{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:AT3OLY2DZLWHUOTBCFOWM37IE5","short_pith_number":"pith:AT3OLY2D","canonical_record":{"source":{"id":"2305.15490","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-05-24T18:23:25Z","cross_cats_sorted":["cs.LG","cs.NA","math-ph","math.MP","physics.comp-ph"],"title_canon_sha256":"a4475330bec74290fb5ebfcd3b582ce3b7f11fdfcd99e29dd851a307d876c7ff","abstract_canon_sha256":"cbff2eeb9857a06646510cd22d5ebad0f33cea03c8ab024454eeada69a187a1a"},"schema_version":"1.0"},"canonical_sha256":"04f6e5e343caec7a3a61115d666fe8277b6d4c0c4afaa814aed39bba04767de1","source":{"kind":"arxiv","id":"2305.15490","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.15490","created_at":"2026-07-05T06:44:19Z"},{"alias_kind":"arxiv_version","alias_value":"2305.15490v2","created_at":"2026-07-05T06:44:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.15490","created_at":"2026-07-05T06:44:19Z"},{"alias_kind":"pith_short_12","alias_value":"AT3OLY2DZLWH","created_at":"2026-07-05T06:44:19Z"},{"alias_kind":"pith_short_16","alias_value":"AT3OLY2DZLWHUOTB","created_at":"2026-07-05T06:44:19Z"},{"alias_kind":"pith_short_8","alias_value":"AT3OLY2D","created_at":"2026-07-05T06:44:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:AT3OLY2DZLWHUOTBCFOWM37IE5","target":"record","payload":{"canonical_record":{"source":{"id":"2305.15490","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-05-24T18:23:25Z","cross_cats_sorted":["cs.LG","cs.NA","math-ph","math.MP","physics.comp-ph"],"title_canon_sha256":"a4475330bec74290fb5ebfcd3b582ce3b7f11fdfcd99e29dd851a307d876c7ff","abstract_canon_sha256":"cbff2eeb9857a06646510cd22d5ebad0f33cea03c8ab024454eeada69a187a1a"},"schema_version":"1.0"},"canonical_sha256":"04f6e5e343caec7a3a61115d666fe8277b6d4c0c4afaa814aed39bba04767de1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:44:19.959116Z","signature_b64":"LbUzzQhw3GpQfeoiuVZ5usWqI1+kQGZOnEXLBTiVBMLpz0ifunJKAxk9kDVotqiO6WVKJ0YkAE62OS9FEmBvCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04f6e5e343caec7a3a61115d666fe8277b6d4c0c4afaa814aed39bba04767de1","last_reissued_at":"2026-07-05T06:44:19.958606Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:44:19.958606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2305.15490","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:44:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dzd56BK485b1pUvshTy6mi/SyKyd3FwsihB7UX0Cg0w1MolfgoMQiQDFWs1bZA8TnZfdXTiu3wtDfomQ8XDcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T16:01:05.292898Z"},"content_sha256":"9a338d0f2db1e40c82a33234db6b11b17a60e97bf617d281f956b9125a531ae9","schema_version":"1.0","event_id":"sha256:9a338d0f2db1e40c82a33234db6b11b17a60e97bf617d281f956b9125a531ae9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:AT3OLY2DZLWHUOTBCFOWM37IE5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","math-ph","math.MP","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Boris Kramer, Harsh Sharma, Hongliang Mu, Patrick Buchfink, Rudy Geelen, Silke Glas","submitted_at":"2023-05-24T18:23:25Z","abstract_excerpt":"This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for representing the high-dimensional system states in a reduced-dimensional coordinate system. While these approximations respect the symplectic nature of Hamiltonian systems, linear basis approximations can suffer from slowly decaying Kolmogorov $N$-width, especially in wave-type problems, which then requires a large basis size. We propose two different model"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.15490","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.15490/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:44:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WX0l5Mlg24sqD+V7KAMUi0frK5IBSBJaGBxxBRm3S0gAVDs10m7HY+Pg3VaQbw3kFQF1I7vOGYbbYsUoQHVKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T16:01:05.293402Z"},"content_sha256":"9a327f7557d7c4b1ba0f8f670bd930b2b817625964d33fd89d865a816c2eec19","schema_version":"1.0","event_id":"sha256:9a327f7557d7c4b1ba0f8f670bd930b2b817625964d33fd89d865a816c2eec19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AT3OLY2DZLWHUOTBCFOWM37IE5/bundle.json","state_url":"https://pith.science/pith/AT3OLY2DZLWHUOTBCFOWM37IE5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AT3OLY2DZLWHUOTBCFOWM37IE5/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":"2026-08-06T16:01:05Z","links":{"resolver":"https://pith.science/pith/AT3OLY2DZLWHUOTBCFOWM37IE5","bundle":"https://pith.science/pith/AT3OLY2DZLWHUOTBCFOWM37IE5/bundle.json","state":"https://pith.science/pith/AT3OLY2DZLWHUOTBCFOWM37IE5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AT3OLY2DZLWHUOTBCFOWM37IE5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:AT3OLY2DZLWHUOTBCFOWM37IE5","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":"cbff2eeb9857a06646510cd22d5ebad0f33cea03c8ab024454eeada69a187a1a","cross_cats_sorted":["cs.LG","cs.NA","math-ph","math.MP","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-05-24T18:23:25Z","title_canon_sha256":"a4475330bec74290fb5ebfcd3b582ce3b7f11fdfcd99e29dd851a307d876c7ff"},"schema_version":"1.0","source":{"id":"2305.15490","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.15490","created_at":"2026-07-05T06:44:19Z"},{"alias_kind":"arxiv_version","alias_value":"2305.15490v2","created_at":"2026-07-05T06:44:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.15490","created_at":"2026-07-05T06:44:19Z"},{"alias_kind":"pith_short_12","alias_value":"AT3OLY2DZLWH","created_at":"2026-07-05T06:44:19Z"},{"alias_kind":"pith_short_16","alias_value":"AT3OLY2DZLWHUOTB","created_at":"2026-07-05T06:44:19Z"},{"alias_kind":"pith_short_8","alias_value":"AT3OLY2D","created_at":"2026-07-05T06:44:19Z"}],"graph_snapshots":[{"event_id":"sha256:9a327f7557d7c4b1ba0f8f670bd930b2b817625964d33fd89d865a816c2eec19","target":"graph","created_at":"2026-07-05T06:44:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2305.15490/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for representing the high-dimensional system states in a reduced-dimensional coordinate system. While these approximations respect the symplectic nature of Hamiltonian systems, linear basis approximations can suffer from slowly decaying Kolmogorov $N$-width, especially in wave-type problems, which then requires a large basis size. We propose two different model","authors_text":"Boris Kramer, Harsh Sharma, Hongliang Mu, Patrick Buchfink, Rudy Geelen, Silke Glas","cross_cats":["cs.LG","cs.NA","math-ph","math.MP","physics.comp-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-05-24T18:23:25Z","title":"Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.15490","kind":"arxiv","version":2},"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":"sha256:9a338d0f2db1e40c82a33234db6b11b17a60e97bf617d281f956b9125a531ae9","target":"record","created_at":"2026-07-05T06:44:19Z","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":"cbff2eeb9857a06646510cd22d5ebad0f33cea03c8ab024454eeada69a187a1a","cross_cats_sorted":["cs.LG","cs.NA","math-ph","math.MP","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-05-24T18:23:25Z","title_canon_sha256":"a4475330bec74290fb5ebfcd3b582ce3b7f11fdfcd99e29dd851a307d876c7ff"},"schema_version":"1.0","source":{"id":"2305.15490","kind":"arxiv","version":2}},"canonical_sha256":"04f6e5e343caec7a3a61115d666fe8277b6d4c0c4afaa814aed39bba04767de1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04f6e5e343caec7a3a61115d666fe8277b6d4c0c4afaa814aed39bba04767de1","first_computed_at":"2026-07-05T06:44:19.958606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:44:19.958606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LbUzzQhw3GpQfeoiuVZ5usWqI1+kQGZOnEXLBTiVBMLpz0ifunJKAxk9kDVotqiO6WVKJ0YkAE62OS9FEmBvCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:44:19.959116Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.15490","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a338d0f2db1e40c82a33234db6b11b17a60e97bf617d281f956b9125a531ae9","sha256:9a327f7557d7c4b1ba0f8f670bd930b2b817625964d33fd89d865a816c2eec19"],"state_sha256":"b6d02c7e59af92a93c1aac0e471c83a5ee6ef407d5835b1195a11e1a39782f22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MtI6B5x9CPa4HlC2NE15Z7VtIZA7R8ETFaPzNPPYkfdPk1fy2wuw0tk+BzcDbSo06uf6d1/QxxmRR9S62bAzCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T16:01:05.297396Z","bundle_sha256":"acdef2445382666c92eb57bcf5b7e4449c61384a18c23ca86408414020b70802"}}