{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XFXQ5FBSBMO72IET6IKHZFEHOT","short_pith_number":"pith:XFXQ5FBS","canonical_record":{"source":{"id":"1803.01427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-04T21:46:09Z","cross_cats_sorted":["math-ph","math.DG","math.MP","math.SG"],"title_canon_sha256":"416adcfc52980941b4490d702082184ba3c34f6d4d849eda171e38f450d2cd0e","abstract_canon_sha256":"c4e7a47fb11eec1235740df776cc55631904301ccfb65248d2550328280c2933"},"schema_version":"1.0"},"canonical_sha256":"b96f0e94320b1dfd2093f2147c948774e299848f3837269c5a28d36ea03f2ccc","source":{"kind":"arxiv","id":"1803.01427","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01427","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01427v1","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01427","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"XFXQ5FBSBMO7","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XFXQ5FBSBMO72IET","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XFXQ5FBS","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XFXQ5FBSBMO72IET6IKHZFEHOT","target":"record","payload":{"canonical_record":{"source":{"id":"1803.01427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-04T21:46:09Z","cross_cats_sorted":["math-ph","math.DG","math.MP","math.SG"],"title_canon_sha256":"416adcfc52980941b4490d702082184ba3c34f6d4d849eda171e38f450d2cd0e","abstract_canon_sha256":"c4e7a47fb11eec1235740df776cc55631904301ccfb65248d2550328280c2933"},"schema_version":"1.0"},"canonical_sha256":"b96f0e94320b1dfd2093f2147c948774e299848f3837269c5a28d36ea03f2ccc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:00.701784Z","signature_b64":"8fb8r4urRhar5GgKg+vh+Sm1rnRu1GnUumZJ53qcz/oJfwPvzRRiqUbMPfQi6nzn8pdGArUq1EpAqFWjJzMPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b96f0e94320b1dfd2093f2147c948774e299848f3837269c5a28d36ea03f2ccc","last_reissued_at":"2026-05-18T00:22:00.701246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:00.701246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.01427","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vmdc63+c5Z7O/d9fulhDEv0ipvUT8TihC1L5bIrj5hIjqHxvsBuzpEJTGq1tkmX3RzqOkND0W0b7H13lNB/RAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:21:12.983148Z"},"content_sha256":"a1ad015fa97b8858c24e5c6845bca213223e074af5c2b46f0c4dd1055c639c01","schema_version":"1.0","event_id":"sha256:a1ad015fa97b8858c24e5c6845bca213223e074af5c2b46f0c4dd1055c639c01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XFXQ5FBSBMO72IET6IKHZFEHOT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lie-Poisson integrators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP","math.SG"],"primary_cat":"math.NA","authors_text":"David Martin de Diego","submitted_at":"2018-03-04T21:46:09Z","abstract_excerpt":"In this paper, we discuss the geometric integration of hamiltonian systems on Poisson manifolds, in particular, in the case, when the Poisson structure is induced by a Lie algebra, that is, it is a Lie-Poisson structure.\n  A Hamiltonian system on a Poisson manifold $(P, \\Pi)$ is a smooth manifold $P$ equipped with a bivector field $\\Pi$ satisfying $[\\Pi, \\Pi]=0$ (Jacobi identity), inducing the Poisson bracket on $C^{\\infty}(P)$, $\\{f, g\\}\\equiv \\Pi(df, dg)$ where $f, g\\in C^{\\infty}(P)$. For any $f\\in C^{\\infty}(P)$ the Hamiltonian vector field is defined by $X_f(g)=\\{g, f\\}$. The Hamiltonian "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01427","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+YBGF7/3v2hcU0L4wjfEQBjO3OSAnCnwuz8dCsk+oXGFnrdoqj0/o2HcTrRQAXB8MoZpsaASkDaITs19rlNBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:21:12.983807Z"},"content_sha256":"400c18fecdbb1224009c917051fb176ed20642e34bc1f7a1731a6acb93e3fb2f","schema_version":"1.0","event_id":"sha256:400c18fecdbb1224009c917051fb176ed20642e34bc1f7a1731a6acb93e3fb2f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XFXQ5FBSBMO72IET6IKHZFEHOT/bundle.json","state_url":"https://pith.science/pith/XFXQ5FBSBMO72IET6IKHZFEHOT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XFXQ5FBSBMO72IET6IKHZFEHOT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T13:21:12Z","links":{"resolver":"https://pith.science/pith/XFXQ5FBSBMO72IET6IKHZFEHOT","bundle":"https://pith.science/pith/XFXQ5FBSBMO72IET6IKHZFEHOT/bundle.json","state":"https://pith.science/pith/XFXQ5FBSBMO72IET6IKHZFEHOT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XFXQ5FBSBMO72IET6IKHZFEHOT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XFXQ5FBSBMO72IET6IKHZFEHOT","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":"c4e7a47fb11eec1235740df776cc55631904301ccfb65248d2550328280c2933","cross_cats_sorted":["math-ph","math.DG","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-04T21:46:09Z","title_canon_sha256":"416adcfc52980941b4490d702082184ba3c34f6d4d849eda171e38f450d2cd0e"},"schema_version":"1.0","source":{"id":"1803.01427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01427","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01427v1","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01427","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"XFXQ5FBSBMO7","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XFXQ5FBSBMO72IET","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XFXQ5FBS","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:400c18fecdbb1224009c917051fb176ed20642e34bc1f7a1731a6acb93e3fb2f","target":"graph","created_at":"2026-05-18T00:22:00Z","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 paper, we discuss the geometric integration of hamiltonian systems on Poisson manifolds, in particular, in the case, when the Poisson structure is induced by a Lie algebra, that is, it is a Lie-Poisson structure.\n  A Hamiltonian system on a Poisson manifold $(P, \\Pi)$ is a smooth manifold $P$ equipped with a bivector field $\\Pi$ satisfying $[\\Pi, \\Pi]=0$ (Jacobi identity), inducing the Poisson bracket on $C^{\\infty}(P)$, $\\{f, g\\}\\equiv \\Pi(df, dg)$ where $f, g\\in C^{\\infty}(P)$. For any $f\\in C^{\\infty}(P)$ the Hamiltonian vector field is defined by $X_f(g)=\\{g, f\\}$. The Hamiltonian ","authors_text":"David Martin de Diego","cross_cats":["math-ph","math.DG","math.MP","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-04T21:46:09Z","title":"Lie-Poisson integrators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01427","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:a1ad015fa97b8858c24e5c6845bca213223e074af5c2b46f0c4dd1055c639c01","target":"record","created_at":"2026-05-18T00:22:00Z","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":"c4e7a47fb11eec1235740df776cc55631904301ccfb65248d2550328280c2933","cross_cats_sorted":["math-ph","math.DG","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-04T21:46:09Z","title_canon_sha256":"416adcfc52980941b4490d702082184ba3c34f6d4d849eda171e38f450d2cd0e"},"schema_version":"1.0","source":{"id":"1803.01427","kind":"arxiv","version":1}},"canonical_sha256":"b96f0e94320b1dfd2093f2147c948774e299848f3837269c5a28d36ea03f2ccc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b96f0e94320b1dfd2093f2147c948774e299848f3837269c5a28d36ea03f2ccc","first_computed_at":"2026-05-18T00:22:00.701246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:00.701246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8fb8r4urRhar5GgKg+vh+Sm1rnRu1GnUumZJ53qcz/oJfwPvzRRiqUbMPfQi6nzn8pdGArUq1EpAqFWjJzMPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:00.701784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.01427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1ad015fa97b8858c24e5c6845bca213223e074af5c2b46f0c4dd1055c639c01","sha256:400c18fecdbb1224009c917051fb176ed20642e34bc1f7a1731a6acb93e3fb2f"],"state_sha256":"1e9a70da630b91943dc4720aa46eee973025a76a1913da0697d2086de14f0f6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NONvap5vF5DccHqsuxI/W1zbsAXC19l2zgAmWvwszTkxUUXgQfoGeH6ur6kS8gAOPIopru4bXUCYOWy9kvPiAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T13:21:12.987040Z","bundle_sha256":"5c2e2c61374f159f6bb52d0ac7f795a6cc3797e184b5cf5f420d754941e3df91"}}