{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RBVOCVRVVXKXOZ3PESV5GAB3LS","short_pith_number":"pith:RBVOCVRV","canonical_record":{"source":{"id":"1503.06425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-22T13:21:13Z","cross_cats_sorted":[],"title_canon_sha256":"9952a7c4559af94269780a411b6e3f72341450eecf0f5be0f386f66f30a69acc","abstract_canon_sha256":"8f46512f9a263ecc98277e12b7d26cd15a6bbe6ffa9ea014145c21babacf67c8"},"schema_version":"1.0"},"canonical_sha256":"886ae15635add577676f24abd3003b5c8f72e26dd6b3be47fdce67824cccbc89","source":{"kind":"arxiv","id":"1503.06425","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06425","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06425v1","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06425","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"pith_short_12","alias_value":"RBVOCVRVVXKX","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RBVOCVRVVXKXOZ3P","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RBVOCVRV","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RBVOCVRVVXKXOZ3PESV5GAB3LS","target":"record","payload":{"canonical_record":{"source":{"id":"1503.06425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-22T13:21:13Z","cross_cats_sorted":[],"title_canon_sha256":"9952a7c4559af94269780a411b6e3f72341450eecf0f5be0f386f66f30a69acc","abstract_canon_sha256":"8f46512f9a263ecc98277e12b7d26cd15a6bbe6ffa9ea014145c21babacf67c8"},"schema_version":"1.0"},"canonical_sha256":"886ae15635add577676f24abd3003b5c8f72e26dd6b3be47fdce67824cccbc89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:03.842391Z","signature_b64":"hY0RtVb8ssY8xq+1/EpIVQYRntRaRNU6syKVQkAYOzaMaEGjbHNNiNm681OgpZ4wBv1Y7zNJWFq5nR29aqTyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"886ae15635add577676f24abd3003b5c8f72e26dd6b3be47fdce67824cccbc89","last_reissued_at":"2026-05-18T01:24:03.841711Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:03.841711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.06425","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":"2026-05-18T01:24:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e9NgV/VFKu5+dQRiqxVx8Zkq4w4J99PeOQg3g2Q4PFJ8OlfJN0neJ9BIN1TwH8l482R9UcZZbvmrN7kHsIXMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T13:23:36.314743Z"},"content_sha256":"07446affb6b8174132f3284ede1c33889d74e8a5cea18f6d590788e7d75b6518","schema_version":"1.0","event_id":"sha256:07446affb6b8174132f3284ede1c33889d74e8a5cea18f6d590788e7d75b6518"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RBVOCVRVVXKXOZ3PESV5GAB3LS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recent development of chaos theory in topological dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jian Li, Xiangdong Ye","submitted_at":"2015-03-22T13:21:13Z","abstract_excerpt":"We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06425","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":"2026-05-18T01:24:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oi2tABDYy1t6o5nFqz+sVJFT/OMkVYptHbDYi2D+5BiV0aAbpJA9x+rIgc2HgyH2ZQM/oBMNqZIWO9EwOpcyDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T13:23:36.315080Z"},"content_sha256":"bc2aeef073f9d8d9a3aa228e9f7267e64f90fc31dc2ab1b309c378c5038d3a32","schema_version":"1.0","event_id":"sha256:bc2aeef073f9d8d9a3aa228e9f7267e64f90fc31dc2ab1b309c378c5038d3a32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBVOCVRVVXKXOZ3PESV5GAB3LS/bundle.json","state_url":"https://pith.science/pith/RBVOCVRVVXKXOZ3PESV5GAB3LS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBVOCVRVVXKXOZ3PESV5GAB3LS/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":"2026-06-24T13:23:36Z","links":{"resolver":"https://pith.science/pith/RBVOCVRVVXKXOZ3PESV5GAB3LS","bundle":"https://pith.science/pith/RBVOCVRVVXKXOZ3PESV5GAB3LS/bundle.json","state":"https://pith.science/pith/RBVOCVRVVXKXOZ3PESV5GAB3LS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBVOCVRVVXKXOZ3PESV5GAB3LS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RBVOCVRVVXKXOZ3PESV5GAB3LS","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":"8f46512f9a263ecc98277e12b7d26cd15a6bbe6ffa9ea014145c21babacf67c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-22T13:21:13Z","title_canon_sha256":"9952a7c4559af94269780a411b6e3f72341450eecf0f5be0f386f66f30a69acc"},"schema_version":"1.0","source":{"id":"1503.06425","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06425","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06425v1","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06425","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"pith_short_12","alias_value":"RBVOCVRVVXKX","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RBVOCVRVVXKXOZ3P","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RBVOCVRV","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:bc2aeef073f9d8d9a3aa228e9f7267e64f90fc31dc2ab1b309c378c5038d3a32","target":"graph","created_at":"2026-05-18T01:24:03Z","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 give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.","authors_text":"Jian Li, Xiangdong Ye","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-22T13:21:13Z","title":"Recent development of chaos theory in topological dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06425","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":"sha256:07446affb6b8174132f3284ede1c33889d74e8a5cea18f6d590788e7d75b6518","target":"record","created_at":"2026-05-18T01:24:03Z","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":"8f46512f9a263ecc98277e12b7d26cd15a6bbe6ffa9ea014145c21babacf67c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-22T13:21:13Z","title_canon_sha256":"9952a7c4559af94269780a411b6e3f72341450eecf0f5be0f386f66f30a69acc"},"schema_version":"1.0","source":{"id":"1503.06425","kind":"arxiv","version":1}},"canonical_sha256":"886ae15635add577676f24abd3003b5c8f72e26dd6b3be47fdce67824cccbc89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"886ae15635add577676f24abd3003b5c8f72e26dd6b3be47fdce67824cccbc89","first_computed_at":"2026-05-18T01:24:03.841711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:03.841711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hY0RtVb8ssY8xq+1/EpIVQYRntRaRNU6syKVQkAYOzaMaEGjbHNNiNm681OgpZ4wBv1Y7zNJWFq5nR29aqTyAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:03.842391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06425","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07446affb6b8174132f3284ede1c33889d74e8a5cea18f6d590788e7d75b6518","sha256:bc2aeef073f9d8d9a3aa228e9f7267e64f90fc31dc2ab1b309c378c5038d3a32"],"state_sha256":"57bf14d75691163e60c6956ee7981522cc7ec736fd5da67a854851c28f26a9aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s7whTEidWY/tjAdMDHUX7/zNqG+AhEW428XSXCEyUE9PKZ4gr0++fGBV1M+4tCkGeAp6xeb/VPrsz+5plDhDAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T13:23:36.316988Z","bundle_sha256":"951597b8e6c541abf3fdefa57d863a74f526511becd06f95cc3d42cde25abd64"}}