{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:YIYTMHZXAKRTWFUKYFS7M5UEF2","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":"ea3c019f2d253d4238c0a95c3a59511c83a9deb8fb8186e7e95cd509a3568108","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-06-03T09:08:04Z","title_canon_sha256":"4fd4e2f9821988a93008d660d8d6dc82991e9cca70a6044c2af818f7eb97c1e2"},"schema_version":"1.0","source":{"id":"2006.02112","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.02112","created_at":"2026-07-05T01:35:33Z"},{"alias_kind":"arxiv_version","alias_value":"2006.02112v2","created_at":"2026-07-05T01:35:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.02112","created_at":"2026-07-05T01:35:33Z"},{"alias_kind":"pith_short_12","alias_value":"YIYTMHZXAKRT","created_at":"2026-07-05T01:35:33Z"},{"alias_kind":"pith_short_16","alias_value":"YIYTMHZXAKRTWFUK","created_at":"2026-07-05T01:35:33Z"},{"alias_kind":"pith_short_8","alias_value":"YIYTMHZX","created_at":"2026-07-05T01:35:33Z"}],"graph_snapshots":[{"event_id":"sha256:1d9663439399ff357cd858a2b90e417dd9a56af13e0847633e4d19ee4c0943f5","target":"graph","created_at":"2026-07-05T01:35:33Z","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/2006.02112/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Black hole photon spheres or light rings are closely linked to astronomical phenomena, such as the gravitational waves and the shadow in spherically symmetric or axi-symmetric spacetime. In Cunha and Herdeiro [Phys. Rev. Lett. 124, 181101 (2020)], a topological argument was applied for the four dimensional stationary, axi-symmetric, asymptotically flat black hole, and the result indicates that at least, there exists one standard light ring outside the black hole horizon for each rotation sense. Inspired by it, in this paper, we would like to consider a similar issue for a nonrotating, static, ","authors_text":"Shao-Wen Wei","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-06-03T09:08:04Z","title":"Topological Charge and Black Hole Photon Spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.02112","kind":"arxiv","version":2},"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:ef969eab6d106a22e27d76bdab2bfcca1eb41fb30965113da7e9e0254d37d0a2","target":"record","created_at":"2026-07-05T01:35:33Z","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":"ea3c019f2d253d4238c0a95c3a59511c83a9deb8fb8186e7e95cd509a3568108","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-06-03T09:08:04Z","title_canon_sha256":"4fd4e2f9821988a93008d660d8d6dc82991e9cca70a6044c2af818f7eb97c1e2"},"schema_version":"1.0","source":{"id":"2006.02112","kind":"arxiv","version":2}},"canonical_sha256":"c231361f3702a33b168ac165f676842e95aa6d58decd37e6fdc1550771d56c74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c231361f3702a33b168ac165f676842e95aa6d58decd37e6fdc1550771d56c74","first_computed_at":"2026-07-05T01:35:33.325258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:35:33.325258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L5UuYNQXvzT/hybJ0lku4wQ8qenJmvlB4yKbrbch/7KeaLjd3awViIj0IeqXVNtWeIE0GzfEm/qkaPRk/8L0Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:35:33.325921Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.02112","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef969eab6d106a22e27d76bdab2bfcca1eb41fb30965113da7e9e0254d37d0a2","sha256:1d9663439399ff357cd858a2b90e417dd9a56af13e0847633e4d19ee4c0943f5"],"state_sha256":"615e81a3a301fb922a6c35a1f8742a8b55e167bb29e06a5ff4358a56167f6f99"}