{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LLWFY5NSQT67OY5G4M7RCII3NG","short_pith_number":"pith:LLWFY5NS","canonical_record":{"source":{"id":"1705.07061","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-05-19T15:46:28Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"75b5ce5b1bcdd06db5a794cd5a375e66f093b0127af702cd1383cca67320a202","abstract_canon_sha256":"26ee59d64ebc67e8866ff165159dbd72790b2bb7a4981f744ae90dcc1a438559"},"schema_version":"1.0"},"canonical_sha256":"5aec5c75b284fdf763a6e33f11211b6997c2474c2a5bc7698f8da4d364233a80","source":{"kind":"arxiv","id":"1705.07061","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07061","created_at":"2026-05-18T00:38:52Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07061v1","created_at":"2026-05-18T00:38:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07061","created_at":"2026-05-18T00:38:52Z"},{"alias_kind":"pith_short_12","alias_value":"LLWFY5NSQT67","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LLWFY5NSQT67OY5G","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LLWFY5NS","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LLWFY5NSQT67OY5G4M7RCII3NG","target":"record","payload":{"canonical_record":{"source":{"id":"1705.07061","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-05-19T15:46:28Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"75b5ce5b1bcdd06db5a794cd5a375e66f093b0127af702cd1383cca67320a202","abstract_canon_sha256":"26ee59d64ebc67e8866ff165159dbd72790b2bb7a4981f744ae90dcc1a438559"},"schema_version":"1.0"},"canonical_sha256":"5aec5c75b284fdf763a6e33f11211b6997c2474c2a5bc7698f8da4d364233a80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:52.310897Z","signature_b64":"QfUwNjOgLczkBdrpr4abO0pnuKZoC5nDXCJsUVS6OshWHyQ9Fjg+MjKR5vn4Fga58yFQO4tk7mybmhXyYh1RBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5aec5c75b284fdf763a6e33f11211b6997c2474c2a5bc7698f8da4d364233a80","last_reissued_at":"2026-05-18T00:38:52.310374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:52.310374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.07061","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":"2026-05-18T00:38:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QWRh+/B/s51ulSSKR5nKkdvkai1V7yqCrmEr9Ozk1WhvSWho7WYh9RxSb4Fhis1My7/36TI96+iQX3Bts8QfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T23:13:32.653097Z"},"content_sha256":"3a5272f07beb542c29dee9cbc9d69490d5a5cdf849319798a58a06c0a61a9475","schema_version":"1.0","event_id":"sha256:3a5272f07beb542c29dee9cbc9d69490d5a5cdf849319798a58a06c0a61a9475"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LLWFY5NSQT67OY5G4M7RCII3NG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Black Hole Shadows and Invariant Phase Space Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"gr-qc","authors_text":"Alexander Wittig, Jai Grover","submitted_at":"2017-05-19T15:46:28Z","abstract_excerpt":"Utilizing concepts from dynamical systems theory, we demonstrate how the existence of light rings, or fixed points, in a spacetime will give rise to families of periodic orbits and invariant manifolds in phase space. It is shown that these structures define the shape of the black hole shadow as well as a number of salient features of the spacetime lensing. We illustrate this through the analysis of lensing by a hairy black hole."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07061","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":"2026-05-18T00:38:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3VBr4Od8WCe/iAt5hUTBUskt7rPmE6KR0xeC39rV1aOdFL6OYshHM8g+yGB2M0NZJY1uqP/cSUHPY5eEpCmbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T23:13:32.653811Z"},"content_sha256":"f098e55bd53b4e0d9bf76603e126df1499578b7685faced02dd5fb07df7fc760","schema_version":"1.0","event_id":"sha256:f098e55bd53b4e0d9bf76603e126df1499578b7685faced02dd5fb07df7fc760"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LLWFY5NSQT67OY5G4M7RCII3NG/bundle.json","state_url":"https://pith.science/pith/LLWFY5NSQT67OY5G4M7RCII3NG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LLWFY5NSQT67OY5G4M7RCII3NG/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":"2026-05-18T23:13:32Z","links":{"resolver":"https://pith.science/pith/LLWFY5NSQT67OY5G4M7RCII3NG","bundle":"https://pith.science/pith/LLWFY5NSQT67OY5G4M7RCII3NG/bundle.json","state":"https://pith.science/pith/LLWFY5NSQT67OY5G4M7RCII3NG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LLWFY5NSQT67OY5G4M7RCII3NG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LLWFY5NSQT67OY5G4M7RCII3NG","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":"26ee59d64ebc67e8866ff165159dbd72790b2bb7a4981f744ae90dcc1a438559","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-05-19T15:46:28Z","title_canon_sha256":"75b5ce5b1bcdd06db5a794cd5a375e66f093b0127af702cd1383cca67320a202"},"schema_version":"1.0","source":{"id":"1705.07061","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07061","created_at":"2026-05-18T00:38:52Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07061v1","created_at":"2026-05-18T00:38:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07061","created_at":"2026-05-18T00:38:52Z"},{"alias_kind":"pith_short_12","alias_value":"LLWFY5NSQT67","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LLWFY5NSQT67OY5G","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LLWFY5NS","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:f098e55bd53b4e0d9bf76603e126df1499578b7685faced02dd5fb07df7fc760","target":"graph","created_at":"2026-05-18T00:38:52Z","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":"Utilizing concepts from dynamical systems theory, we demonstrate how the existence of light rings, or fixed points, in a spacetime will give rise to families of periodic orbits and invariant manifolds in phase space. It is shown that these structures define the shape of the black hole shadow as well as a number of salient features of the spacetime lensing. We illustrate this through the analysis of lensing by a hairy black hole.","authors_text":"Alexander Wittig, Jai Grover","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-05-19T15:46:28Z","title":"Black Hole Shadows and Invariant Phase Space Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07061","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":"sha256:3a5272f07beb542c29dee9cbc9d69490d5a5cdf849319798a58a06c0a61a9475","target":"record","created_at":"2026-05-18T00:38:52Z","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":"26ee59d64ebc67e8866ff165159dbd72790b2bb7a4981f744ae90dcc1a438559","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-05-19T15:46:28Z","title_canon_sha256":"75b5ce5b1bcdd06db5a794cd5a375e66f093b0127af702cd1383cca67320a202"},"schema_version":"1.0","source":{"id":"1705.07061","kind":"arxiv","version":1}},"canonical_sha256":"5aec5c75b284fdf763a6e33f11211b6997c2474c2a5bc7698f8da4d364233a80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5aec5c75b284fdf763a6e33f11211b6997c2474c2a5bc7698f8da4d364233a80","first_computed_at":"2026-05-18T00:38:52.310374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:52.310374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QfUwNjOgLczkBdrpr4abO0pnuKZoC5nDXCJsUVS6OshWHyQ9Fjg+MjKR5vn4Fga58yFQO4tk7mybmhXyYh1RBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:52.310897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.07061","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a5272f07beb542c29dee9cbc9d69490d5a5cdf849319798a58a06c0a61a9475","sha256:f098e55bd53b4e0d9bf76603e126df1499578b7685faced02dd5fb07df7fc760"],"state_sha256":"b978e90b2605b910fe4275531b6045f1dc4fcf87ae8a2632808666e4d464f92b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AzlKK6kcX1G3M6Sod1OE0KFDrU7LeM6qmN2gvcrVjPCQnO5ravfWSUMqqlwyWqQ3mc+kMDG2wBnQA4wQus0DCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T23:13:32.656060Z","bundle_sha256":"cd40ea6bc9c891f4ff8b6f44f4bb8edd8b5cafd85536305244e8e4c1740e1822"}}