{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:EVBTTLBO3XB36RVLRNJU2WEKCC","short_pith_number":"pith:EVBTTLBO","canonical_record":{"source":{"id":"2208.02084","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2022-08-03T14:09:06Z","cross_cats_sorted":[],"title_canon_sha256":"e9e0430ba3f20c1fe781aeb14ca078b8cfa8d20b35f22ed2e244c631cd3883db","abstract_canon_sha256":"0d862578b0094885b721c34df2259549801e66ccb87f044f52f56962d47c0bdd"},"schema_version":"1.0"},"canonical_sha256":"254339ac2eddc3bf46ab8b534d588a108cf0d6aa8eb6cc59b57f5cf40bfe4262","source":{"kind":"arxiv","id":"2208.02084","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.02084","created_at":"2026-07-05T04:58:38Z"},{"alias_kind":"arxiv_version","alias_value":"2208.02084v2","created_at":"2026-07-05T04:58:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.02084","created_at":"2026-07-05T04:58:38Z"},{"alias_kind":"pith_short_12","alias_value":"EVBTTLBO3XB3","created_at":"2026-07-05T04:58:38Z"},{"alias_kind":"pith_short_16","alias_value":"EVBTTLBO3XB36RVL","created_at":"2026-07-05T04:58:38Z"},{"alias_kind":"pith_short_8","alias_value":"EVBTTLBO","created_at":"2026-07-05T04:58:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:EVBTTLBO3XB36RVLRNJU2WEKCC","target":"record","payload":{"canonical_record":{"source":{"id":"2208.02084","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2022-08-03T14:09:06Z","cross_cats_sorted":[],"title_canon_sha256":"e9e0430ba3f20c1fe781aeb14ca078b8cfa8d20b35f22ed2e244c631cd3883db","abstract_canon_sha256":"0d862578b0094885b721c34df2259549801e66ccb87f044f52f56962d47c0bdd"},"schema_version":"1.0"},"canonical_sha256":"254339ac2eddc3bf46ab8b534d588a108cf0d6aa8eb6cc59b57f5cf40bfe4262","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:58:38.305897Z","signature_b64":"wtX+nQHeCpZ0yXv0ARzSRH2U+awb7fyIrqx9Sh9RudYT3Cs7hNQ2jAOkzRq8uo7uHXC85beqhfONjsNFFEGFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"254339ac2eddc3bf46ab8b534d588a108cf0d6aa8eb6cc59b57f5cf40bfe4262","last_reissued_at":"2026-07-05T04:58:38.305359Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:58:38.305359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.02084","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:58:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uOxUMDsng4NHmoxwSfxhf5LGXjujqePCPmxYmd2ngmekjePmysKm+E3tX8NU7AItp8E6inm/wyZ7HRUysLxoCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:57:15.119992Z"},"content_sha256":"6265ba6812a59ac2b7446582f739fd393111c5b16ce4c3fc58cfa75d46eaf08f","schema_version":"1.0","event_id":"sha256:6265ba6812a59ac2b7446582f739fd393111c5b16ce4c3fc58cfa75d46eaf08f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:EVBTTLBO3XB36RVLRNJU2WEKCC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shape of higher-order images of equatorial emission rings around a Schwarzschild black hole: Analytical description with polar curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Oleg Yu. Tsupko","submitted_at":"2022-08-03T14:09:06Z","abstract_excerpt":"Higher-order photon rings can be expected to be detected in a more detailed image of the black hole found in future observations. These rings are lensed images of the luminous matter surrounding the black hole and are formed by photons that loop around it. In this paper we have succeeded to derive an analytical expression for the shape of the higher-order rings in the form that is most convenient for application: the explicit equation of the curve in polar coordinates. The formula describes the apparent shape of the higher-order image of the circular ring with the given radius around Schwarzsc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.02084","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.02084/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:58:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eiuxfphF1KTmHPyofEprb/z8mxeLiZsnlLzfVvLivz0ib3i6sxzBIJYc1WmkJVuiheARNWf2NaQTboOyCk+GAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:57:15.120491Z"},"content_sha256":"f8003691e15380fe19e878914731d403885428cffb49223231c21f107639e50a","schema_version":"1.0","event_id":"sha256:f8003691e15380fe19e878914731d403885428cffb49223231c21f107639e50a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EVBTTLBO3XB36RVLRNJU2WEKCC/bundle.json","state_url":"https://pith.science/pith/EVBTTLBO3XB36RVLRNJU2WEKCC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EVBTTLBO3XB36RVLRNJU2WEKCC/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":"2026-08-16T22:57:15Z","links":{"resolver":"https://pith.science/pith/EVBTTLBO3XB36RVLRNJU2WEKCC","bundle":"https://pith.science/pith/EVBTTLBO3XB36RVLRNJU2WEKCC/bundle.json","state":"https://pith.science/pith/EVBTTLBO3XB36RVLRNJU2WEKCC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EVBTTLBO3XB36RVLRNJU2WEKCC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:EVBTTLBO3XB36RVLRNJU2WEKCC","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":"0d862578b0094885b721c34df2259549801e66ccb87f044f52f56962d47c0bdd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2022-08-03T14:09:06Z","title_canon_sha256":"e9e0430ba3f20c1fe781aeb14ca078b8cfa8d20b35f22ed2e244c631cd3883db"},"schema_version":"1.0","source":{"id":"2208.02084","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.02084","created_at":"2026-07-05T04:58:38Z"},{"alias_kind":"arxiv_version","alias_value":"2208.02084v2","created_at":"2026-07-05T04:58:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.02084","created_at":"2026-07-05T04:58:38Z"},{"alias_kind":"pith_short_12","alias_value":"EVBTTLBO3XB3","created_at":"2026-07-05T04:58:38Z"},{"alias_kind":"pith_short_16","alias_value":"EVBTTLBO3XB36RVL","created_at":"2026-07-05T04:58:38Z"},{"alias_kind":"pith_short_8","alias_value":"EVBTTLBO","created_at":"2026-07-05T04:58:38Z"}],"graph_snapshots":[{"event_id":"sha256:f8003691e15380fe19e878914731d403885428cffb49223231c21f107639e50a","target":"graph","created_at":"2026-07-05T04:58:38Z","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/2208.02084/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Higher-order photon rings can be expected to be detected in a more detailed image of the black hole found in future observations. These rings are lensed images of the luminous matter surrounding the black hole and are formed by photons that loop around it. In this paper we have succeeded to derive an analytical expression for the shape of the higher-order rings in the form that is most convenient for application: the explicit equation of the curve in polar coordinates. The formula describes the apparent shape of the higher-order image of the circular ring with the given radius around Schwarzsc","authors_text":"Oleg Yu. Tsupko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2022-08-03T14:09:06Z","title":"Shape of higher-order images of equatorial emission rings around a Schwarzschild black hole: Analytical description with polar curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.02084","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":"sha256:6265ba6812a59ac2b7446582f739fd393111c5b16ce4c3fc58cfa75d46eaf08f","target":"record","created_at":"2026-07-05T04:58:38Z","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":"0d862578b0094885b721c34df2259549801e66ccb87f044f52f56962d47c0bdd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2022-08-03T14:09:06Z","title_canon_sha256":"e9e0430ba3f20c1fe781aeb14ca078b8cfa8d20b35f22ed2e244c631cd3883db"},"schema_version":"1.0","source":{"id":"2208.02084","kind":"arxiv","version":2}},"canonical_sha256":"254339ac2eddc3bf46ab8b534d588a108cf0d6aa8eb6cc59b57f5cf40bfe4262","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"254339ac2eddc3bf46ab8b534d588a108cf0d6aa8eb6cc59b57f5cf40bfe4262","first_computed_at":"2026-07-05T04:58:38.305359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:58:38.305359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wtX+nQHeCpZ0yXv0ARzSRH2U+awb7fyIrqx9Sh9RudYT3Cs7hNQ2jAOkzRq8uo7uHXC85beqhfONjsNFFEGFAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:58:38.305897Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.02084","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6265ba6812a59ac2b7446582f739fd393111c5b16ce4c3fc58cfa75d46eaf08f","sha256:f8003691e15380fe19e878914731d403885428cffb49223231c21f107639e50a"],"state_sha256":"88dc694eaaa78f921c2c4d8385bee74ca2fbd84e760caefd9363264b21f03a27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RE6TtERYjzFtaux6fKXAzgHCTme1BZJkuT3O2B57Y5OEoBRWHSxOd1cDUbzXRJdYpUJPZ+dQyXPS2SIpnLrJDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T22:57:15.124636Z","bundle_sha256":"73b72b1283a605dcd5749dfebe8372ef85fbb253aaf58de58d5619104f953fc1"}}