{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SVHAEYL74Z2G5XSIHDAOCUCLMC","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":"b4debcfb4946f243aac0e5edf736dcd445897cdcafc549a81717ffb9dcbf29b5","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-12-31T05:08:27Z","title_canon_sha256":"5c267bafb0469f53ab5a4f6203a335a2b75f58400859ae92651d479b902dfb7d"},"schema_version":"1.0","source":{"id":"1201.0225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0225","created_at":"2026-05-18T04:05:25Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0225v1","created_at":"2026-05-18T04:05:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0225","created_at":"2026-05-18T04:05:25Z"},{"alias_kind":"pith_short_12","alias_value":"SVHAEYL74Z2G","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SVHAEYL74Z2G5XSI","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SVHAEYL7","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:0f32a823cdd7a29fe0114b7454fc7547f070aee544285c4cea2f71332cfcfd32","target":"graph","created_at":"2026-05-18T04:05:25Z","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":"Symplectic integrators constructed from Hamiltonian and Lie formalisms are obtained as symplectic maps whose flow follows the exact solution of a \"sourrounded\" Hamiltonian K = H + h^k H_1. Those modified Hamiltonians depends virtually on the time by h. When the numerical integration of a Hamiltonian system involves more than one symplectic scheme as in the parallel-in-time algorithms, there are not a simple way to control the dynamical behavior of the error Hamiltonian. The interplay of to different symplectic integrators can degenerate their behavior if both have different dynamical propertie","authors_text":"Hugo Jim\\'enez-P\\'erez","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-12-31T05:08:27Z","title":"Symplectic integrators in the realm of Hofer's geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0225","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":"sha256:88633e328af112919ea5b86f643bf752624ba8a4bd6bba174e385276b3e8612d","target":"record","created_at":"2026-05-18T04:05:25Z","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":"b4debcfb4946f243aac0e5edf736dcd445897cdcafc549a81717ffb9dcbf29b5","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-12-31T05:08:27Z","title_canon_sha256":"5c267bafb0469f53ab5a4f6203a335a2b75f58400859ae92651d479b902dfb7d"},"schema_version":"1.0","source":{"id":"1201.0225","kind":"arxiv","version":1}},"canonical_sha256":"954e02617fe6746ede4838c0e1504b60be1ea61270b867b4946b4c7059fa15fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"954e02617fe6746ede4838c0e1504b60be1ea61270b867b4946b4c7059fa15fb","first_computed_at":"2026-05-18T04:05:25.806907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:25.806907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ITfrCfATvObSVvCQpwni8ztslanE5WIRj9tS0HXmmYfeSUMNbeOMxTSSHbI/jTFnfHS5CDAuK8dVGA13h96LDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:25.807670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88633e328af112919ea5b86f643bf752624ba8a4bd6bba174e385276b3e8612d","sha256:0f32a823cdd7a29fe0114b7454fc7547f070aee544285c4cea2f71332cfcfd32"],"state_sha256":"d0f7c7056388502bc1c788d85489118eff62a105072359c30b58ff5bb3c30de0"}