{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YV6WSTGXK5VPLTKIQUUPC2JDED","short_pith_number":"pith:YV6WSTGX","canonical_record":{"source":{"id":"1406.3856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-15T19:48:29Z","cross_cats_sorted":[],"title_canon_sha256":"f31a7a84efa2b5b3aa59ba23c718011f6c7121d5455532bbe2de417bf3da30a3","abstract_canon_sha256":"552743e24e52ece1645a29617852d851b320d9260cf219494ce649c0aee46064"},"schema_version":"1.0"},"canonical_sha256":"c57d694cd7576af5cd488528f1692320c15d7eebd88fefb4d3dca4b0635ac5d1","source":{"kind":"arxiv","id":"1406.3856","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3856","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3856v1","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3856","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"pith_short_12","alias_value":"YV6WSTGXK5VP","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YV6WSTGXK5VPLTKI","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YV6WSTGX","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YV6WSTGXK5VPLTKIQUUPC2JDED","target":"record","payload":{"canonical_record":{"source":{"id":"1406.3856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-15T19:48:29Z","cross_cats_sorted":[],"title_canon_sha256":"f31a7a84efa2b5b3aa59ba23c718011f6c7121d5455532bbe2de417bf3da30a3","abstract_canon_sha256":"552743e24e52ece1645a29617852d851b320d9260cf219494ce649c0aee46064"},"schema_version":"1.0"},"canonical_sha256":"c57d694cd7576af5cd488528f1692320c15d7eebd88fefb4d3dca4b0635ac5d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:39.604392Z","signature_b64":"prZrN92GzHp7Mo866tUbytD42Orh4UzEjrVvMdBigj2Jy6naNjIBgVU2dhtizQJy99e0IpmCjvWq1C46XyEkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c57d694cd7576af5cd488528f1692320c15d7eebd88fefb4d3dca4b0635ac5d1","last_reissued_at":"2026-05-18T02:49:39.604063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:39.604063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.3856","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":"2026-05-18T02:49:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sPgwAQWBad+65fNJvsYJ5yQQCFuZe6sTUfkmAwxiEdqMtyNXg0+eOaNEh14PkIhwB12IWhZVRLJYhR9hmJ1tAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:38:32.470235Z"},"content_sha256":"921d504dee130e25739a917af8eb29804bf2e0008c6ab60c7a44a38f934ae9bc","schema_version":"1.0","event_id":"sha256:921d504dee130e25739a917af8eb29804bf2e0008c6ab60c7a44a38f934ae9bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YV6WSTGXK5VPLTKIQUUPC2JDED","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hopf bifurcation and heteroclinic cycles in a class of $\\mathbb{D}_2-$equivariant systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adrian C. Murza","submitted_at":"2014-06-15T19:48:29Z","abstract_excerpt":"In this paper we analyze a generic dynamical system with $\\mathbb{D}_2$ constructed via a Cayley graph. We study the Hopf bifurcation and find conditions for obtaining a unique branch of periodic solutions. Our main result comes from analyzing the system under weak coupling, where we identify the conditions for heteroclinic cycle between four equilibria in the two-dimensional fixed point subspace of some of the isotropy subgroups of $\\mathbb{D}_2\\times\\mathbb{S}^1.$ We also analyze the stability of the heteroclinic cycle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3856","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":"2026-05-18T02:49:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KD/zDLRBmkmFUecjvw/dMWV1LIEAO3lQCKVQtzjzCChp6V80VAc3c5QLOcCllQegblhwU3Qh91hG2+X8UcYGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:38:32.470989Z"},"content_sha256":"e4a670a8ffeb137a9d1fb527d67ac40fe117466b1851a1f18f874d4ac67166e9","schema_version":"1.0","event_id":"sha256:e4a670a8ffeb137a9d1fb527d67ac40fe117466b1851a1f18f874d4ac67166e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YV6WSTGXK5VPLTKIQUUPC2JDED/bundle.json","state_url":"https://pith.science/pith/YV6WSTGXK5VPLTKIQUUPC2JDED/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YV6WSTGXK5VPLTKIQUUPC2JDED/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":"2026-05-31T09:38:32Z","links":{"resolver":"https://pith.science/pith/YV6WSTGXK5VPLTKIQUUPC2JDED","bundle":"https://pith.science/pith/YV6WSTGXK5VPLTKIQUUPC2JDED/bundle.json","state":"https://pith.science/pith/YV6WSTGXK5VPLTKIQUUPC2JDED/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YV6WSTGXK5VPLTKIQUUPC2JDED/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YV6WSTGXK5VPLTKIQUUPC2JDED","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":"552743e24e52ece1645a29617852d851b320d9260cf219494ce649c0aee46064","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-15T19:48:29Z","title_canon_sha256":"f31a7a84efa2b5b3aa59ba23c718011f6c7121d5455532bbe2de417bf3da30a3"},"schema_version":"1.0","source":{"id":"1406.3856","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3856","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3856v1","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3856","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"pith_short_12","alias_value":"YV6WSTGXK5VP","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YV6WSTGXK5VPLTKI","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YV6WSTGX","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:e4a670a8ffeb137a9d1fb527d67ac40fe117466b1851a1f18f874d4ac67166e9","target":"graph","created_at":"2026-05-18T02:49:39Z","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":"In this paper we analyze a generic dynamical system with $\\mathbb{D}_2$ constructed via a Cayley graph. We study the Hopf bifurcation and find conditions for obtaining a unique branch of periodic solutions. Our main result comes from analyzing the system under weak coupling, where we identify the conditions for heteroclinic cycle between four equilibria in the two-dimensional fixed point subspace of some of the isotropy subgroups of $\\mathbb{D}_2\\times\\mathbb{S}^1.$ We also analyze the stability of the heteroclinic cycle.","authors_text":"Adrian C. Murza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-15T19:48:29Z","title":"Hopf bifurcation and heteroclinic cycles in a class of $\\mathbb{D}_2-$equivariant systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3856","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":"sha256:921d504dee130e25739a917af8eb29804bf2e0008c6ab60c7a44a38f934ae9bc","target":"record","created_at":"2026-05-18T02:49:39Z","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":"552743e24e52ece1645a29617852d851b320d9260cf219494ce649c0aee46064","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-15T19:48:29Z","title_canon_sha256":"f31a7a84efa2b5b3aa59ba23c718011f6c7121d5455532bbe2de417bf3da30a3"},"schema_version":"1.0","source":{"id":"1406.3856","kind":"arxiv","version":1}},"canonical_sha256":"c57d694cd7576af5cd488528f1692320c15d7eebd88fefb4d3dca4b0635ac5d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c57d694cd7576af5cd488528f1692320c15d7eebd88fefb4d3dca4b0635ac5d1","first_computed_at":"2026-05-18T02:49:39.604063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:39.604063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"prZrN92GzHp7Mo866tUbytD42Orh4UzEjrVvMdBigj2Jy6naNjIBgVU2dhtizQJy99e0IpmCjvWq1C46XyEkAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:39.604392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3856","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:921d504dee130e25739a917af8eb29804bf2e0008c6ab60c7a44a38f934ae9bc","sha256:e4a670a8ffeb137a9d1fb527d67ac40fe117466b1851a1f18f874d4ac67166e9"],"state_sha256":"6c4cbc34ac323a53105abbf16ef4031b4d2bed25400a356327659fc596664aa0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zRUOoJrwZTVz891zkzBtkFw5FVDdwZOKA6hplJfgq3TOEI5tVmo56XcUY1sEqdzzXhTd0seleEPOehKoGHcQBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T09:38:32.475155Z","bundle_sha256":"a71e94e1a005ca64166745d798cf0043827b807e86f951378f96acc785a72fd1"}}