{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DLMPSNPIOORBNZGKWK3SKIAWJQ","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":"04f64b3c412a83a93029fb2bffd17d684e317ab857b1ffd2622affdab9302299","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-10-16T06:03:48Z","title_canon_sha256":"1eec84749424c2d0cbdb684a45062d7c7e25227e4b05b48b9fb9884e4091f277"},"schema_version":"1.0","source":{"id":"1410.4306","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.4306","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"arxiv_version","alias_value":"1410.4306v1","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4306","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"pith_short_12","alias_value":"DLMPSNPIOORB","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DLMPSNPIOORBNZGK","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DLMPSNPI","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:afef3bbd91ebbe44c058be585aad0deea749e8092b28b09d0cd7f433db72918d","target":"graph","created_at":"2026-05-18T02:39:56Z","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":"The well known stability conjecture of Palis and Smale states that if a diffeomorphism is structurally stable then the chain recurrent set is hyperbolic. It is natural to ask if this type of results is true for an individual chain class, that is, whether or not every structurally stable chain class is hyperbolic. Regarding the notion of structural stability, there is a subtle difference between the case of a whole system and the case of an individual chain class. The later case is more delicate and contains additional difficulties. In this paper we prove a result of this type for the later cas","authors_text":"Lan Wen, Xiao Wen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-10-16T06:03:48Z","title":"Codimension one structurally stable chain classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4306","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":"sha256:10fabd5faea3a09436b93809459686ce92377c7f9e62345f38451f1975932bc1","target":"record","created_at":"2026-05-18T02:39:56Z","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":"04f64b3c412a83a93029fb2bffd17d684e317ab857b1ffd2622affdab9302299","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-10-16T06:03:48Z","title_canon_sha256":"1eec84749424c2d0cbdb684a45062d7c7e25227e4b05b48b9fb9884e4091f277"},"schema_version":"1.0","source":{"id":"1410.4306","kind":"arxiv","version":1}},"canonical_sha256":"1ad8f935e873a216e4cab2b72520164c0161978e5ad40b9496af559e4ec24e50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ad8f935e873a216e4cab2b72520164c0161978e5ad40b9496af559e4ec24e50","first_computed_at":"2026-05-18T02:39:56.454132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:56.454132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gaFPzVdczzQH8J35EWyhQ6Q+x6CmO7VeoQmnmRc07qEw4y9QWwcQJR6/kLGqGSv7/m8PCzHI2LRT5TUGEbn4Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:56.454529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.4306","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10fabd5faea3a09436b93809459686ce92377c7f9e62345f38451f1975932bc1","sha256:afef3bbd91ebbe44c058be585aad0deea749e8092b28b09d0cd7f433db72918d"],"state_sha256":"d60e1d653a900004d4b9802f934d593f7aa4958409abddb4a0d03d5bc50af2b8"}