{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KUMR542SXHTCHAKTU4DEZYGZSX","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":"a4cf514caea4bcc9a50941357d71493e7bbb48300bbe0dabadd8ec05fa5c0a43","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-12-02T01:57:36Z","title_canon_sha256":"6c2949450b755c8aeaaa77bba68353e2de38014a302747e59ca8ff41f719a235"},"schema_version":"1.0","source":{"id":"1812.00299","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00299","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00299v2","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00299","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"pith_short_12","alias_value":"KUMR542SXHTC","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KUMR542SXHTCHAKT","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KUMR542S","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:3785f5ff0b000db9efe6e957bcc5d9f5a45c5c2bbf08c923a326616a833b7d00","target":"graph","created_at":"2026-05-17T23:54:06Z","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 note we discuss three interconnected problems about dynamics of Hamiltonian or, more generally, just smooth diffeomorphisms. The first two concern the existence and properties of the maps whose iterations approximate the identity map with respect to some norm, e.g., $C^1$- or $C^0$-norm for general diffeomorphisms and the $\\gamma$-norm in the Hamiltonian case, and the third problem is the Lagrangian Poincar\\'e recurrence conjecture.","authors_text":"Basak Z. Gurel, Viktor L. Ginzburg","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-12-02T01:57:36Z","title":"Approximate Identities and Lagrangian Poincar\\'e Recurrence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00299","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":"sha256:81b83550e0f9aabbf35480b53daebefd3c69f9abacc4873f027554af5b1a2383","target":"record","created_at":"2026-05-17T23:54:06Z","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":"a4cf514caea4bcc9a50941357d71493e7bbb48300bbe0dabadd8ec05fa5c0a43","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-12-02T01:57:36Z","title_canon_sha256":"6c2949450b755c8aeaaa77bba68353e2de38014a302747e59ca8ff41f719a235"},"schema_version":"1.0","source":{"id":"1812.00299","kind":"arxiv","version":2}},"canonical_sha256":"55191ef352b9e6238153a7064ce0d995d9d865d963f4d3c2d8432e7b43e2d29e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55191ef352b9e6238153a7064ce0d995d9d865d963f4d3c2d8432e7b43e2d29e","first_computed_at":"2026-05-17T23:54:06.965900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:06.965900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eGuvjbUObK4YMvRCH/sSXZNrpsOMbZoqTUVYWm+YuZ2pibP4GMo6yUknt4vDidGAlxxPbSOWTopqK2Og7uDVBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:06.966394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.00299","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81b83550e0f9aabbf35480b53daebefd3c69f9abacc4873f027554af5b1a2383","sha256:3785f5ff0b000db9efe6e957bcc5d9f5a45c5c2bbf08c923a326616a833b7d00"],"state_sha256":"abc608e451edec568882bdb5e688325cbacfba9ebbbfa6ef0ac9e202353fc93f"}