas to the case of a time-periodic massive scalar field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08024","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:28:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nPgXckLRvybuu5glCMJ9wlFVvAPNK0XdYjSnLuOJFI21RpcTDLCd3E20epdaIVFiDi8V6pZHO5KVT/zTrj9pBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:02:42.379562Z"},"content_sha256":"eae73cb078b4de1f06df6a93ea690f7986f3eafd30ca2e785be8dccd62b15a53","schema_version":"1.0","event_id":"sha256:eae73cb078b4de1f06df6a93ea690f7986f3eafd30ca2e785be8dccd62b15a53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6WQYRHJVVSPRYGHJQBXD7ODBY6/bundle.json","state_url":"https://pith.science/pith/6WQYRHJVVSPRYGHJQBXD7ODBY6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6WQYRHJVVSPRYGHJQBXD7ODBY6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T18:02:42Z","links":{"resolver":"https://pith.science/pith/6WQYRHJVVSPRYGHJQBXD7ODBY6","bundle":"https://pith.science/pith/6WQYRHJVVSPRYGHJQBXD7ODBY6/bundle.json","state":"https://pith.science/pith/6WQYRHJVVSPRYGHJQBXD7ODBY6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6WQYRHJVVSPRYGHJQBXD7ODBY6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6WQYRHJVVSPRYGHJQBXD7ODBY6","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":"74532da1a71da6b1fda5c77e69de605f8710db73ca00285d6c86129346492787","cross_cats_sorted":["math-ph","math.AP","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-10-27T18:39:53Z","title_canon_sha256":"868b7bf80b0eae051dfe3b056017d3f181f8f1dafaeedc0facab0550eb227ae2"},"schema_version":"1.0","source":{"id":"1510.08024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08024","created_at":"2026-05-18T01:28:44Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08024v1","created_at":"2026-05-18T01:28:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08024","created_at":"2026-05-18T01:28:44Z"},{"alias_kind":"pith_short_12","alias_value":"6WQYRHJVVSPR","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6WQYRHJVVSPRYGHJ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6WQYRHJV","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:eae73cb078b4de1f06df6a93ea690f7986f3eafd30ca2e785be8dccd62b15a53","target":"graph","created_at":"2026-05-18T01:28:44Z","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":"We provide a geometric framework for the construction of non-vacuum black holes whose metrics are stationary and axisymmetric. Under suitable assumptions we show that the Einstein equations reduce to an Einstein-harmonic map type system and analyze the compatibility of the resulting equations.\n  This framework will be fundamental to our forthcoming construction of metric-stationary axisymmetric bifurcations of Kerr solving the Einstein--Klein--Gordon system, and as such, we include specializations of all of our formulas to the case of a time-periodic massive scalar field.","authors_text":"Otis Chodosh, Yakov Shlapentokh-Rothman","cross_cats":["math-ph","math.AP","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-10-27T18:39:53Z","title":"Stationary axisymmetric black holes with matter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08024","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":"sha256:1914ae512120be17ed0462c14cf591e871c168da3a13e7bb00ca2e6b255d2d0b","target":"record","created_at":"2026-05-18T01:28:44Z","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":"74532da1a71da6b1fda5c77e69de605f8710db73ca00285d6c86129346492787","cross_cats_sorted":["math-ph","math.AP","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-10-27T18:39:53Z","title_canon_sha256":"868b7bf80b0eae051dfe3b056017d3f181f8f1dafaeedc0facab0550eb227ae2"},"schema_version":"1.0","source":{"id":"1510.08024","kind":"arxiv","version":1}},"canonical_sha256":"f5a1889d35ac9f1c18e9806e3fb861c7b642eeb7a4ae26a4c196bf2ac0bbc323","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5a1889d35ac9f1c18e9806e3fb861c7b642eeb7a4ae26a4c196bf2ac0bbc323","first_computed_at":"2026-05-18T01:28:44.804742Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:44.804742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bBXFAI2u+eNXfioxlvl3mv0x+XgTgPVDw7886eF6+/D83n/O0Ti4Nwg56LvwF39QYl+dTlX+oDD8EXECAFxjAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:44.805305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1914ae512120be17ed0462c14cf591e871c168da3a13e7bb00ca2e6b255d2d0b","sha256:eae73cb078b4de1f06df6a93ea690f7986f3eafd30ca2e785be8dccd62b15a53"],"state_sha256":"7d56dc1ea9b51c7279f54debcdad021f289bdf0e5e1408b727c3e014964b66c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DgtxniECNO5L5M8db6H+H3MLXRTeGPNuJua7+70FEhpQJsY6Q24nBO4beoIAk4UGSYpVlEUgTipcUWaWaxckCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:02:42.381527Z","bundle_sha256":"686fc7c63bf0830a7581b2837bf6d10ff9a7fee752bbfe75aa7d60be55ec59c0"}}