{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:B6RQVX3FJ7DN2MC2JGUZNDU43B","short_pith_number":"pith:B6RQVX3F","canonical_record":{"source":{"id":"1703.08466","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-24T15:35:31Z","cross_cats_sorted":[],"title_canon_sha256":"4b334ff908dd47f448ebf5fbd3a4df489fedbe0add5e0d33b292437d5479a45f","abstract_canon_sha256":"ad9936cf3a092e760272bed96eca1baa12fc5717b74f98a2ec505b73f16051e1"},"schema_version":"1.0"},"canonical_sha256":"0fa30adf654fc6dd305a49a9968e9cd87daca95b30e21d7b0d1d5d9fe7add3a9","source":{"kind":"arxiv","id":"1703.08466","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08466","created_at":"2026-05-18T00:34:57Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08466v2","created_at":"2026-05-18T00:34:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08466","created_at":"2026-05-18T00:34:57Z"},{"alias_kind":"pith_short_12","alias_value":"B6RQVX3FJ7DN","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B6RQVX3FJ7DN2MC2","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B6RQVX3F","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:B6RQVX3FJ7DN2MC2JGUZNDU43B","target":"record","payload":{"canonical_record":{"source":{"id":"1703.08466","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-24T15:35:31Z","cross_cats_sorted":[],"title_canon_sha256":"4b334ff908dd47f448ebf5fbd3a4df489fedbe0add5e0d33b292437d5479a45f","abstract_canon_sha256":"ad9936cf3a092e760272bed96eca1baa12fc5717b74f98a2ec505b73f16051e1"},"schema_version":"1.0"},"canonical_sha256":"0fa30adf654fc6dd305a49a9968e9cd87daca95b30e21d7b0d1d5d9fe7add3a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:57.403761Z","signature_b64":"7E5OETBSADVJV1zOO+funIGnR1S01QJMOzajR1jWi3N16ysIG2ochKuxuzd4+PCWh3pcz5tgU5YeW9wW2ZjIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fa30adf654fc6dd305a49a9968e9cd87daca95b30e21d7b0d1d5d9fe7add3a9","last_reissued_at":"2026-05-18T00:34:57.403185Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:57.403185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.08466","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":"2026-05-18T00:34:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KNJ8GNMlKiMG99mgrdcKe3iviLDXbLmtWPc8AAnsUxsqIVYQXodYs+EENDJAeozCrgKgR9kbM60fljQjJr55DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:16:05.097103Z"},"content_sha256":"15e66b087ea67e893d429472d35ba3d267d9504c71384ccc21459cc8b0b178c2","schema_version":"1.0","event_id":"sha256:15e66b087ea67e893d429472d35ba3d267d9504c71384ccc21459cc8b0b178c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:B6RQVX3FJ7DN2MC2JGUZNDU43B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear parallel-in-time multilevel Schur complement solvers for ordinary differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Marc Olm, Santiago Badia","submitted_at":"2017-03-24T15:35:31Z","abstract_excerpt":"In this work, we propose a parallel-in-time solver for linear and nonlinear ordinary differential equations. The approach is based on an efficient multilevel solver of the Schur complement related to a multilevel time partition. For linear problems, the scheme leads to a fast direct method. Next, two different strategies for solving nonlinear ODEs are proposed. First, we consider a Newton method over the global nonlinear ODE, using the multilevel Schur complement solver at every nonlinear iteration. Second, we state the global nonlinear problem in terms of the nonlinear Schur complement (at an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08466","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":""},"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":"2026-05-18T00:34:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q55hxqkn+R4MG4+opvP7GNGqrt8ZnG737OjNCHejOz5VznaiTqvFGLQ4hDx6CUnuJz7+XdF5fgoT0Or+eqIJAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:16:05.097457Z"},"content_sha256":"d1e73e8460b5a9795bb6f54f12f1b3137c7a7e77420820dadc1940a4ebb8ff5f","schema_version":"1.0","event_id":"sha256:d1e73e8460b5a9795bb6f54f12f1b3137c7a7e77420820dadc1940a4ebb8ff5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6RQVX3FJ7DN2MC2JGUZNDU43B/bundle.json","state_url":"https://pith.science/pith/B6RQVX3FJ7DN2MC2JGUZNDU43B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6RQVX3FJ7DN2MC2JGUZNDU43B/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":"2026-06-20T21:16:05Z","links":{"resolver":"https://pith.science/pith/B6RQVX3FJ7DN2MC2JGUZNDU43B","bundle":"https://pith.science/pith/B6RQVX3FJ7DN2MC2JGUZNDU43B/bundle.json","state":"https://pith.science/pith/B6RQVX3FJ7DN2MC2JGUZNDU43B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6RQVX3FJ7DN2MC2JGUZNDU43B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:B6RQVX3FJ7DN2MC2JGUZNDU43B","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":"ad9936cf3a092e760272bed96eca1baa12fc5717b74f98a2ec505b73f16051e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-24T15:35:31Z","title_canon_sha256":"4b334ff908dd47f448ebf5fbd3a4df489fedbe0add5e0d33b292437d5479a45f"},"schema_version":"1.0","source":{"id":"1703.08466","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08466","created_at":"2026-05-18T00:34:57Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08466v2","created_at":"2026-05-18T00:34:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08466","created_at":"2026-05-18T00:34:57Z"},{"alias_kind":"pith_short_12","alias_value":"B6RQVX3FJ7DN","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B6RQVX3FJ7DN2MC2","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B6RQVX3F","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:d1e73e8460b5a9795bb6f54f12f1b3137c7a7e77420820dadc1940a4ebb8ff5f","target":"graph","created_at":"2026-05-18T00:34:57Z","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":"In this work, we propose a parallel-in-time solver for linear and nonlinear ordinary differential equations. The approach is based on an efficient multilevel solver of the Schur complement related to a multilevel time partition. For linear problems, the scheme leads to a fast direct method. Next, two different strategies for solving nonlinear ODEs are proposed. First, we consider a Newton method over the global nonlinear ODE, using the multilevel Schur complement solver at every nonlinear iteration. Second, we state the global nonlinear problem in terms of the nonlinear Schur complement (at an","authors_text":"Marc Olm, Santiago Badia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-24T15:35:31Z","title":"Nonlinear parallel-in-time multilevel Schur complement solvers for ordinary differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08466","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":"sha256:15e66b087ea67e893d429472d35ba3d267d9504c71384ccc21459cc8b0b178c2","target":"record","created_at":"2026-05-18T00:34:57Z","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":"ad9936cf3a092e760272bed96eca1baa12fc5717b74f98a2ec505b73f16051e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-24T15:35:31Z","title_canon_sha256":"4b334ff908dd47f448ebf5fbd3a4df489fedbe0add5e0d33b292437d5479a45f"},"schema_version":"1.0","source":{"id":"1703.08466","kind":"arxiv","version":2}},"canonical_sha256":"0fa30adf654fc6dd305a49a9968e9cd87daca95b30e21d7b0d1d5d9fe7add3a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fa30adf654fc6dd305a49a9968e9cd87daca95b30e21d7b0d1d5d9fe7add3a9","first_computed_at":"2026-05-18T00:34:57.403185Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:57.403185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7E5OETBSADVJV1zOO+funIGnR1S01QJMOzajR1jWi3N16ysIG2ochKuxuzd4+PCWh3pcz5tgU5YeW9wW2ZjIDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:57.403761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.08466","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15e66b087ea67e893d429472d35ba3d267d9504c71384ccc21459cc8b0b178c2","sha256:d1e73e8460b5a9795bb6f54f12f1b3137c7a7e77420820dadc1940a4ebb8ff5f"],"state_sha256":"f09a095921c0203595e63f53a86a464cd992294789f410cbb301fff6203cb814"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zx+Sil6wffN66NP2/mvW5kf8UrjVrSYG2LLwR3lQN6kFyt4nFIsPSAvimAYf3YYcFteR1bnJmlUrMlX8L0kIDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T21:16:05.099278Z","bundle_sha256":"15ca2b514ebd73fe41e162e712ff112adcbc0c3c262f45c78b8af80414b95380"}}