{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KXTEG3SSY6SKZ5JN7VAT6VNO37","short_pith_number":"pith:KXTEG3SS","canonical_record":{"source":{"id":"1302.1904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2013-02-07T22:58:06Z","cross_cats_sorted":[],"title_canon_sha256":"59027698f13c57753adefa6326b45d0a1a636aaef4bc4f08e7d3ca1ee557ceb2","abstract_canon_sha256":"388b4ee6d226dbf9b3dd57c9c30f4064ee81847158e8c6948309b2b91ea74b8b"},"schema_version":"1.0"},"canonical_sha256":"55e6436e52c7a4acf52dfd413f55aedfcb6a6f311d600668ab03b6a55882a2e0","source":{"kind":"arxiv","id":"1302.1904","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1904","created_at":"2026-05-18T03:34:13Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1904v1","created_at":"2026-05-18T03:34:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1904","created_at":"2026-05-18T03:34:13Z"},{"alias_kind":"pith_short_12","alias_value":"KXTEG3SSY6SK","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KXTEG3SSY6SKZ5JN","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KXTEG3SS","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KXTEG3SSY6SKZ5JN7VAT6VNO37","target":"record","payload":{"canonical_record":{"source":{"id":"1302.1904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2013-02-07T22:58:06Z","cross_cats_sorted":[],"title_canon_sha256":"59027698f13c57753adefa6326b45d0a1a636aaef4bc4f08e7d3ca1ee557ceb2","abstract_canon_sha256":"388b4ee6d226dbf9b3dd57c9c30f4064ee81847158e8c6948309b2b91ea74b8b"},"schema_version":"1.0"},"canonical_sha256":"55e6436e52c7a4acf52dfd413f55aedfcb6a6f311d600668ab03b6a55882a2e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:13.427011Z","signature_b64":"mvbN/+CAyMvFhJxlXxmDJ5DJNyVsKTmoI9EQUicEKLPeNLdQtK4nAlK/rdA57R1JBPdq81i7jiezLhtuynEVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55e6436e52c7a4acf52dfd413f55aedfcb6a6f311d600668ab03b6a55882a2e0","last_reissued_at":"2026-05-18T03:34:13.426551Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:13.426551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.1904","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":"2026-05-18T03:34:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DtP7Hjpwadz7bM02VK7vMr2upHsWWLWb3iLgDfFHIbQDL/TI6VToy4CTPO506axJlDqMqvYJdX15Tgxj94e5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:41:39.524480Z"},"content_sha256":"81b53169ada38b44268c0e9398f2b843f4f5aad0e18f7400dd0c30e55694002a","schema_version":"1.0","event_id":"sha256:81b53169ada38b44268c0e9398f2b843f4f5aad0e18f7400dd0c30e55694002a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KXTEG3SSY6SKZ5JN7VAT6VNO37","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Unified Approach to Integration and Optimization of Parametric Ordinary Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.QM","authors_text":"Daniel Kaschek, Jens Timmer","submitted_at":"2013-02-07T22:58:06Z","abstract_excerpt":"Parameter estimation in ordinary differential equations, although applied and refined in various fields of the quantitative sciences, is still confronted with a variety of difficulties. One major challenge is finding the global optimum of a log-likelihood function that has several local optima, e.g. in oscillatory systems. In this publication, we introduce a formulation based on continuation of the log-likelihood function that allows to restate the parameter estimation problem as a boundary value problem. By construction, the ordinary differential equations are solved and the parameters are es"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1904","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":"2026-05-18T03:34:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6L5aiiqH29436cdli1fKavbprx7+Gn7XhbYl9K5PuxwHqCwtEthNhCd4jbIumfDMuAGnWKvgcx+rfv7eceiMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:41:39.524832Z"},"content_sha256":"5b9dad7861503851c6afc5ffa406c7118c73c6ccf0d2c78e0d7d9ca18ae4b5b3","schema_version":"1.0","event_id":"sha256:5b9dad7861503851c6afc5ffa406c7118c73c6ccf0d2c78e0d7d9ca18ae4b5b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KXTEG3SSY6SKZ5JN7VAT6VNO37/bundle.json","state_url":"https://pith.science/pith/KXTEG3SSY6SKZ5JN7VAT6VNO37/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KXTEG3SSY6SKZ5JN7VAT6VNO37/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":"2026-06-05T11:41:39Z","links":{"resolver":"https://pith.science/pith/KXTEG3SSY6SKZ5JN7VAT6VNO37","bundle":"https://pith.science/pith/KXTEG3SSY6SKZ5JN7VAT6VNO37/bundle.json","state":"https://pith.science/pith/KXTEG3SSY6SKZ5JN7VAT6VNO37/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KXTEG3SSY6SKZ5JN7VAT6VNO37/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KXTEG3SSY6SKZ5JN7VAT6VNO37","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":"388b4ee6d226dbf9b3dd57c9c30f4064ee81847158e8c6948309b2b91ea74b8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2013-02-07T22:58:06Z","title_canon_sha256":"59027698f13c57753adefa6326b45d0a1a636aaef4bc4f08e7d3ca1ee557ceb2"},"schema_version":"1.0","source":{"id":"1302.1904","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1904","created_at":"2026-05-18T03:34:13Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1904v1","created_at":"2026-05-18T03:34:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1904","created_at":"2026-05-18T03:34:13Z"},{"alias_kind":"pith_short_12","alias_value":"KXTEG3SSY6SK","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KXTEG3SSY6SKZ5JN","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KXTEG3SS","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:5b9dad7861503851c6afc5ffa406c7118c73c6ccf0d2c78e0d7d9ca18ae4b5b3","target":"graph","created_at":"2026-05-18T03:34:13Z","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":"Parameter estimation in ordinary differential equations, although applied and refined in various fields of the quantitative sciences, is still confronted with a variety of difficulties. One major challenge is finding the global optimum of a log-likelihood function that has several local optima, e.g. in oscillatory systems. In this publication, we introduce a formulation based on continuation of the log-likelihood function that allows to restate the parameter estimation problem as a boundary value problem. By construction, the ordinary differential equations are solved and the parameters are es","authors_text":"Daniel Kaschek, Jens Timmer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2013-02-07T22:58:06Z","title":"A Unified Approach to Integration and Optimization of Parametric Ordinary Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1904","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":"sha256:81b53169ada38b44268c0e9398f2b843f4f5aad0e18f7400dd0c30e55694002a","target":"record","created_at":"2026-05-18T03:34:13Z","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":"388b4ee6d226dbf9b3dd57c9c30f4064ee81847158e8c6948309b2b91ea74b8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2013-02-07T22:58:06Z","title_canon_sha256":"59027698f13c57753adefa6326b45d0a1a636aaef4bc4f08e7d3ca1ee557ceb2"},"schema_version":"1.0","source":{"id":"1302.1904","kind":"arxiv","version":1}},"canonical_sha256":"55e6436e52c7a4acf52dfd413f55aedfcb6a6f311d600668ab03b6a55882a2e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55e6436e52c7a4acf52dfd413f55aedfcb6a6f311d600668ab03b6a55882a2e0","first_computed_at":"2026-05-18T03:34:13.426551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:13.426551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mvbN/+CAyMvFhJxlXxmDJ5DJNyVsKTmoI9EQUicEKLPeNLdQtK4nAlK/rdA57R1JBPdq81i7jiezLhtuynEVBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:13.427011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.1904","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81b53169ada38b44268c0e9398f2b843f4f5aad0e18f7400dd0c30e55694002a","sha256:5b9dad7861503851c6afc5ffa406c7118c73c6ccf0d2c78e0d7d9ca18ae4b5b3"],"state_sha256":"b579ab07f68d55d05d4b0d1ed0ceec7a20eca49ab07be6fc4243b8a25410c231"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3dtiHAzVlTXKetMv5RNNjS/ascLvhwh+nLjRlmwDA0Oa5GTlfo+YEN/fsY71dxd/Wcqa2CYlkmSoO+fUAYGXBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:41:39.526748Z","bundle_sha256":"0acf6c0d2c7553a85a845239e8c09889a008b064afabf5c7fe0d91af1f0cd37c"}}