{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JHUXHQJVKPEJNAANTUPUOF3BB3","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":"f30eba96350ede15e74b2355d3799f837db6a0ee923dbbedf7ac92f58a80f805","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-10-01T13:58:32Z","title_canon_sha256":"325345be376e263d5abc4b426974657e4665a2bc3604fdbfd0db66b960ce1315"},"schema_version":"1.0","source":{"id":"1310.0298","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0298","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0298v2","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0298","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"pith_short_12","alias_value":"JHUXHQJVKPEJ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JHUXHQJVKPEJNAAN","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JHUXHQJV","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:5005eb27e8376b45b6697ecc16e554c1a1ebd62ede3ca42382922d73bdf5b499","target":"graph","created_at":"2026-05-18T02:28:55Z","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 generic dynamical systems heteroclinic cycles are invariant sets of codimension at least one, but they can be structurally stable in systems which are equivariant under the action of a symmetry group, due to the existence of flow-invariant subspaces. For dynamical systems in R^n the minimal dimension for which such robust heteroclinic cycles can exist is n=3. In this case the list of admissible symmetry groups is short and well-known. The situation is different and more interesting when n=4. In this paper we list all finite groups Gamma such that an open set of smooth Gamma-equivariant dyna","authors_text":"Olga Podvigina, Pascal Chossat","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-10-01T13:58:32Z","title":"Simple heteroclinic cycles in R^4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0298","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:c3902f254a1798bb53d9372d8845f59494d8f38c30d61b605a1ca8ebae10e870","target":"record","created_at":"2026-05-18T02:28:55Z","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":"f30eba96350ede15e74b2355d3799f837db6a0ee923dbbedf7ac92f58a80f805","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-10-01T13:58:32Z","title_canon_sha256":"325345be376e263d5abc4b426974657e4665a2bc3604fdbfd0db66b960ce1315"},"schema_version":"1.0","source":{"id":"1310.0298","kind":"arxiv","version":2}},"canonical_sha256":"49e973c13553c896800d9d1f4717610edbbfc0fb364ef60fb4c2e7251d2cfd63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49e973c13553c896800d9d1f4717610edbbfc0fb364ef60fb4c2e7251d2cfd63","first_computed_at":"2026-05-18T02:28:55.298676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:55.298676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Eghp85OuzuNiY3UBkWxVdwoGi6gXKFKgQLY4h+EhaSS3qvGqDHjnQCCfipcF2yaSJWH6KRJuxoW6qexwyYVHAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:55.299188Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0298","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3902f254a1798bb53d9372d8845f59494d8f38c30d61b605a1ca8ebae10e870","sha256:5005eb27e8376b45b6697ecc16e554c1a1ebd62ede3ca42382922d73bdf5b499"],"state_sha256":"f0ade180f467a4c6a292870c218f150e8f9cb025365a645877cbcb444240d360"}