{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WXXHV3KFQK4CEO4Z6GKGVPXDDC","short_pith_number":"pith:WXXHV3KF","canonical_record":{"source":{"id":"1509.00419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-01T17:59:17Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"f1aab1282753159fae5bc8e930405d2a3a9974c1050f4e04c8b1e4537b83d06b","abstract_canon_sha256":"096e7c85f00e754eb8ef610ed4b032e0cc80e962b4f17db20a3c41b23a2aaab5"},"schema_version":"1.0"},"canonical_sha256":"b5ee7aed4582b8223b99f1946abee31897088a0bb698d7e06d6d1538217cac09","source":{"kind":"arxiv","id":"1509.00419","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00419","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00419v1","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00419","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"pith_short_12","alias_value":"WXXHV3KFQK4C","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WXXHV3KFQK4CEO4Z","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WXXHV3KF","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WXXHV3KFQK4CEO4Z6GKGVPXDDC","target":"record","payload":{"canonical_record":{"source":{"id":"1509.00419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-01T17:59:17Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"f1aab1282753159fae5bc8e930405d2a3a9974c1050f4e04c8b1e4537b83d06b","abstract_canon_sha256":"096e7c85f00e754eb8ef610ed4b032e0cc80e962b4f17db20a3c41b23a2aaab5"},"schema_version":"1.0"},"canonical_sha256":"b5ee7aed4582b8223b99f1946abee31897088a0bb698d7e06d6d1538217cac09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:14.140275Z","signature_b64":"x35EIT3i7EJ1cmxy5MW4SkfJB3IqHA5vx784yFzvFLevxgXaLnSYW7JNHlu7QCqmn0ylO0MoAWDVMbDgGCQeAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5ee7aed4582b8223b99f1946abee31897088a0bb698d7e06d6d1538217cac09","last_reissued_at":"2026-05-18T01:34:14.139516Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:14.139516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.00419","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":"2026-05-18T01:34:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VcOcQW3Cx0WRabr80jSfchvBEhheN1OthTeMyCrVLz/QKg3HV4/vewKB5dDIWFjI/CxqVdpL+Te+jlaxrRgVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:51:55.678226Z"},"content_sha256":"0dd7a7d665c631105b9d43f1cc8cd22f10006f6ce02ab64486ad0dadf71e54f3","schema_version":"1.0","event_id":"sha256:0dd7a7d665c631105b9d43f1cc8cd22f10006f6ce02ab64486ad0dadf71e54f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WXXHV3KFQK4CEO4Z6GKGVPXDDC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hamilton-Jacobi theory, Symmetries and Coisotropic Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"David Mart\\'in de Diego, Manuel de Le\\'on, Miguel Vaquero","submitted_at":"2015-09-01T17:59:17Z","abstract_excerpt":"Reduction theory has played a major role in the study of Hamiltonian systems. On the other hand, the Hamilton-Jacobi theory is one of the main tools to integrate the dynamics of certain Hamiltonian problems and a topic of research on its own. Moreover, the construction of several symplectic integrators rely on approximations of a complete solution of the Hamilton-Jacobi equation. The natural question that we address in this paper is how these two topics (reduction and Hamilton-Jacobi theory) fit together. We obtain a reduction and reconstruction procedure for the Hamilton-Jacobi equation with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00419","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":"2026-05-18T01:34:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/RpH0IF72Nrea0E1ul3ZYkBTCDLdMV5kBWn+FaIHNqIZDWbnw2tsYX6g5q9c2j2PBtLAMkYyp5jvsJa0CZAlBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:51:55.678584Z"},"content_sha256":"e9dda1d6c05d322a9911386766e016bedbdea33670d8e78296fd4f89cafc4aac","schema_version":"1.0","event_id":"sha256:e9dda1d6c05d322a9911386766e016bedbdea33670d8e78296fd4f89cafc4aac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WXXHV3KFQK4CEO4Z6GKGVPXDDC/bundle.json","state_url":"https://pith.science/pith/WXXHV3KFQK4CEO4Z6GKGVPXDDC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WXXHV3KFQK4CEO4Z6GKGVPXDDC/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":"2026-05-31T01:51:55Z","links":{"resolver":"https://pith.science/pith/WXXHV3KFQK4CEO4Z6GKGVPXDDC","bundle":"https://pith.science/pith/WXXHV3KFQK4CEO4Z6GKGVPXDDC/bundle.json","state":"https://pith.science/pith/WXXHV3KFQK4CEO4Z6GKGVPXDDC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WXXHV3KFQK4CEO4Z6GKGVPXDDC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WXXHV3KFQK4CEO4Z6GKGVPXDDC","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":"096e7c85f00e754eb8ef610ed4b032e0cc80e962b4f17db20a3c41b23a2aaab5","cross_cats_sorted":["math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-01T17:59:17Z","title_canon_sha256":"f1aab1282753159fae5bc8e930405d2a3a9974c1050f4e04c8b1e4537b83d06b"},"schema_version":"1.0","source":{"id":"1509.00419","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00419","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00419v1","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00419","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"pith_short_12","alias_value":"WXXHV3KFQK4C","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WXXHV3KFQK4CEO4Z","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WXXHV3KF","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:e9dda1d6c05d322a9911386766e016bedbdea33670d8e78296fd4f89cafc4aac","target":"graph","created_at":"2026-05-18T01:34:14Z","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":"Reduction theory has played a major role in the study of Hamiltonian systems. On the other hand, the Hamilton-Jacobi theory is one of the main tools to integrate the dynamics of certain Hamiltonian problems and a topic of research on its own. Moreover, the construction of several symplectic integrators rely on approximations of a complete solution of the Hamilton-Jacobi equation. The natural question that we address in this paper is how these two topics (reduction and Hamilton-Jacobi theory) fit together. We obtain a reduction and reconstruction procedure for the Hamilton-Jacobi equation with ","authors_text":"David Mart\\'in de Diego, Manuel de Le\\'on, Miguel Vaquero","cross_cats":["math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-01T17:59:17Z","title":"Hamilton-Jacobi theory, Symmetries and Coisotropic Reduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00419","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":"sha256:0dd7a7d665c631105b9d43f1cc8cd22f10006f6ce02ab64486ad0dadf71e54f3","target":"record","created_at":"2026-05-18T01:34:14Z","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":"096e7c85f00e754eb8ef610ed4b032e0cc80e962b4f17db20a3c41b23a2aaab5","cross_cats_sorted":["math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-01T17:59:17Z","title_canon_sha256":"f1aab1282753159fae5bc8e930405d2a3a9974c1050f4e04c8b1e4537b83d06b"},"schema_version":"1.0","source":{"id":"1509.00419","kind":"arxiv","version":1}},"canonical_sha256":"b5ee7aed4582b8223b99f1946abee31897088a0bb698d7e06d6d1538217cac09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5ee7aed4582b8223b99f1946abee31897088a0bb698d7e06d6d1538217cac09","first_computed_at":"2026-05-18T01:34:14.139516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:14.139516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x35EIT3i7EJ1cmxy5MW4SkfJB3IqHA5vx784yFzvFLevxgXaLnSYW7JNHlu7QCqmn0ylO0MoAWDVMbDgGCQeAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:14.140275Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00419","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dd7a7d665c631105b9d43f1cc8cd22f10006f6ce02ab64486ad0dadf71e54f3","sha256:e9dda1d6c05d322a9911386766e016bedbdea33670d8e78296fd4f89cafc4aac"],"state_sha256":"7fd33011b0706cdb4f93770d4935e51df3edce090e4a7bea05f79c763d5b1256"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/OmTxerHKNhhBbzaYYxjMJdkiqRFfqyBx0WEckJWbq5pUNwifr78ESLiZBcNtSfuTNov6GwNB6FOnAy77eSHBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:51:55.680554Z","bundle_sha256":"fd4f444a615baff23090a3976cd4ce2969e9e710cb8dfafba7c923795173b411"}}