{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:W63WDGYEOSPWFNHRRCXOCC6ZU7","short_pith_number":"pith:W63WDGYE","canonical_record":{"source":{"id":"1712.02674","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-07T15:39:54Z","cross_cats_sorted":[],"title_canon_sha256":"5a4a862e202038e47d46c7ec0daeacd296c405765d23249099888c7273e296fd","abstract_canon_sha256":"d46def4179baa187f749e394f57c3540ebef54eab9899587018dd56f7a03d77d"},"schema_version":"1.0"},"canonical_sha256":"b7b7619b04749f62b4f188aee10bd9a7d7aa94919ba6bb745e191afbc54b6b09","source":{"kind":"arxiv","id":"1712.02674","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02674","created_at":"2026-05-17T23:51:20Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02674v2","created_at":"2026-05-17T23:51:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02674","created_at":"2026-05-17T23:51:20Z"},{"alias_kind":"pith_short_12","alias_value":"W63WDGYEOSPW","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"W63WDGYEOSPWFNHR","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"W63WDGYE","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:W63WDGYEOSPWFNHRRCXOCC6ZU7","target":"record","payload":{"canonical_record":{"source":{"id":"1712.02674","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-07T15:39:54Z","cross_cats_sorted":[],"title_canon_sha256":"5a4a862e202038e47d46c7ec0daeacd296c405765d23249099888c7273e296fd","abstract_canon_sha256":"d46def4179baa187f749e394f57c3540ebef54eab9899587018dd56f7a03d77d"},"schema_version":"1.0"},"canonical_sha256":"b7b7619b04749f62b4f188aee10bd9a7d7aa94919ba6bb745e191afbc54b6b09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:20.008195Z","signature_b64":"ql96ACSr4qiB01G/AVLcSXbCCzQWv/LWhy6AIFc42sml+BWfAOgfnOpEJ8laorj04IhsLWmox9FkHzSyPcOoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7b7619b04749f62b4f188aee10bd9a7d7aa94919ba6bb745e191afbc54b6b09","last_reissued_at":"2026-05-17T23:51:20.007636Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:20.007636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.02674","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2D+J+tB9Y+GKN1dHlhrJOWb9XsfbFcG204I+de7THk6hhBqaVVgln0EHaospaJn23yZtT155TGgb7cbiE+cmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:53:00.944727Z"},"content_sha256":"43cc45b2c6ffe18037cbe3a9ef19601b6e433674e3de6e3f07a3ea0ee145d62d","schema_version":"1.0","event_id":"sha256:43cc45b2c6ffe18037cbe3a9ef19601b6e433674e3de6e3f07a3ea0ee145d62d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:W63WDGYEOSPWFNHRRCXOCC6ZU7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dmitry Turaev, Dongchen Li","submitted_at":"2017-12-07T15:39:54Z","abstract_excerpt":"We prove that heterodimensional cycles can be created by unfolding a pair of homoclinic tangencies in a certain class of C-infinity diffeomorphisms. This implies the existence of a C2- open domain in the space of dynamical systems with a certain type of symmetry where systems with heterodimensional cycles are dense in C-infinity. In particular, we describe a class of three-dimensional flows with a Lorenz-like attractor such that an arbitrarily small perturbation of any such flow can belong to this domain - in this case the corresponding heterodimensional cycles belong to a chain-transitive att"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02674","kind":"arxiv","version":2},"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":"2026-05-17T23:51:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dVC9z/D/1Y7ojfBZG/YAV8OqydGyzJrnFGlW6tbhgHdu30xWbtbEkCMDnCmAM9n0lUEhnrKtK+u0Ev3MCQ8pAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:53:00.945442Z"},"content_sha256":"371986213273a8010c901cdc9416259876c4ad1f645a366806b40dfa118a418f","schema_version":"1.0","event_id":"sha256:371986213273a8010c901cdc9416259876c4ad1f645a366806b40dfa118a418f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W63WDGYEOSPWFNHRRCXOCC6ZU7/bundle.json","state_url":"https://pith.science/pith/W63WDGYEOSPWFNHRRCXOCC6ZU7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W63WDGYEOSPWFNHRRCXOCC6ZU7/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":"2026-06-09T08:53:00Z","links":{"resolver":"https://pith.science/pith/W63WDGYEOSPWFNHRRCXOCC6ZU7","bundle":"https://pith.science/pith/W63WDGYEOSPWFNHRRCXOCC6ZU7/bundle.json","state":"https://pith.science/pith/W63WDGYEOSPWFNHRRCXOCC6ZU7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W63WDGYEOSPWFNHRRCXOCC6ZU7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:W63WDGYEOSPWFNHRRCXOCC6ZU7","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":"d46def4179baa187f749e394f57c3540ebef54eab9899587018dd56f7a03d77d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-07T15:39:54Z","title_canon_sha256":"5a4a862e202038e47d46c7ec0daeacd296c405765d23249099888c7273e296fd"},"schema_version":"1.0","source":{"id":"1712.02674","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02674","created_at":"2026-05-17T23:51:20Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02674v2","created_at":"2026-05-17T23:51:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02674","created_at":"2026-05-17T23:51:20Z"},{"alias_kind":"pith_short_12","alias_value":"W63WDGYEOSPW","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"W63WDGYEOSPWFNHR","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"W63WDGYE","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:371986213273a8010c901cdc9416259876c4ad1f645a366806b40dfa118a418f","target":"graph","created_at":"2026-05-17T23:51:20Z","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 prove that heterodimensional cycles can be created by unfolding a pair of homoclinic tangencies in a certain class of C-infinity diffeomorphisms. This implies the existence of a C2- open domain in the space of dynamical systems with a certain type of symmetry where systems with heterodimensional cycles are dense in C-infinity. In particular, we describe a class of three-dimensional flows with a Lorenz-like attractor such that an arbitrarily small perturbation of any such flow can belong to this domain - in this case the corresponding heterodimensional cycles belong to a chain-transitive att","authors_text":"Dmitry Turaev, Dongchen Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-07T15:39:54Z","title":"Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02674","kind":"arxiv","version":2},"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":"sha256:43cc45b2c6ffe18037cbe3a9ef19601b6e433674e3de6e3f07a3ea0ee145d62d","target":"record","created_at":"2026-05-17T23:51:20Z","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":"d46def4179baa187f749e394f57c3540ebef54eab9899587018dd56f7a03d77d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-07T15:39:54Z","title_canon_sha256":"5a4a862e202038e47d46c7ec0daeacd296c405765d23249099888c7273e296fd"},"schema_version":"1.0","source":{"id":"1712.02674","kind":"arxiv","version":2}},"canonical_sha256":"b7b7619b04749f62b4f188aee10bd9a7d7aa94919ba6bb745e191afbc54b6b09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7b7619b04749f62b4f188aee10bd9a7d7aa94919ba6bb745e191afbc54b6b09","first_computed_at":"2026-05-17T23:51:20.007636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:20.007636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ql96ACSr4qiB01G/AVLcSXbCCzQWv/LWhy6AIFc42sml+BWfAOgfnOpEJ8laorj04IhsLWmox9FkHzSyPcOoBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:20.008195Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.02674","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43cc45b2c6ffe18037cbe3a9ef19601b6e433674e3de6e3f07a3ea0ee145d62d","sha256:371986213273a8010c901cdc9416259876c4ad1f645a366806b40dfa118a418f"],"state_sha256":"baa01c7d6129b4ba3878d93c455644fc87a0cb2f60e36b8d66a185a6959f51c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QodA6VzC6dwdN6BCGdQZhgSMngNUHuhudHtKgTzEOaH6Eq9gJuBtbD+Rrg/cOquKzBgMCbxPdJ7LXGTqyRqNAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:53:00.949721Z","bundle_sha256":"e1488f0e54e27e04896e7c0a9ce8c7719b26bceb4a5487d4b8db619cad9fbedb"}}