{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NXJPR3Y6L2ZGAYTO7TXA3ZZCXR","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":"d8e8f338c4d01f79acd3bf815269543eab64848f952176496ce0b6a6860d2734","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-08-13T15:37:22Z","title_canon_sha256":"be59ff52bb4c6fecc9f5ce039df8e4a49f3a4fca00c94cf4c89af405a0678631"},"schema_version":"1.0","source":{"id":"1508.03250","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03250","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03250v4","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03250","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"pith_short_12","alias_value":"NXJPR3Y6L2ZG","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NXJPR3Y6L2ZGAYTO","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NXJPR3Y6","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:73ad98b13a6c87749177c4ee30e5f30cda9a3cee3cc4861e1a90d0b448b2a4d3","target":"graph","created_at":"2026-05-18T00:50:29Z","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 article we introduce a new method for constructing implicit symplectic maps using special symplectic manifolds and Liouvillian forms. This method extends, in a natural way, the method of generating functions to 1-forms which are globally defined on the symplectic manifold. The maps constructed by this method, are related to the symplectic Cayley's transformation and belong to a continuous space of dimension n(2n+1). Applying the implicit map to the discrete Hamilton equations we obtain the generalized symplectic Euler scheme. We show the relations of the elements of this family with ot","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":"2015-08-13T15:37:22Z","title":"Symplectic maps: from generating functions to Liouvillian forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03250","kind":"arxiv","version":4},"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":"sha256:6aaee4ea4c3ae1f49467dbcf7172ba380d1682c5d2373c5a32b0b7f7ae62af66","target":"record","created_at":"2026-05-18T00:50:29Z","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":"d8e8f338c4d01f79acd3bf815269543eab64848f952176496ce0b6a6860d2734","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-08-13T15:37:22Z","title_canon_sha256":"be59ff52bb4c6fecc9f5ce039df8e4a49f3a4fca00c94cf4c89af405a0678631"},"schema_version":"1.0","source":{"id":"1508.03250","kind":"arxiv","version":4}},"canonical_sha256":"6dd2f8ef1e5eb260626efcee0de722bc7950286fd552707debb9301dd9275e45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dd2f8ef1e5eb260626efcee0de722bc7950286fd552707debb9301dd9275e45","first_computed_at":"2026-05-18T00:50:29.889421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:29.889421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IvaBG3Xs9+iJ820RxuCjtW7nFzNCf5Vp4tqqngA4tZ1r0H3mtwzY5bY8KgefBL7ZX0kVpVO5AKSxImr+6zDWBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:29.890018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03250","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6aaee4ea4c3ae1f49467dbcf7172ba380d1682c5d2373c5a32b0b7f7ae62af66","sha256:73ad98b13a6c87749177c4ee30e5f30cda9a3cee3cc4861e1a90d0b448b2a4d3"],"state_sha256":"747b89cb9432de61f2754813df85e4b5d07b791a7f04cde4b6427ba91565c4fa"}