{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:73ITJ4CETOHBXS4X2OAJKDDGWH","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":"f057f28289de1b0e1c51ea5ccc10c1d833d618458de0f9b2edc2342aa5a73f8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-27T02:34:59Z","title_canon_sha256":"5fec652064a79059674a1d911aa3ce31161b0590a63e86ee782e7e078b8b4399"},"schema_version":"1.0","source":{"id":"1104.5063","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5063","created_at":"2026-05-18T04:00:01Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5063v2","created_at":"2026-05-18T04:00:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5063","created_at":"2026-05-18T04:00:01Z"},{"alias_kind":"pith_short_12","alias_value":"73ITJ4CETOHB","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"73ITJ4CETOHBXS4X","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"73ITJ4CE","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:accfbc7e889a313389aa9e6f04eafe33048344a67d6e49daa74c5583e856808a","target":"graph","created_at":"2026-05-18T04:00:01Z","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":"Let f be a volume-preserving diffeomorphism of a closed C1 n-dimensional Riemannian manifold M: In this paper, we prove the equivalence between the following conditions: (a) f belongs to the C1-interior of the set of volume-preserving diffeomorphisms which satisfy the weak shadowing property, (b) f belongs to the C1-interior of the set of volume-preserving diffeomorphisms which satisfy the limit weak shadowing property, (c) f is Anosov.","authors_text":"Manseob Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-27T02:34:59Z","title":"Volume Preserving Diffeomorphisms with Weak and Limit Weak Shadowing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5063","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":"sha256:0c8deaaa94da3eef6a5a37da1a2ea7445686498cf5e7b4940062de79ea342668","target":"record","created_at":"2026-05-18T04:00:01Z","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":"f057f28289de1b0e1c51ea5ccc10c1d833d618458de0f9b2edc2342aa5a73f8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-27T02:34:59Z","title_canon_sha256":"5fec652064a79059674a1d911aa3ce31161b0590a63e86ee782e7e078b8b4399"},"schema_version":"1.0","source":{"id":"1104.5063","kind":"arxiv","version":2}},"canonical_sha256":"fed134f0449b8e1bcb97d380950c66b1f29f54a6c213af39d4478ea7791c315e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fed134f0449b8e1bcb97d380950c66b1f29f54a6c213af39d4478ea7791c315e","first_computed_at":"2026-05-18T04:00:01.291291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:01.291291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1GjligmKw4mrjSU1KX2v85L2jR1/Op3Oiuemasbm7JgXqcYborZ+6bC19EUqDnDBxNI9XH3RJ0QEMXCWWhO+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:01.291820Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.5063","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c8deaaa94da3eef6a5a37da1a2ea7445686498cf5e7b4940062de79ea342668","sha256:accfbc7e889a313389aa9e6f04eafe33048344a67d6e49daa74c5583e856808a"],"state_sha256":"ead3298c9094f3c614661cbdd4b204fa18efdb367452fe59e1a91dc206c27c40"}