{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3GNPGO5M6AOWD6TP76UAJL5VIQ","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":"f0da604ca0bcd789d1a60a0574ff8fd664a5d39bec7a5e486dbeecb319f8d64f","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-03T18:52:30Z","title_canon_sha256":"d55526ef2a625720b23833d6220d762e2fcc5b14ee63b27450c949d6074d68c4"},"schema_version":"1.0","source":{"id":"1310.1063","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1063","created_at":"2026-05-18T02:48:09Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1063v1","created_at":"2026-05-18T02:48:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1063","created_at":"2026-05-18T02:48:09Z"},{"alias_kind":"pith_short_12","alias_value":"3GNPGO5M6AOW","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3GNPGO5M6AOWD6TP","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3GNPGO5M","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:5d2b5f58acfbdb55b31296100e74dce9224d99d6bb265e87dfde1db22f3a7943","target":"graph","created_at":"2026-05-18T02:48:09Z","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 prove that any perturbation of the symplectic part of the derivative of a Poisson diffeomorphism can be realized as the derivative of a $C^1$-close Poisson diffeomorphism. We also show that a similar property holds for the Poincar\\'e map of a Hamiltonian on a Poisson manifold. These results are the conservative counterparts of the Franks lemma, a perturbation tool used in several contexts most notably in the theory of smooth dynamical systems.","authors_text":"Hassan Najafi Alishah, Jo\\~ao Lopes Dias","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-03T18:52:30Z","title":"Realization of tangent perturbations in discrete and continuous time conservative systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1063","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":"sha256:7b2c61360694dd1b3cb65ff1f2a7b24e5021254368b0de429f795250ae9e9272","target":"record","created_at":"2026-05-18T02:48:09Z","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":"f0da604ca0bcd789d1a60a0574ff8fd664a5d39bec7a5e486dbeecb319f8d64f","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-03T18:52:30Z","title_canon_sha256":"d55526ef2a625720b23833d6220d762e2fcc5b14ee63b27450c949d6074d68c4"},"schema_version":"1.0","source":{"id":"1310.1063","kind":"arxiv","version":1}},"canonical_sha256":"d99af33bacf01d61fa6fffa804afb5440f2c4f9dbefc6e05101225a623bd9cf8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d99af33bacf01d61fa6fffa804afb5440f2c4f9dbefc6e05101225a623bd9cf8","first_computed_at":"2026-05-18T02:48:09.905057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:09.905057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L51uDKyZibNt5Ygzpq2ASqag828nRPYVzVzg/VTaFx+2sX6IWj1XEthOHiV9xozmTHsfesNFfPctWOYiV5X8AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:09.905490Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1063","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b2c61360694dd1b3cb65ff1f2a7b24e5021254368b0de429f795250ae9e9272","sha256:5d2b5f58acfbdb55b31296100e74dce9224d99d6bb265e87dfde1db22f3a7943"],"state_sha256":"cab2d556b8e36462787defb8ea741b1d7c15996c91c76d6373170ef58cf0ab0d"}