{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:T4EGEPPNVD35ZQYFZMW5XPG5DZ","short_pith_number":"pith:T4EGEPPN","canonical_record":{"source":{"id":"2404.19626","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-04-30T15:24:53Z","cross_cats_sorted":["cs.NA","math.DS"],"title_canon_sha256":"fcafc3755d51dbaebebfb6d9cc8ded40f7282ac2ed6b3d46c2c29c40a91d3341","abstract_canon_sha256":"eb35aafeebf15429450a60b647e05a8c3822158868df759647ab5253469dfa53"},"schema_version":"1.0"},"canonical_sha256":"9f08623deda8f7dcc305cb2ddbbcdd1e6bb5e3dec33411eed594d2d3fdb66356","source":{"kind":"arxiv","id":"2404.19626","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.19626","created_at":"2026-07-05T11:28:59Z"},{"alias_kind":"arxiv_version","alias_value":"2404.19626v3","created_at":"2026-07-05T11:28:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.19626","created_at":"2026-07-05T11:28:59Z"},{"alias_kind":"pith_short_12","alias_value":"T4EGEPPNVD35","created_at":"2026-07-05T11:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"T4EGEPPNVD35ZQYF","created_at":"2026-07-05T11:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"T4EGEPPN","created_at":"2026-07-05T11:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:T4EGEPPNVD35ZQYFZMW5XPG5DZ","target":"record","payload":{"canonical_record":{"source":{"id":"2404.19626","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-04-30T15:24:53Z","cross_cats_sorted":["cs.NA","math.DS"],"title_canon_sha256":"fcafc3755d51dbaebebfb6d9cc8ded40f7282ac2ed6b3d46c2c29c40a91d3341","abstract_canon_sha256":"eb35aafeebf15429450a60b647e05a8c3822158868df759647ab5253469dfa53"},"schema_version":"1.0"},"canonical_sha256":"9f08623deda8f7dcc305cb2ddbbcdd1e6bb5e3dec33411eed594d2d3fdb66356","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:28:59.013779Z","signature_b64":"ied4QGJd5BiR4AF2fV+TAH4G5RY192D3fDrfbq6Fk7pK8XzaL3Lc32dBWmpcO+6KQFw37wE6vGf3k6bF3C3bDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f08623deda8f7dcc305cb2ddbbcdd1e6bb5e3dec33411eed594d2d3fdb66356","last_reissued_at":"2026-07-05T11:28:59.013249Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:28:59.013249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.19626","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:28:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7uYjxLn0hR7M+KdwSbMGVnh0RWsUg8tVUHHvI3C+SuBgQ3BBNfv6A499GC+N5XSHHOOT6KhyWpXS+kmN4G7+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:22:28.885827Z"},"content_sha256":"bc9518ad9501aac37720cca999dec2bf41e29ac0fec42ce866772c6429d61aff","schema_version":"1.0","event_id":"sha256:bc9518ad9501aac37720cca999dec2bf41e29ac0fec42ce866772c6429d61aff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:T4EGEPPNVD35ZQYFZMW5XPG5DZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.DS"],"primary_cat":"math.NA","authors_text":"Christian Offen","submitted_at":"2024-04-30T15:24:53Z","abstract_excerpt":"The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore, structure preserving by design. A rigorous proof of convergence as the distance between observation data points converges to zero and lower bounds for convergence rates are provided. Next to convergence guarantees, the method allows for quantification of model uncertainty, which can provide a basis of adaptive sampling techniques. We provide efficient uncertain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.19626","kind":"arxiv","version":3},"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/2404.19626/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":"2026-07-05T11:28:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J/YA7tZhOB6Ge4RPE1X+v4e6IG+JBAOAFpIzLtkpgZ0x4vJGXhq1H1aBDV7SuBrcgk8uDhqE07x4269sx5/4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:22:28.886429Z"},"content_sha256":"ea03cffd6d208ee74173e14f910cf988351c4333eef62be9f40b752f8be58011","schema_version":"1.0","event_id":"sha256:ea03cffd6d208ee74173e14f910cf988351c4333eef62be9f40b752f8be58011"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T4EGEPPNVD35ZQYFZMW5XPG5DZ/bundle.json","state_url":"https://pith.science/pith/T4EGEPPNVD35ZQYFZMW5XPG5DZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T4EGEPPNVD35ZQYFZMW5XPG5DZ/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":"2026-08-08T16:22:28Z","links":{"resolver":"https://pith.science/pith/T4EGEPPNVD35ZQYFZMW5XPG5DZ","bundle":"https://pith.science/pith/T4EGEPPNVD35ZQYFZMW5XPG5DZ/bundle.json","state":"https://pith.science/pith/T4EGEPPNVD35ZQYFZMW5XPG5DZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T4EGEPPNVD35ZQYFZMW5XPG5DZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:T4EGEPPNVD35ZQYFZMW5XPG5DZ","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":"eb35aafeebf15429450a60b647e05a8c3822158868df759647ab5253469dfa53","cross_cats_sorted":["cs.NA","math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-04-30T15:24:53Z","title_canon_sha256":"fcafc3755d51dbaebebfb6d9cc8ded40f7282ac2ed6b3d46c2c29c40a91d3341"},"schema_version":"1.0","source":{"id":"2404.19626","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.19626","created_at":"2026-07-05T11:28:59Z"},{"alias_kind":"arxiv_version","alias_value":"2404.19626v3","created_at":"2026-07-05T11:28:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.19626","created_at":"2026-07-05T11:28:59Z"},{"alias_kind":"pith_short_12","alias_value":"T4EGEPPNVD35","created_at":"2026-07-05T11:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"T4EGEPPNVD35ZQYF","created_at":"2026-07-05T11:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"T4EGEPPN","created_at":"2026-07-05T11:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:ea03cffd6d208ee74173e14f910cf988351c4333eef62be9f40b752f8be58011","target":"graph","created_at":"2026-07-05T11:28:59Z","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/2404.19626/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore, structure preserving by design. A rigorous proof of convergence as the distance between observation data points converges to zero and lower bounds for convergence rates are provided. Next to convergence guarantees, the method allows for quantification of model uncertainty, which can provide a basis of adaptive sampling techniques. We provide efficient uncertain","authors_text":"Christian Offen","cross_cats":["cs.NA","math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-04-30T15:24:53Z","title":"Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.19626","kind":"arxiv","version":3},"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:bc9518ad9501aac37720cca999dec2bf41e29ac0fec42ce866772c6429d61aff","target":"record","created_at":"2026-07-05T11:28:59Z","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":"eb35aafeebf15429450a60b647e05a8c3822158868df759647ab5253469dfa53","cross_cats_sorted":["cs.NA","math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-04-30T15:24:53Z","title_canon_sha256":"fcafc3755d51dbaebebfb6d9cc8ded40f7282ac2ed6b3d46c2c29c40a91d3341"},"schema_version":"1.0","source":{"id":"2404.19626","kind":"arxiv","version":3}},"canonical_sha256":"9f08623deda8f7dcc305cb2ddbbcdd1e6bb5e3dec33411eed594d2d3fdb66356","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f08623deda8f7dcc305cb2ddbbcdd1e6bb5e3dec33411eed594d2d3fdb66356","first_computed_at":"2026-07-05T11:28:59.013249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:28:59.013249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ied4QGJd5BiR4AF2fV+TAH4G5RY192D3fDrfbq6Fk7pK8XzaL3Lc32dBWmpcO+6KQFw37wE6vGf3k6bF3C3bDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:28:59.013779Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.19626","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc9518ad9501aac37720cca999dec2bf41e29ac0fec42ce866772c6429d61aff","sha256:ea03cffd6d208ee74173e14f910cf988351c4333eef62be9f40b752f8be58011"],"state_sha256":"6f45daa8db5838569395164bc4175a7b84c9df55c565c0dc6a83d976acd6ceff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mz6rXLKJ1X9et3C0W538DPhb7WLzGtFN0JUdN2OvsTKfd8ezD0R80si9RBQcxSpAvVNxULtvWymN2UaLdOpoCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T16:22:28.891336Z","bundle_sha256":"e9c0e84fa8f1d1970abcc04a403f2194dd172595d7a5a8b92c241ce41eaf2ea1"}}