{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ITPWQZU6JA7PO3P5T4H2KY4JVY","short_pith_number":"pith:ITPWQZU6","canonical_record":{"source":{"id":"1802.02247","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2018-02-06T22:13:26Z","cross_cats_sorted":[],"title_canon_sha256":"617f8e4cf49e25b35f8308a5e589630242230a9d6386e8198049c66ef404148b","abstract_canon_sha256":"019495a078b58c99e73fa0e1cbff099d1f5cd4d4da0888ccf2ce4eebe77af1f6"},"schema_version":"1.0"},"canonical_sha256":"44df68669e483ef76dfd9f0fa56389ae160d6b7d89c971ad36499a3b7038be00","source":{"kind":"arxiv","id":"1802.02247","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02247","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02247v1","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02247","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"pith_short_12","alias_value":"ITPWQZU6JA7P","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"ITPWQZU6JA7PO3P5","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"ITPWQZU6","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ITPWQZU6JA7PO3P5T4H2KY4JVY","target":"record","payload":{"canonical_record":{"source":{"id":"1802.02247","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2018-02-06T22:13:26Z","cross_cats_sorted":[],"title_canon_sha256":"617f8e4cf49e25b35f8308a5e589630242230a9d6386e8198049c66ef404148b","abstract_canon_sha256":"019495a078b58c99e73fa0e1cbff099d1f5cd4d4da0888ccf2ce4eebe77af1f6"},"schema_version":"1.0"},"canonical_sha256":"44df68669e483ef76dfd9f0fa56389ae160d6b7d89c971ad36499a3b7038be00","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:08.783302Z","signature_b64":"D15eHwP6YGTF7TYZrOwQg2lIxmIig3A39YfPoHKjtS0kb2JHY+9D/hhHzSV8duq6SSgXAJklulF7qegcYoa/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44df68669e483ef76dfd9f0fa56389ae160d6b7d89c971ad36499a3b7038be00","last_reissued_at":"2026-05-18T00:24:08.782585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:08.782585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.02247","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":"2026-05-18T00:24:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/4+9gdgzzZHJskDC4CcMcZVQgUcGQGF0eCPaJW9TnX0MkLZxY/17T3NM8hfJoVm4YWZ1BkqF+PIwY4/0cI8GBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:54:39.601224Z"},"content_sha256":"7dd1e443c8a0def390da1dd504ccd993fff78d5bf7cf78e9a4a8a4f8fca955f2","schema_version":"1.0","event_id":"sha256:7dd1e443c8a0def390da1dd504ccd993fff78d5bf7cf78e9a4a8a4f8fca955f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ITPWQZU6JA7PO3P5T4H2KY4JVY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automatic differentiation of ODE integration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.MS","authors_text":"Johannes Willkomm","submitted_at":"2018-02-06T22:13:26Z","abstract_excerpt":"We discuss the calculation of the derivatives of ODE systems with the automatic differentiation tool ADiMat. Using the well-known Lotka-Volterra equations and the ode23 ODE solver as examples we show the analytic derivatives and detail how to differentiate a top-level function that calls ode23 somewhere with ADiMat. This involves the manual construction of substitution function to propagate the derivatives in forward and reverse mode. We also show how to use the reverse mode code to evaluate the Hessian in forward-over-reverse mode."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02247","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":"2026-05-18T00:24:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+6HDpdS9mLllTQWabTWPAmeRVIiWmd3yzIWe5k0I5mtRNUIpDCI99Ec6onnQIZafGZ5zsIFV6HLtAWbj4MmxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:54:39.601947Z"},"content_sha256":"cbcbe7c3ea8e81dfa814b2850f17a40b8c6562ac38a7a0318d7e2dffd1853ef5","schema_version":"1.0","event_id":"sha256:cbcbe7c3ea8e81dfa814b2850f17a40b8c6562ac38a7a0318d7e2dffd1853ef5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ITPWQZU6JA7PO3P5T4H2KY4JVY/bundle.json","state_url":"https://pith.science/pith/ITPWQZU6JA7PO3P5T4H2KY4JVY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ITPWQZU6JA7PO3P5T4H2KY4JVY/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":"2026-06-10T13:54:39Z","links":{"resolver":"https://pith.science/pith/ITPWQZU6JA7PO3P5T4H2KY4JVY","bundle":"https://pith.science/pith/ITPWQZU6JA7PO3P5T4H2KY4JVY/bundle.json","state":"https://pith.science/pith/ITPWQZU6JA7PO3P5T4H2KY4JVY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ITPWQZU6JA7PO3P5T4H2KY4JVY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ITPWQZU6JA7PO3P5T4H2KY4JVY","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":"019495a078b58c99e73fa0e1cbff099d1f5cd4d4da0888ccf2ce4eebe77af1f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2018-02-06T22:13:26Z","title_canon_sha256":"617f8e4cf49e25b35f8308a5e589630242230a9d6386e8198049c66ef404148b"},"schema_version":"1.0","source":{"id":"1802.02247","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02247","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02247v1","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02247","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"pith_short_12","alias_value":"ITPWQZU6JA7P","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"ITPWQZU6JA7PO3P5","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"ITPWQZU6","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:cbcbe7c3ea8e81dfa814b2850f17a40b8c6562ac38a7a0318d7e2dffd1853ef5","target":"graph","created_at":"2026-05-18T00:24:08Z","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":"We discuss the calculation of the derivatives of ODE systems with the automatic differentiation tool ADiMat. Using the well-known Lotka-Volterra equations and the ode23 ODE solver as examples we show the analytic derivatives and detail how to differentiate a top-level function that calls ode23 somewhere with ADiMat. This involves the manual construction of substitution function to propagate the derivatives in forward and reverse mode. We also show how to use the reverse mode code to evaluate the Hessian in forward-over-reverse mode.","authors_text":"Johannes Willkomm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2018-02-06T22:13:26Z","title":"Automatic differentiation of ODE integration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02247","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":"sha256:7dd1e443c8a0def390da1dd504ccd993fff78d5bf7cf78e9a4a8a4f8fca955f2","target":"record","created_at":"2026-05-18T00:24:08Z","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":"019495a078b58c99e73fa0e1cbff099d1f5cd4d4da0888ccf2ce4eebe77af1f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2018-02-06T22:13:26Z","title_canon_sha256":"617f8e4cf49e25b35f8308a5e589630242230a9d6386e8198049c66ef404148b"},"schema_version":"1.0","source":{"id":"1802.02247","kind":"arxiv","version":1}},"canonical_sha256":"44df68669e483ef76dfd9f0fa56389ae160d6b7d89c971ad36499a3b7038be00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44df68669e483ef76dfd9f0fa56389ae160d6b7d89c971ad36499a3b7038be00","first_computed_at":"2026-05-18T00:24:08.782585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:08.782585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D15eHwP6YGTF7TYZrOwQg2lIxmIig3A39YfPoHKjtS0kb2JHY+9D/hhHzSV8duq6SSgXAJklulF7qegcYoa/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:08.783302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.02247","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7dd1e443c8a0def390da1dd504ccd993fff78d5bf7cf78e9a4a8a4f8fca955f2","sha256:cbcbe7c3ea8e81dfa814b2850f17a40b8c6562ac38a7a0318d7e2dffd1853ef5"],"state_sha256":"dd9592f90de4b8dca93272d0dffbaa02ebe1089a9ff924d5b481aae47e42f282"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G8ohdteovx/668Pxiv9VYxAr9lExnRCrrHVjMSwSycuBCQePo7anOKqYPsXirpxsuQjNwqtXj568EkLat37ZAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T13:54:39.605948Z","bundle_sha256":"c48ea57dc82f0c1aed966acd17bc403c7abcf406e02d0f06edffa4ba61a22d1b"}}