{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RC6QXNRV5JQOW5TZBGSKCII4HY","short_pith_number":"pith:RC6QXNRV","canonical_record":{"source":{"id":"1609.08299","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-27T07:53:35Z","cross_cats_sorted":[],"title_canon_sha256":"8bc37fa550064e46f3f94326cee8de5aeef6f6a73bd9d6ec3a8d62f294f0ea98","abstract_canon_sha256":"d4204ed612769cdde5b118a230e6be22683b8c61207c20dc7652c8ccd7faddf1"},"schema_version":"1.0"},"canonical_sha256":"88bd0bb635ea60eb767909a4a1211c3e275830fc5e60ef2b2c64bc8fa8d29086","source":{"kind":"arxiv","id":"1609.08299","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08299","created_at":"2026-05-18T00:43:59Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08299v2","created_at":"2026-05-18T00:43:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08299","created_at":"2026-05-18T00:43:59Z"},{"alias_kind":"pith_short_12","alias_value":"RC6QXNRV5JQO","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RC6QXNRV5JQOW5TZ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RC6QXNRV","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RC6QXNRV5JQOW5TZBGSKCII4HY","target":"record","payload":{"canonical_record":{"source":{"id":"1609.08299","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-27T07:53:35Z","cross_cats_sorted":[],"title_canon_sha256":"8bc37fa550064e46f3f94326cee8de5aeef6f6a73bd9d6ec3a8d62f294f0ea98","abstract_canon_sha256":"d4204ed612769cdde5b118a230e6be22683b8c61207c20dc7652c8ccd7faddf1"},"schema_version":"1.0"},"canonical_sha256":"88bd0bb635ea60eb767909a4a1211c3e275830fc5e60ef2b2c64bc8fa8d29086","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:59.988292Z","signature_b64":"wueHrwqYQdtt1I3JUmgvrNEeEOAScDEYSSCBM7kuaOgDbaR53JaYvxpthQ6drH0nY4LpOPYF6+PQEYUFuLGsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88bd0bb635ea60eb767909a4a1211c3e275830fc5e60ef2b2c64bc8fa8d29086","last_reissued_at":"2026-05-18T00:43:59.987829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:59.987829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.08299","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":"2026-05-18T00:43:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P4gVScfdIA6A1SnErM3K2y/yO+xd1xdinee5IprmSn6YAEmM1N/UyjtBIWqk0bclJ8Nun7bSE4OsrZn1/geqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:51:13.760810Z"},"content_sha256":"f6dc9e9cb473564a89f671e677dd523a6899b90b79b1d5f13bf2f65c4c1d2c61","schema_version":"1.0","event_id":"sha256:f6dc9e9cb473564a89f671e677dd523a6899b90b79b1d5f13bf2f65c4c1d2c61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RC6QXNRV5JQOW5TZBGSKCII4HY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parareal algorithms applied to stochastic differential equations with conserved quantities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Lihai Ji, Liying Zhang, Weien Zhou","submitted_at":"2016-09-27T07:53:35Z","abstract_excerpt":"In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are introduced as the coarse and fine propagators. Second, we also apply the projection methods for systems with conserved quantities in the correction step of original parareal algorithm. Finally, three numerical experiments are performed by different kinds of algorithms to show the property of convergence in iteration, and preservation in conserved quantities of mode"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08299","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":"2026-05-18T00:43:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5e81todymtP+046a8+WLC3/qKgjYB2yBJkBW6RZnmQBJzSVX80KI24GgwhbdCmIyhMhiyyn5WRSOW0/9u3U3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:51:13.761151Z"},"content_sha256":"f287ffe7f2be1071ee9ad8f82bf97b6b4c107b43f418c8adab6d489a54a13fc6","schema_version":"1.0","event_id":"sha256:f287ffe7f2be1071ee9ad8f82bf97b6b4c107b43f418c8adab6d489a54a13fc6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RC6QXNRV5JQOW5TZBGSKCII4HY/bundle.json","state_url":"https://pith.science/pith/RC6QXNRV5JQOW5TZBGSKCII4HY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RC6QXNRV5JQOW5TZBGSKCII4HY/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":"2026-06-01T21:51:13Z","links":{"resolver":"https://pith.science/pith/RC6QXNRV5JQOW5TZBGSKCII4HY","bundle":"https://pith.science/pith/RC6QXNRV5JQOW5TZBGSKCII4HY/bundle.json","state":"https://pith.science/pith/RC6QXNRV5JQOW5TZBGSKCII4HY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RC6QXNRV5JQOW5TZBGSKCII4HY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RC6QXNRV5JQOW5TZBGSKCII4HY","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":"d4204ed612769cdde5b118a230e6be22683b8c61207c20dc7652c8ccd7faddf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-27T07:53:35Z","title_canon_sha256":"8bc37fa550064e46f3f94326cee8de5aeef6f6a73bd9d6ec3a8d62f294f0ea98"},"schema_version":"1.0","source":{"id":"1609.08299","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08299","created_at":"2026-05-18T00:43:59Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08299v2","created_at":"2026-05-18T00:43:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08299","created_at":"2026-05-18T00:43:59Z"},{"alias_kind":"pith_short_12","alias_value":"RC6QXNRV5JQO","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RC6QXNRV5JQOW5TZ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RC6QXNRV","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:f287ffe7f2be1071ee9ad8f82bf97b6b4c107b43f418c8adab6d489a54a13fc6","target":"graph","created_at":"2026-05-18T00:43:59Z","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"},"paper":{"abstract_excerpt":"In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are introduced as the coarse and fine propagators. Second, we also apply the projection methods for systems with conserved quantities in the correction step of original parareal algorithm. Finally, three numerical experiments are performed by different kinds of algorithms to show the property of convergence in iteration, and preservation in conserved quantities of mode","authors_text":"Lihai Ji, Liying Zhang, Weien Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-27T07:53:35Z","title":"Parareal algorithms applied to stochastic differential equations with conserved quantities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08299","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:f6dc9e9cb473564a89f671e677dd523a6899b90b79b1d5f13bf2f65c4c1d2c61","target":"record","created_at":"2026-05-18T00:43:59Z","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":"d4204ed612769cdde5b118a230e6be22683b8c61207c20dc7652c8ccd7faddf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-27T07:53:35Z","title_canon_sha256":"8bc37fa550064e46f3f94326cee8de5aeef6f6a73bd9d6ec3a8d62f294f0ea98"},"schema_version":"1.0","source":{"id":"1609.08299","kind":"arxiv","version":2}},"canonical_sha256":"88bd0bb635ea60eb767909a4a1211c3e275830fc5e60ef2b2c64bc8fa8d29086","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88bd0bb635ea60eb767909a4a1211c3e275830fc5e60ef2b2c64bc8fa8d29086","first_computed_at":"2026-05-18T00:43:59.987829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:59.987829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wueHrwqYQdtt1I3JUmgvrNEeEOAScDEYSSCBM7kuaOgDbaR53JaYvxpthQ6drH0nY4LpOPYF6+PQEYUFuLGsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:59.988292Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08299","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6dc9e9cb473564a89f671e677dd523a6899b90b79b1d5f13bf2f65c4c1d2c61","sha256:f287ffe7f2be1071ee9ad8f82bf97b6b4c107b43f418c8adab6d489a54a13fc6"],"state_sha256":"491e559a4946eca4247308ae649ddf1fd5326ba96ad2cf56ca6fc130d4a39230"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"howkOote+Hc3BDMhAp6IaT7nfV+GUPwhIKqlqnJxULegolQh2uZwirmOMXHV7Mtoky77bGKPpHu8E68iqS93BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:51:13.763083Z","bundle_sha256":"88476e14e4e5a9d9f856c48b2871ba5e1fc9c9d171aa84cda3128890a58eae0b"}}