{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:JKREZKQPQM362ZPXXXRCPFEOYC","short_pith_number":"pith:JKREZKQP","schema_version":"1.0","canonical_sha256":"4aa24caa0f8337ed65f7bde227948ec08bfb222aa14cfd7b412af8c25e4eac27","source":{"kind":"arxiv","id":"1805.07970","version":3},"attestation_state":"computed","paper":{"title":"Implicit Probabilistic Integrators for ODEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"stat.ME","authors_text":"Ben Calderhead, Han Cheng Lie, Onur Teymur, Tim Sullivan","submitted_at":"2018-05-21T10:17:31Z","abstract_excerpt":"We introduce a family of implicit probabilistic integrators for initial value problems (IVPs), taking as a starting point the multistep Adams-Moulton method. The implicit construction allows for dynamic feedback from the forthcoming time-step, in contrast to previous probabilistic integrators, all of which are based on explicit methods. We begin with a concise survey of the rapidly-expanding field of probabilistic ODE solvers. We then introduce our method, which builds on and adapts the work of Conrad et al. (2016) and Teymur et al. (2016), and provide a rigorous proof of its well-definedness "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1805.07970","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-05-21T10:17:31Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"9a64ba29ebd04c4d3e1fcfd6d4f6645777a9ee29dcbbb2792e93085eef391e4f","abstract_canon_sha256":"22fe4de63c411e447d6a15e994df6aee3382beaf90747eebda0c66a50c6b1a4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:17.360657Z","signature_b64":"JQW8iVYCix6aG1DaAQQIfV29/Dnpx7+E0KdyP0JC/ySb+rq5ZD9LxdQg0bRtQxrz8c4e6YvyYpseS/xnrniyBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4aa24caa0f8337ed65f7bde227948ec08bfb222aa14cfd7b412af8c25e4eac27","last_reissued_at":"2026-05-17T23:48:17.360129Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:17.360129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Implicit Probabilistic Integrators for ODEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"stat.ME","authors_text":"Ben Calderhead, Han Cheng Lie, Onur Teymur, Tim Sullivan","submitted_at":"2018-05-21T10:17:31Z","abstract_excerpt":"We introduce a family of implicit probabilistic integrators for initial value problems (IVPs), taking as a starting point the multistep Adams-Moulton method. The implicit construction allows for dynamic feedback from the forthcoming time-step, in contrast to previous probabilistic integrators, all of which are based on explicit methods. We begin with a concise survey of the rapidly-expanding field of probabilistic ODE solvers. We then introduce our method, which builds on and adapts the work of Conrad et al. (2016) and Teymur et al. (2016), and provide a rigorous proof of its well-definedness "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07970","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1805.07970","created_at":"2026-05-17T23:48:17.360204+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.07970v3","created_at":"2026-05-17T23:48:17.360204+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07970","created_at":"2026-05-17T23:48:17.360204+00:00"},{"alias_kind":"pith_short_12","alias_value":"JKREZKQPQM36","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"JKREZKQPQM362ZPX","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"JKREZKQP","created_at":"2026-05-18T12:32:31.084164+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JKREZKQPQM362ZPXXXRCPFEOYC","json":"https://pith.science/pith/JKREZKQPQM362ZPXXXRCPFEOYC.json","graph_json":"https://pith.science/api/pith-number/JKREZKQPQM362ZPXXXRCPFEOYC/graph.json","events_json":"https://pith.science/api/pith-number/JKREZKQPQM362ZPXXXRCPFEOYC/events.json","paper":"https://pith.science/paper/JKREZKQP"},"agent_actions":{"view_html":"https://pith.science/pith/JKREZKQPQM362ZPXXXRCPFEOYC","download_json":"https://pith.science/pith/JKREZKQPQM362ZPXXXRCPFEOYC.json","view_paper":"https://pith.science/paper/JKREZKQP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.07970&json=true","fetch_graph":"https://pith.science/api/pith-number/JKREZKQPQM362ZPXXXRCPFEOYC/graph.json","fetch_events":"https://pith.science/api/pith-number/JKREZKQPQM362ZPXXXRCPFEOYC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JKREZKQPQM362ZPXXXRCPFEOYC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JKREZKQPQM362ZPXXXRCPFEOYC/action/storage_attestation","attest_author":"https://pith.science/pith/JKREZKQPQM362ZPXXXRCPFEOYC/action/author_attestation","sign_citation":"https://pith.science/pith/JKREZKQPQM362ZPXXXRCPFEOYC/action/citation_signature","submit_replication":"https://pith.science/pith/JKREZKQPQM362ZPXXXRCPFEOYC/action/replication_record"}},"created_at":"2026-05-17T23:48:17.360204+00:00","updated_at":"2026-05-17T23:48:17.360204+00:00"}