{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XJ53RKGXJX5TJHZGEZNK3MSLT2","short_pith_number":"pith:XJ53RKGX","canonical_record":{"source":{"id":"1601.05614","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-21T12:49:56Z","cross_cats_sorted":[],"title_canon_sha256":"c2319a57a0f341ae6cb76045bad9ff07219fd5afcbef931030f23dfd2812f667","abstract_canon_sha256":"f57c1a6eea7bfd981fb75216dc2780bb2670854a281b264bc2369db113d9e5f4"},"schema_version":"1.0"},"canonical_sha256":"ba7bb8a8d74dfb349f26265aadb24b9e9a848e575566be0c9b224c4fd6e7edd6","source":{"kind":"arxiv","id":"1601.05614","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05614","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05614v1","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05614","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"XJ53RKGXJX5T","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XJ53RKGXJX5TJHZG","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XJ53RKGX","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XJ53RKGXJX5TJHZGEZNK3MSLT2","target":"record","payload":{"canonical_record":{"source":{"id":"1601.05614","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-21T12:49:56Z","cross_cats_sorted":[],"title_canon_sha256":"c2319a57a0f341ae6cb76045bad9ff07219fd5afcbef931030f23dfd2812f667","abstract_canon_sha256":"f57c1a6eea7bfd981fb75216dc2780bb2670854a281b264bc2369db113d9e5f4"},"schema_version":"1.0"},"canonical_sha256":"ba7bb8a8d74dfb349f26265aadb24b9e9a848e575566be0c9b224c4fd6e7edd6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:13.375335Z","signature_b64":"MfPQ37FbHhcxeuLn7461KFySXH/AUy3RDb+/tB9Ugcmd5nsed8KJidBfpcvxJXtC7Ua5ptOlq+jSIi5yQf2DAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba7bb8a8d74dfb349f26265aadb24b9e9a848e575566be0c9b224c4fd6e7edd6","last_reissued_at":"2026-05-18T01:22:13.374837Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:13.374837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.05614","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":"2026-05-18T01:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7M56mRmea6orCzfaR7n7VikByTOLb2vvFWdy10c5gjPNRIOFApO0pE1jqyRRs6RIDZ9CDoCHZ9TLMVGtZy1+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:43:11.852210Z"},"content_sha256":"d4e1ca234850f1229ff975cd07cfacc31d15c6e9635fd0890a7de5a846e50a15","schema_version":"1.0","event_id":"sha256:d4e1ca234850f1229ff975cd07cfacc31d15c6e9635fd0890a7de5a846e50a15"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XJ53RKGXJX5TJHZGEZNK3MSLT2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variations on the Concept of Topological Transitivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anima Nagar, Ethan Akin, Joseph Auslander","submitted_at":"2016-01-21T12:49:56Z","abstract_excerpt":"We describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among ten reasonable notions of transitivity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05614","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":"2026-05-18T01:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uigaIXfkOTFm9j8JksMFLErjvmlsHIR29B+1/Gtym3fm1CY2Qfumukwv8EJt5+DabbI4MS5N65W/jB/nP9sYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:43:11.852778Z"},"content_sha256":"f2479851fba20e55db214446e9ee26d79c26e94c72b14e36c44f685e05b25c16","schema_version":"1.0","event_id":"sha256:f2479851fba20e55db214446e9ee26d79c26e94c72b14e36c44f685e05b25c16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XJ53RKGXJX5TJHZGEZNK3MSLT2/bundle.json","state_url":"https://pith.science/pith/XJ53RKGXJX5TJHZGEZNK3MSLT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XJ53RKGXJX5TJHZGEZNK3MSLT2/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":"2026-06-03T05:43:11Z","links":{"resolver":"https://pith.science/pith/XJ53RKGXJX5TJHZGEZNK3MSLT2","bundle":"https://pith.science/pith/XJ53RKGXJX5TJHZGEZNK3MSLT2/bundle.json","state":"https://pith.science/pith/XJ53RKGXJX5TJHZGEZNK3MSLT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XJ53RKGXJX5TJHZGEZNK3MSLT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XJ53RKGXJX5TJHZGEZNK3MSLT2","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":"f57c1a6eea7bfd981fb75216dc2780bb2670854a281b264bc2369db113d9e5f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-21T12:49:56Z","title_canon_sha256":"c2319a57a0f341ae6cb76045bad9ff07219fd5afcbef931030f23dfd2812f667"},"schema_version":"1.0","source":{"id":"1601.05614","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05614","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05614v1","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05614","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"XJ53RKGXJX5T","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XJ53RKGXJX5TJHZG","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XJ53RKGX","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:f2479851fba20e55db214446e9ee26d79c26e94c72b14e36c44f685e05b25c16","target":"graph","created_at":"2026-05-18T01:22:13Z","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 describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among ten reasonable notions of transitivity.","authors_text":"Anima Nagar, Ethan Akin, Joseph Auslander","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-21T12:49:56Z","title":"Variations on the Concept of Topological Transitivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05614","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:d4e1ca234850f1229ff975cd07cfacc31d15c6e9635fd0890a7de5a846e50a15","target":"record","created_at":"2026-05-18T01:22:13Z","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":"f57c1a6eea7bfd981fb75216dc2780bb2670854a281b264bc2369db113d9e5f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-21T12:49:56Z","title_canon_sha256":"c2319a57a0f341ae6cb76045bad9ff07219fd5afcbef931030f23dfd2812f667"},"schema_version":"1.0","source":{"id":"1601.05614","kind":"arxiv","version":1}},"canonical_sha256":"ba7bb8a8d74dfb349f26265aadb24b9e9a848e575566be0c9b224c4fd6e7edd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba7bb8a8d74dfb349f26265aadb24b9e9a848e575566be0c9b224c4fd6e7edd6","first_computed_at":"2026-05-18T01:22:13.374837Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:13.374837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MfPQ37FbHhcxeuLn7461KFySXH/AUy3RDb+/tB9Ugcmd5nsed8KJidBfpcvxJXtC7Ua5ptOlq+jSIi5yQf2DAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:13.375335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05614","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4e1ca234850f1229ff975cd07cfacc31d15c6e9635fd0890a7de5a846e50a15","sha256:f2479851fba20e55db214446e9ee26d79c26e94c72b14e36c44f685e05b25c16"],"state_sha256":"27b826f7135e0f6d09a2ea9fbdae32baecc5ddbe7468ff87cb2a3a42eef22f96"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+pi1IQKxwtAH56tPWdE6spTyMA7sW1DzUnSyUxnHen9YXJMxlklLTx8uAoFE9fOA9dFZF/cVoC1l10NdRx1fAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:43:11.854767Z","bundle_sha256":"9cbb35fbda718ada184f1da7c5af41a698eddf3d7cdd50fa917ed153107d4085"}}