{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UGYZNF7S77PEQAFZSQHIPUWGDO","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":"a82780cdfbc46f8e16474d78b020d21391f2631d827ee7b13ba85ec1497669f4","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-06T11:02:09Z","title_canon_sha256":"c45b89d3adbbaa6b8506bbbd52cd3eb321b8907b469d5a7c34e6be933dda5b9f"},"schema_version":"1.0","source":{"id":"1111.1402","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1402","created_at":"2026-05-18T04:03:42Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1402v4","created_at":"2026-05-18T04:03:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1402","created_at":"2026-05-18T04:03:42Z"},{"alias_kind":"pith_short_12","alias_value":"UGYZNF7S77PE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UGYZNF7S77PEQAFZ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UGYZNF7S","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:6e2dc3467481e0198f204047e4ad7ad4c0a83a7deb14455ffb9449cc386c689b","target":"graph","created_at":"2026-05-18T04:03:42Z","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 show that nontrivial homoclinic trajectories of a family of discrete, nonautonomous, asymptotically hyperbolic systems parametrized by a circle bifurcate from a stationary solution if the asymptotic stable bundles Es(+{\\infty}) and Es(-{\\infty}) of the linearization at the stationary branch are twisted in different ways.","authors_text":"Jacobo Pejsachowicz, Robert Skiba","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-06T11:02:09Z","title":"Topology and Homoclinic Trajectories of Discrete Dynamical Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1402","kind":"arxiv","version":4},"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":"sha256:3749ea35e8b033194c794ac1b7199b3896a42214ad7f956b0df054841ee270b9","target":"record","created_at":"2026-05-18T04:03:42Z","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":"a82780cdfbc46f8e16474d78b020d21391f2631d827ee7b13ba85ec1497669f4","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-06T11:02:09Z","title_canon_sha256":"c45b89d3adbbaa6b8506bbbd52cd3eb321b8907b469d5a7c34e6be933dda5b9f"},"schema_version":"1.0","source":{"id":"1111.1402","kind":"arxiv","version":4}},"canonical_sha256":"a1b19697f2ffde4800b9940e87d2c61bb000debbca22a058c42740edfd499583","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1b19697f2ffde4800b9940e87d2c61bb000debbca22a058c42740edfd499583","first_computed_at":"2026-05-18T04:03:42.741970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:42.741970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4lzLEUF7df3jP8emINST2GnP49V40NajJubgA+O+U0e291AkAUePBuxidfMQcN8puk69p6RSYfEVawGYN5rIDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:42.742428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1402","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3749ea35e8b033194c794ac1b7199b3896a42214ad7f956b0df054841ee270b9","sha256:6e2dc3467481e0198f204047e4ad7ad4c0a83a7deb14455ffb9449cc386c689b"],"state_sha256":"8499d99a72d22e18eb4f8531fe6b4722fdf2744dfca65fa82c1c773c956c8f41"}