{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MGIMLXNBSPKBB2EXB6LMCNPLXD","short_pith_number":"pith:MGIMLXNB","canonical_record":{"source":{"id":"1308.4306","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-08-20T13:31:55Z","cross_cats_sorted":["astro-ph.GA","nlin.CD"],"title_canon_sha256":"a832be261158cfba39dd7f2d118f170e0a5af4f6da622f4ae77e8e2ef5fafee7","abstract_canon_sha256":"490ac23f47b423290c794f8da464c0f9f9769a4448dddedb8a376ca47b9864bd"},"schema_version":"1.0"},"canonical_sha256":"6190c5dda193d410e8970f96c135ebb8c15c5a72beb37df3aa6f515f1721fcc6","source":{"kind":"arxiv","id":"1308.4306","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4306","created_at":"2026-05-18T03:07:10Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4306v1","created_at":"2026-05-18T03:07:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4306","created_at":"2026-05-18T03:07:10Z"},{"alias_kind":"pith_short_12","alias_value":"MGIMLXNBSPKB","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MGIMLXNBSPKBB2EX","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MGIMLXNB","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MGIMLXNBSPKBB2EXB6LMCNPLXD","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4306","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-08-20T13:31:55Z","cross_cats_sorted":["astro-ph.GA","nlin.CD"],"title_canon_sha256":"a832be261158cfba39dd7f2d118f170e0a5af4f6da622f4ae77e8e2ef5fafee7","abstract_canon_sha256":"490ac23f47b423290c794f8da464c0f9f9769a4448dddedb8a376ca47b9864bd"},"schema_version":"1.0"},"canonical_sha256":"6190c5dda193d410e8970f96c135ebb8c15c5a72beb37df3aa6f515f1721fcc6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:10.959305Z","signature_b64":"05MRWGNyNGtlkPO5xZPJD8/lJh8URXuXhKyx9cCZbodG2LsTBfNP12IAS45+lxGnAIu+zAiFVBMQ2sCCt8SYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6190c5dda193d410e8970f96c135ebb8c15c5a72beb37df3aa6f515f1721fcc6","last_reissued_at":"2026-05-18T03:07:10.958818Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:10.958818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4306","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":"2026-05-18T03:07:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s+RgZHQlTDjx3mPQ39AIN0pBdw8HqKshsJTAXQcZHzTU6m7hmF2p1tqjScDAitYfiIf6DVgepPrUWTXNi+a5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:53:31.188847Z"},"content_sha256":"762d2c7e80607595d67da690105e4d31ac80af83bae8567f8837aa593a2c4da8","schema_version":"1.0","event_id":"sha256:762d2c7e80607595d67da690105e4d31ac80af83bae8567f8837aa593a2c4da8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MGIMLXNBSPKBB2EXB6LMCNPLXD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free motion around black holes with discs or rings: between integrability and chaos - III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.GA","nlin.CD"],"primary_cat":"gr-qc","authors_text":"O. Semer\\'ak, P. Sukov\\'a","submitted_at":"2013-08-20T13:31:55Z","abstract_excerpt":"We continue the study of time-like geodesic dynamics in exact static, axially and reflection symmetric space-times describing the fields of a Schwarzschild black hole surrounded by thin discs or rings. In the first paper of this series, the rise (and decline) of geodesic chaos with ring/disc mass and position and with test particle energy was revealed on Poincar\\'e sections and on time series of position or velocity and their power spectra. In the second paper we compared these results with those obtained by two recurrence methods, focusing on \"sticky\" orbits whose different parts show differe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4306","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":"2026-05-18T03:07:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mXtzvR2zuQ4QIuU6m/tXrudaOJ6zhKDy20Xzaxju3aXS3jKK/GDFk3BsTwU3DIx9dm5YnNGiIO1NPFoelWDeDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:53:31.189181Z"},"content_sha256":"732ad45738cda5abcd65965827cae7af42e08c3d8558d8f873de694ae384810d","schema_version":"1.0","event_id":"sha256:732ad45738cda5abcd65965827cae7af42e08c3d8558d8f873de694ae384810d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MGIMLXNBSPKBB2EXB6LMCNPLXD/bundle.json","state_url":"https://pith.science/pith/MGIMLXNBSPKBB2EXB6LMCNPLXD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MGIMLXNBSPKBB2EXB6LMCNPLXD/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":"2026-07-02T12:53:31Z","links":{"resolver":"https://pith.science/pith/MGIMLXNBSPKBB2EXB6LMCNPLXD","bundle":"https://pith.science/pith/MGIMLXNBSPKBB2EXB6LMCNPLXD/bundle.json","state":"https://pith.science/pith/MGIMLXNBSPKBB2EXB6LMCNPLXD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MGIMLXNBSPKBB2EXB6LMCNPLXD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MGIMLXNBSPKBB2EXB6LMCNPLXD","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":"490ac23f47b423290c794f8da464c0f9f9769a4448dddedb8a376ca47b9864bd","cross_cats_sorted":["astro-ph.GA","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-08-20T13:31:55Z","title_canon_sha256":"a832be261158cfba39dd7f2d118f170e0a5af4f6da622f4ae77e8e2ef5fafee7"},"schema_version":"1.0","source":{"id":"1308.4306","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4306","created_at":"2026-05-18T03:07:10Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4306v1","created_at":"2026-05-18T03:07:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4306","created_at":"2026-05-18T03:07:10Z"},{"alias_kind":"pith_short_12","alias_value":"MGIMLXNBSPKB","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MGIMLXNBSPKBB2EX","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MGIMLXNB","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:732ad45738cda5abcd65965827cae7af42e08c3d8558d8f873de694ae384810d","target":"graph","created_at":"2026-05-18T03:07:10Z","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 continue the study of time-like geodesic dynamics in exact static, axially and reflection symmetric space-times describing the fields of a Schwarzschild black hole surrounded by thin discs or rings. In the first paper of this series, the rise (and decline) of geodesic chaos with ring/disc mass and position and with test particle energy was revealed on Poincar\\'e sections and on time series of position or velocity and their power spectra. In the second paper we compared these results with those obtained by two recurrence methods, focusing on \"sticky\" orbits whose different parts show differe","authors_text":"O. Semer\\'ak, P. Sukov\\'a","cross_cats":["astro-ph.GA","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-08-20T13:31:55Z","title":"Free motion around black holes with discs or rings: between integrability and chaos - III"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4306","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":"sha256:762d2c7e80607595d67da690105e4d31ac80af83bae8567f8837aa593a2c4da8","target":"record","created_at":"2026-05-18T03:07:10Z","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":"490ac23f47b423290c794f8da464c0f9f9769a4448dddedb8a376ca47b9864bd","cross_cats_sorted":["astro-ph.GA","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-08-20T13:31:55Z","title_canon_sha256":"a832be261158cfba39dd7f2d118f170e0a5af4f6da622f4ae77e8e2ef5fafee7"},"schema_version":"1.0","source":{"id":"1308.4306","kind":"arxiv","version":1}},"canonical_sha256":"6190c5dda193d410e8970f96c135ebb8c15c5a72beb37df3aa6f515f1721fcc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6190c5dda193d410e8970f96c135ebb8c15c5a72beb37df3aa6f515f1721fcc6","first_computed_at":"2026-05-18T03:07:10.958818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:10.958818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"05MRWGNyNGtlkPO5xZPJD8/lJh8URXuXhKyx9cCZbodG2LsTBfNP12IAS45+lxGnAIu+zAiFVBMQ2sCCt8SYAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:10.959305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4306","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:762d2c7e80607595d67da690105e4d31ac80af83bae8567f8837aa593a2c4da8","sha256:732ad45738cda5abcd65965827cae7af42e08c3d8558d8f873de694ae384810d"],"state_sha256":"f0dfb5cd2b28605536c7574bc20646441a492a1412f64f30e7f4345569259316"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1gqnv+Z0BOoaElb66pniqONrj77rKf8SDNzR4GBA0PBNc4hOxiIBHXMVyPaN7f03iAGzbcx0IqEhrlR/Yo7JDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T12:53:31.191084Z","bundle_sha256":"d0581c62f55e80bfc72268cff36d7bff69a483307007cae81f64e3fc71e48c99"}}