{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RIGRWMA5S4DFD7YJMQTNPQA64N","short_pith_number":"pith:RIGRWMA5","canonical_record":{"source":{"id":"1604.02417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-04-08T18:12:12Z","cross_cats_sorted":[],"title_canon_sha256":"39d70d376893ad878c0d152fe59cf67d595fa038f99541ad02a71672b9070192","abstract_canon_sha256":"fb558bc9d5f8becc6e4a672fe65ed90b1faa6350419eb2a1348d95d110e2ae41"},"schema_version":"1.0"},"canonical_sha256":"8a0d1b301d970651ff096426d7c01ee36406d2b4b0249d2b7bb50efae182ddb4","source":{"kind":"arxiv","id":"1604.02417","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02417","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02417v1","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02417","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"pith_short_12","alias_value":"RIGRWMA5S4DF","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RIGRWMA5S4DFD7YJ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RIGRWMA5","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RIGRWMA5S4DFD7YJMQTNPQA64N","target":"record","payload":{"canonical_record":{"source":{"id":"1604.02417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-04-08T18:12:12Z","cross_cats_sorted":[],"title_canon_sha256":"39d70d376893ad878c0d152fe59cf67d595fa038f99541ad02a71672b9070192","abstract_canon_sha256":"fb558bc9d5f8becc6e4a672fe65ed90b1faa6350419eb2a1348d95d110e2ae41"},"schema_version":"1.0"},"canonical_sha256":"8a0d1b301d970651ff096426d7c01ee36406d2b4b0249d2b7bb50efae182ddb4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:01.266396Z","signature_b64":"sL7Ixu2+E1BRu1yIQfGfpuyckxhAfaGFTlu8IOpsvQcnulTKWt/bqGUq79cAy5kZEZ+tuzcZTsDXKWmbi5/jAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a0d1b301d970651ff096426d7c01ee36406d2b4b0249d2b7bb50efae182ddb4","last_reissued_at":"2026-05-18T00:44:01.265934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:01.265934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.02417","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":"2026-05-18T00:44:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lTcJGYsOeUIFqH4ElfLXX2Yf/8er9YmW+HFKh6IJfCBUr3XrU0Q3k5eBcZQOB3Kk7dfTB9gM/ZW3cM5Lbn0UBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:37:51.597357Z"},"content_sha256":"eca03310a7263f5f714a871f804acdab686a62a8aa260db4416024c187ffa12f","schema_version":"1.0","event_id":"sha256:eca03310a7263f5f714a871f804acdab686a62a8aa260db4416024c187ffa12f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RIGRWMA5S4DFD7YJMQTNPQA64N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexander S. Gonchenko, Alexey O. Kazakov, Dmitry V. Turaev, Sergey V. Gonchenko","submitted_at":"2016-04-08T18:12:12Z","abstract_excerpt":"A one-parameter family of time-reversible systems on $\\mathbb{T}^3$ is considered. It is shown that the dynamics is not conservative, namely the attractor and repeller intersect but not coincide. We explain this as the manifestation of the so-called mixed dynamics phenomenon which corresponds to a persistent intersection of the closure of stable periodic orbits and the closure of the completely unstable periodic orbits. We search for the stable and unstable periodic orbits indirectly, by finding non-conservative saddle periodic orbits and heteroclinic connections between them. In this way, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02417","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":"2026-05-18T00:44:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XTwcBSSMCafj1A0IbKVjGyTiMLOoX9vsQ+uZgLrEWZic4VRWKHCN0hQNqvjxAin0045kDUPApW0kD5wb2lNyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:37:51.597712Z"},"content_sha256":"2d6a5ec03a8d61beb3c3d011b3e1a70270f21caab269d6fef178c0475abc1089","schema_version":"1.0","event_id":"sha256:2d6a5ec03a8d61beb3c3d011b3e1a70270f21caab269d6fef178c0475abc1089"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RIGRWMA5S4DFD7YJMQTNPQA64N/bundle.json","state_url":"https://pith.science/pith/RIGRWMA5S4DFD7YJMQTNPQA64N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RIGRWMA5S4DFD7YJMQTNPQA64N/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":"2026-06-03T09:37:51Z","links":{"resolver":"https://pith.science/pith/RIGRWMA5S4DFD7YJMQTNPQA64N","bundle":"https://pith.science/pith/RIGRWMA5S4DFD7YJMQTNPQA64N/bundle.json","state":"https://pith.science/pith/RIGRWMA5S4DFD7YJMQTNPQA64N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RIGRWMA5S4DFD7YJMQTNPQA64N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RIGRWMA5S4DFD7YJMQTNPQA64N","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":"fb558bc9d5f8becc6e4a672fe65ed90b1faa6350419eb2a1348d95d110e2ae41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-04-08T18:12:12Z","title_canon_sha256":"39d70d376893ad878c0d152fe59cf67d595fa038f99541ad02a71672b9070192"},"schema_version":"1.0","source":{"id":"1604.02417","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02417","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02417v1","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02417","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"pith_short_12","alias_value":"RIGRWMA5S4DF","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RIGRWMA5S4DFD7YJ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RIGRWMA5","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:2d6a5ec03a8d61beb3c3d011b3e1a70270f21caab269d6fef178c0475abc1089","target":"graph","created_at":"2026-05-18T00:44:01Z","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":"A one-parameter family of time-reversible systems on $\\mathbb{T}^3$ is considered. It is shown that the dynamics is not conservative, namely the attractor and repeller intersect but not coincide. We explain this as the manifestation of the so-called mixed dynamics phenomenon which corresponds to a persistent intersection of the closure of stable periodic orbits and the closure of the completely unstable periodic orbits. We search for the stable and unstable periodic orbits indirectly, by finding non-conservative saddle periodic orbits and heteroclinic connections between them. In this way, we ","authors_text":"Alexander S. Gonchenko, Alexey O. Kazakov, Dmitry V. Turaev, Sergey V. Gonchenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-04-08T18:12:12Z","title":"On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02417","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:eca03310a7263f5f714a871f804acdab686a62a8aa260db4416024c187ffa12f","target":"record","created_at":"2026-05-18T00:44:01Z","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":"fb558bc9d5f8becc6e4a672fe65ed90b1faa6350419eb2a1348d95d110e2ae41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-04-08T18:12:12Z","title_canon_sha256":"39d70d376893ad878c0d152fe59cf67d595fa038f99541ad02a71672b9070192"},"schema_version":"1.0","source":{"id":"1604.02417","kind":"arxiv","version":1}},"canonical_sha256":"8a0d1b301d970651ff096426d7c01ee36406d2b4b0249d2b7bb50efae182ddb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a0d1b301d970651ff096426d7c01ee36406d2b4b0249d2b7bb50efae182ddb4","first_computed_at":"2026-05-18T00:44:01.265934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:01.265934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sL7Ixu2+E1BRu1yIQfGfpuyckxhAfaGFTlu8IOpsvQcnulTKWt/bqGUq79cAy5kZEZ+tuzcZTsDXKWmbi5/jAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:01.266396Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.02417","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eca03310a7263f5f714a871f804acdab686a62a8aa260db4416024c187ffa12f","sha256:2d6a5ec03a8d61beb3c3d011b3e1a70270f21caab269d6fef178c0475abc1089"],"state_sha256":"a5bf39f330c292c50667e989b451d2036f998ac3b6846d24798c52597dc9069b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yjwqMOOdBVCQURmq6kTOIy10pUT65iIl+p+WvXegxU6Q5qopg8LyNihTEKRagptdjZQ0uET9ZTjKNVWKcDFhBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:37:51.599659Z","bundle_sha256":"c21b6eda8a3c166218eb6789946502310a3ff41b55cfa49250a399ece3a07294"}}