{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UARDQH37QA5R6IMRUQPOYRXUV3","short_pith_number":"pith:UARDQH37","canonical_record":{"source":{"id":"1501.03375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-01-14T15:45:54Z","cross_cats_sorted":[],"title_canon_sha256":"de902a068a9ecb16423f45ae73ddb1ad7418d3f17ea6e5676934aa0c04d1c20a","abstract_canon_sha256":"d37fb2603f354e36a9a57b0d0e41e2069bce01309e61bbfe901cd948ae656609"},"schema_version":"1.0"},"canonical_sha256":"a022381f7f803b1f2191a41eec46f4aef8ad8d04b28e178e1a6ce2e0ab463857","source":{"kind":"arxiv","id":"1501.03375","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03375","created_at":"2026-05-18T01:41:11Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03375v1","created_at":"2026-05-18T01:41:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03375","created_at":"2026-05-18T01:41:11Z"},{"alias_kind":"pith_short_12","alias_value":"UARDQH37QA5R","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UARDQH37QA5R6IMR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UARDQH37","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UARDQH37QA5R6IMRUQPOYRXUV3","target":"record","payload":{"canonical_record":{"source":{"id":"1501.03375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-01-14T15:45:54Z","cross_cats_sorted":[],"title_canon_sha256":"de902a068a9ecb16423f45ae73ddb1ad7418d3f17ea6e5676934aa0c04d1c20a","abstract_canon_sha256":"d37fb2603f354e36a9a57b0d0e41e2069bce01309e61bbfe901cd948ae656609"},"schema_version":"1.0"},"canonical_sha256":"a022381f7f803b1f2191a41eec46f4aef8ad8d04b28e178e1a6ce2e0ab463857","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:11.003966Z","signature_b64":"mXe+yoSathRCVvmvwUAfBvdBb1C4ILoC1cFZwhexioyVViv5liqeAPtn/zkj0xBmtFeDKNWua6TlaWXR6qqNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a022381f7f803b1f2191a41eec46f4aef8ad8d04b28e178e1a6ce2e0ab463857","last_reissued_at":"2026-05-18T01:41:11.003385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:11.003385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.03375","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":"2026-05-18T01:41:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AzF6CDVWgf/TrgXYlKuLNpfsEXxpRkwWMRF/FQpx8B7zFEMQowB4aPMVm7SpNiSrTSk9hY+F2yKgy+2fAwwABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:33:00.016411Z"},"content_sha256":"9cfed0e689c902976ee0d603d8a5a9805fa89037ca49aaa3e0452e21969db171","schema_version":"1.0","event_id":"sha256:9cfed0e689c902976ee0d603d8a5a9805fa89037ca49aaa3e0452e21969db171"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UARDQH37QA5R6IMRUQPOYRXUV3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The invariant tori of knot type and the interlinked invariant tori in the Nos\\'e-Hoover system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Lei Wang, Xiao-Song Yang","submitted_at":"2015-01-14T15:45:54Z","abstract_excerpt":"We revisit the famous Nos\\'e-Hoover system in this paper and show the existence of some averagely conservative regions which are filled with an infinite sequence of nested tori. Depending on initial conditions, some invariant tori are of trefoil knot type, while the others are of trivial knot type. Moreover, we present a variety of interlinked invariant tori whose initial conditions are chosen from different averagely conservative regions and give all the interlinking numbers of those interlinked tori, showing that this quadratic system possesses so rich dynamic properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03375","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":"2026-05-18T01:41:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CxsW6rpxlI/v/thARkH2W5ZbccGFEldMjuEW1bXqHZmfiNwJntMjZvroWS4534B5B6QiPTBQxB6kajQHNGRkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:33:00.016772Z"},"content_sha256":"e78b7116fbc8a02af0b44d8fa3b0d3bb811a21e5e197a6731d8e5299ff6dbd52","schema_version":"1.0","event_id":"sha256:e78b7116fbc8a02af0b44d8fa3b0d3bb811a21e5e197a6731d8e5299ff6dbd52"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UARDQH37QA5R6IMRUQPOYRXUV3/bundle.json","state_url":"https://pith.science/pith/UARDQH37QA5R6IMRUQPOYRXUV3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UARDQH37QA5R6IMRUQPOYRXUV3/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":"2026-06-12T07:33:00Z","links":{"resolver":"https://pith.science/pith/UARDQH37QA5R6IMRUQPOYRXUV3","bundle":"https://pith.science/pith/UARDQH37QA5R6IMRUQPOYRXUV3/bundle.json","state":"https://pith.science/pith/UARDQH37QA5R6IMRUQPOYRXUV3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UARDQH37QA5R6IMRUQPOYRXUV3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UARDQH37QA5R6IMRUQPOYRXUV3","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":"d37fb2603f354e36a9a57b0d0e41e2069bce01309e61bbfe901cd948ae656609","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-01-14T15:45:54Z","title_canon_sha256":"de902a068a9ecb16423f45ae73ddb1ad7418d3f17ea6e5676934aa0c04d1c20a"},"schema_version":"1.0","source":{"id":"1501.03375","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03375","created_at":"2026-05-18T01:41:11Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03375v1","created_at":"2026-05-18T01:41:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03375","created_at":"2026-05-18T01:41:11Z"},{"alias_kind":"pith_short_12","alias_value":"UARDQH37QA5R","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UARDQH37QA5R6IMR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UARDQH37","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:e78b7116fbc8a02af0b44d8fa3b0d3bb811a21e5e197a6731d8e5299ff6dbd52","target":"graph","created_at":"2026-05-18T01:41:11Z","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 revisit the famous Nos\\'e-Hoover system in this paper and show the existence of some averagely conservative regions which are filled with an infinite sequence of nested tori. Depending on initial conditions, some invariant tori are of trefoil knot type, while the others are of trivial knot type. Moreover, we present a variety of interlinked invariant tori whose initial conditions are chosen from different averagely conservative regions and give all the interlinking numbers of those interlinked tori, showing that this quadratic system possesses so rich dynamic properties.","authors_text":"Lei Wang, Xiao-Song Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-01-14T15:45:54Z","title":"The invariant tori of knot type and the interlinked invariant tori in the Nos\\'e-Hoover system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03375","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":"sha256:9cfed0e689c902976ee0d603d8a5a9805fa89037ca49aaa3e0452e21969db171","target":"record","created_at":"2026-05-18T01:41:11Z","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":"d37fb2603f354e36a9a57b0d0e41e2069bce01309e61bbfe901cd948ae656609","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-01-14T15:45:54Z","title_canon_sha256":"de902a068a9ecb16423f45ae73ddb1ad7418d3f17ea6e5676934aa0c04d1c20a"},"schema_version":"1.0","source":{"id":"1501.03375","kind":"arxiv","version":1}},"canonical_sha256":"a022381f7f803b1f2191a41eec46f4aef8ad8d04b28e178e1a6ce2e0ab463857","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a022381f7f803b1f2191a41eec46f4aef8ad8d04b28e178e1a6ce2e0ab463857","first_computed_at":"2026-05-18T01:41:11.003385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:11.003385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mXe+yoSathRCVvmvwUAfBvdBb1C4ILoC1cFZwhexioyVViv5liqeAPtn/zkj0xBmtFeDKNWua6TlaWXR6qqNCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:11.003966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03375","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cfed0e689c902976ee0d603d8a5a9805fa89037ca49aaa3e0452e21969db171","sha256:e78b7116fbc8a02af0b44d8fa3b0d3bb811a21e5e197a6731d8e5299ff6dbd52"],"state_sha256":"df64442d58ed67d489a92a3cbcdc13bd247aa5cb10e6d9a3896769d9df9fdd59"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S4SZ0Y3qdXvP5ytMFZSHgfZN9TzzViztXUP3wavK819QVlfq3qvzYNyqvbC2jwf6VYxBGQtmGy+4A4ayLjAAAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T07:33:00.018728Z","bundle_sha256":"35e7fb614cee8ff98da2e52d025d38413ff21c4faf11d0ff360ad206f9235f41"}}