{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:R5WDTEN77I2WSWISK3QLVU3JDX","short_pith_number":"pith:R5WDTEN7","canonical_record":{"source":{"id":"1701.01910","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-08T03:33:09Z","cross_cats_sorted":[],"title_canon_sha256":"f49b2c211488d07e1c7c1cbc5e01168f79107f9ad434ee3255307d77f04ae413","abstract_canon_sha256":"9acc072cc560c18083adce71ff235c2263b37a95ff44d3808c6a937d64bb888d"},"schema_version":"1.0"},"canonical_sha256":"8f6c3991bffa3569591256e0bad3691ddaae9a8ccb8b7dcd6e8a81568331eec2","source":{"kind":"arxiv","id":"1701.01910","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01910","created_at":"2026-07-05T10:02:38Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01910v5","created_at":"2026-07-05T10:02:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01910","created_at":"2026-07-05T10:02:38Z"},{"alias_kind":"pith_short_12","alias_value":"R5WDTEN77I2W","created_at":"2026-07-05T10:02:38Z"},{"alias_kind":"pith_short_16","alias_value":"R5WDTEN77I2WSWIS","created_at":"2026-07-05T10:02:38Z"},{"alias_kind":"pith_short_8","alias_value":"R5WDTEN7","created_at":"2026-07-05T10:02:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:R5WDTEN77I2WSWISK3QLVU3JDX","target":"record","payload":{"canonical_record":{"source":{"id":"1701.01910","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-08T03:33:09Z","cross_cats_sorted":[],"title_canon_sha256":"f49b2c211488d07e1c7c1cbc5e01168f79107f9ad434ee3255307d77f04ae413","abstract_canon_sha256":"9acc072cc560c18083adce71ff235c2263b37a95ff44d3808c6a937d64bb888d"},"schema_version":"1.0"},"canonical_sha256":"8f6c3991bffa3569591256e0bad3691ddaae9a8ccb8b7dcd6e8a81568331eec2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:02:38.220038Z","signature_b64":"Z7nlN20x5kCsaUCN+w/xuorJB0tPfyQzf2Sf2IKWNqwfUQc0wJbTuGvRAgor+qC18/jkbrkSkZNkw0JW7TEHDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f6c3991bffa3569591256e0bad3691ddaae9a8ccb8b7dcd6e8a81568331eec2","last_reissued_at":"2026-07-05T10:02:38.219592Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:02:38.219592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.01910","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:02:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a7mXGMjoH4R1GSftKfKon+zbfm+yWol0J3PoRvNvfocXA1CICuDOjR6NWaLPoB03nJEybuVqV/bPRukx8RsJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:24:57.991092Z"},"content_sha256":"301151d9c2e83511b0e28d3a72b8a749ae300191055995dad6ffe7db8acaa372","schema_version":"1.0","event_id":"sha256:301151d9c2e83511b0e28d3a72b8a749ae300191055995dad6ffe7db8acaa372"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:R5WDTEN77I2WSWISK3QLVU3JDX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Different Statistical Behaviors of Orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Wanshan Lin, Xiaobo Hou, Xueting Tian, Yiwei Dong","submitted_at":"2017-01-08T03:33:09Z","abstract_excerpt":"In this paper, we will study the statistical behaviors of orbits. Firstly, we will show that for a dynamical systems have the shadowing property or almost specification property, the set of nonrecurrent points has full topological entropy. After that, we introduce a criteria for classification of dynamical orbits in order to study the complexity theory of dynamical systems. The criteria is to use upper and lower natural density, upper and lower Banach density to divide different statistical future of dynamical orbits into 56 cases, 28 cases for recurrent orbits and 28 cases for nonrecurrent or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01910","kind":"arxiv","version":5},"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/1701.01910/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":"2026-07-05T10:02:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bmuJ0Ifyp+X7rqCvOFXPQDWr8jJcK7pJswgS2BVaYWZfI6u5A3zYe1RMzoPoPtz+b3QpMV8kIcRl/jkiu0jNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:24:57.991482Z"},"content_sha256":"86cec5d9b76667219a37a2389edecf037f31f682f3e1dbb2c1ec35ef598c53e4","schema_version":"1.0","event_id":"sha256:86cec5d9b76667219a37a2389edecf037f31f682f3e1dbb2c1ec35ef598c53e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R5WDTEN77I2WSWISK3QLVU3JDX/bundle.json","state_url":"https://pith.science/pith/R5WDTEN77I2WSWISK3QLVU3JDX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R5WDTEN77I2WSWISK3QLVU3JDX/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":"2026-07-07T11:24:57Z","links":{"resolver":"https://pith.science/pith/R5WDTEN77I2WSWISK3QLVU3JDX","bundle":"https://pith.science/pith/R5WDTEN77I2WSWISK3QLVU3JDX/bundle.json","state":"https://pith.science/pith/R5WDTEN77I2WSWISK3QLVU3JDX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R5WDTEN77I2WSWISK3QLVU3JDX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R5WDTEN77I2WSWISK3QLVU3JDX","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":"9acc072cc560c18083adce71ff235c2263b37a95ff44d3808c6a937d64bb888d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-08T03:33:09Z","title_canon_sha256":"f49b2c211488d07e1c7c1cbc5e01168f79107f9ad434ee3255307d77f04ae413"},"schema_version":"1.0","source":{"id":"1701.01910","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01910","created_at":"2026-07-05T10:02:38Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01910v5","created_at":"2026-07-05T10:02:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01910","created_at":"2026-07-05T10:02:38Z"},{"alias_kind":"pith_short_12","alias_value":"R5WDTEN77I2W","created_at":"2026-07-05T10:02:38Z"},{"alias_kind":"pith_short_16","alias_value":"R5WDTEN77I2WSWIS","created_at":"2026-07-05T10:02:38Z"},{"alias_kind":"pith_short_8","alias_value":"R5WDTEN7","created_at":"2026-07-05T10:02:38Z"}],"graph_snapshots":[{"event_id":"sha256:86cec5d9b76667219a37a2389edecf037f31f682f3e1dbb2c1ec35ef598c53e4","target":"graph","created_at":"2026-07-05T10:02:38Z","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/1701.01910/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we will study the statistical behaviors of orbits. Firstly, we will show that for a dynamical systems have the shadowing property or almost specification property, the set of nonrecurrent points has full topological entropy. After that, we introduce a criteria for classification of dynamical orbits in order to study the complexity theory of dynamical systems. The criteria is to use upper and lower natural density, upper and lower Banach density to divide different statistical future of dynamical orbits into 56 cases, 28 cases for recurrent orbits and 28 cases for nonrecurrent or","authors_text":"Wanshan Lin, Xiaobo Hou, Xueting Tian, Yiwei Dong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-08T03:33:09Z","title":"Different Statistical Behaviors of Orbits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01910","kind":"arxiv","version":5},"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":"sha256:301151d9c2e83511b0e28d3a72b8a749ae300191055995dad6ffe7db8acaa372","target":"record","created_at":"2026-07-05T10:02:38Z","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":"9acc072cc560c18083adce71ff235c2263b37a95ff44d3808c6a937d64bb888d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-08T03:33:09Z","title_canon_sha256":"f49b2c211488d07e1c7c1cbc5e01168f79107f9ad434ee3255307d77f04ae413"},"schema_version":"1.0","source":{"id":"1701.01910","kind":"arxiv","version":5}},"canonical_sha256":"8f6c3991bffa3569591256e0bad3691ddaae9a8ccb8b7dcd6e8a81568331eec2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f6c3991bffa3569591256e0bad3691ddaae9a8ccb8b7dcd6e8a81568331eec2","first_computed_at":"2026-07-05T10:02:38.219592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:02:38.219592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z7nlN20x5kCsaUCN+w/xuorJB0tPfyQzf2Sf2IKWNqwfUQc0wJbTuGvRAgor+qC18/jkbrkSkZNkw0JW7TEHDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:02:38.220038Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01910","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:301151d9c2e83511b0e28d3a72b8a749ae300191055995dad6ffe7db8acaa372","sha256:86cec5d9b76667219a37a2389edecf037f31f682f3e1dbb2c1ec35ef598c53e4"],"state_sha256":"29db37f3ddaea0561049d347d23cc89bf96fcdeb52627a5dd752adba5ea84387"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Bj7wCX8Q15e/jf+eekG0s2x9qFGLOdLdIeW6bG2vDf0EFOKDcJdVKs01b2mV4ljBAO9u/3Cle+Glgd9KmlUCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T11:24:57.993419Z","bundle_sha256":"386dfbd7ac1a4f3252d8acd852029ddeaa58f86ce4d806ad7062ccba3de8cffb"}}