{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SRDIFLNBSP2QWDJM3FAPAWVECV","short_pith_number":"pith:SRDIFLNB","canonical_record":{"source":{"id":"1410.6293","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-23T08:54:23Z","cross_cats_sorted":[],"title_canon_sha256":"0c761f61bcbd9d5fa693eca4beb14d54006682da7673317a47a08acb0a093fa7","abstract_canon_sha256":"f093454827d6480e9d84a68b13f159380a2ee70b116ded0fd041d95715782752"},"schema_version":"1.0"},"canonical_sha256":"944682ada193f50b0d2cd940f05aa41542262aac9858682f66fe71f73796f16b","source":{"kind":"arxiv","id":"1410.6293","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6293","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6293v1","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6293","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"pith_short_12","alias_value":"SRDIFLNBSP2Q","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SRDIFLNBSP2QWDJM","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SRDIFLNB","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SRDIFLNBSP2QWDJM3FAPAWVECV","target":"record","payload":{"canonical_record":{"source":{"id":"1410.6293","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-23T08:54:23Z","cross_cats_sorted":[],"title_canon_sha256":"0c761f61bcbd9d5fa693eca4beb14d54006682da7673317a47a08acb0a093fa7","abstract_canon_sha256":"f093454827d6480e9d84a68b13f159380a2ee70b116ded0fd041d95715782752"},"schema_version":"1.0"},"canonical_sha256":"944682ada193f50b0d2cd940f05aa41542262aac9858682f66fe71f73796f16b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:31.177849Z","signature_b64":"yJriJjHTsoDpIKeGUJBPTiVV76zkAHL2P/7ksZQcI5HCjCn4EQWKVENfEYLvajjKsyQQaCzcupmXDeUJ577WCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"944682ada193f50b0d2cd940f05aa41542262aac9858682f66fe71f73796f16b","last_reissued_at":"2026-05-18T02:39:31.177169Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:31.177169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.6293","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":"2026-05-18T02:39:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uLhPhbNbpNRnozqMjILqXB8J7ZkSfcqCpFqFG80tpTtQyCyeVMM3UONNxng+45UBp9gRah6x1eTCrH19iz5nAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:22:48.920338Z"},"content_sha256":"8bd9d9466beceab8d4ff431828a92158c6c453c0939db1ffc9907f9244e15916","schema_version":"1.0","event_id":"sha256:8bd9d9466beceab8d4ff431828a92158c6c453c0939db1ffc9907f9244e15916"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SRDIFLNBSP2QWDJM3FAPAWVECV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Near Preservation of Quadratic Invariants by Stochastic Runge-Kutta Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dongsheng Xu, Jialin Hong, Lijin Wang, Liying Zhang","submitted_at":"2014-10-23T08:54:23Z","abstract_excerpt":"Based on the combinatory theory of rooted colored trees, we investigate the conditions for the explicit stochastic Runge-Kutta (SRK) methods to preserve quadratic invariants (QI) up to certain orders of accuracy. These conditions can supply a practical approach of constructing explicit nearly conservative SRK methods. Meanwhile, we estimate errors in the preservation of QI resulting from iterative implementation of implicit conservative SRK methods with fixed-point and Newton's iterations. Finally, numerical experiments are performed to test the behavior of the methods in preserving QI."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6293","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":"2026-05-18T02:39:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wdpr1cT8zwYRnxqnuc0cgqoAkhcS6giaP7gUxvVi7REInGZieWeGX2Jah2aRbDqO9aOeU2HZvRZeKNVqQ42sCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:22:48.921274Z"},"content_sha256":"5834d84690d16febcdee440de84dce6865a1d71515d34edae758347af813d0db","schema_version":"1.0","event_id":"sha256:5834d84690d16febcdee440de84dce6865a1d71515d34edae758347af813d0db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SRDIFLNBSP2QWDJM3FAPAWVECV/bundle.json","state_url":"https://pith.science/pith/SRDIFLNBSP2QWDJM3FAPAWVECV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SRDIFLNBSP2QWDJM3FAPAWVECV/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":"2026-05-30T05:22:48Z","links":{"resolver":"https://pith.science/pith/SRDIFLNBSP2QWDJM3FAPAWVECV","bundle":"https://pith.science/pith/SRDIFLNBSP2QWDJM3FAPAWVECV/bundle.json","state":"https://pith.science/pith/SRDIFLNBSP2QWDJM3FAPAWVECV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SRDIFLNBSP2QWDJM3FAPAWVECV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SRDIFLNBSP2QWDJM3FAPAWVECV","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":"f093454827d6480e9d84a68b13f159380a2ee70b116ded0fd041d95715782752","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-23T08:54:23Z","title_canon_sha256":"0c761f61bcbd9d5fa693eca4beb14d54006682da7673317a47a08acb0a093fa7"},"schema_version":"1.0","source":{"id":"1410.6293","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6293","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6293v1","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6293","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"pith_short_12","alias_value":"SRDIFLNBSP2Q","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SRDIFLNBSP2QWDJM","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SRDIFLNB","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:5834d84690d16febcdee440de84dce6865a1d71515d34edae758347af813d0db","target":"graph","created_at":"2026-05-18T02:39:31Z","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":"Based on the combinatory theory of rooted colored trees, we investigate the conditions for the explicit stochastic Runge-Kutta (SRK) methods to preserve quadratic invariants (QI) up to certain orders of accuracy. These conditions can supply a practical approach of constructing explicit nearly conservative SRK methods. Meanwhile, we estimate errors in the preservation of QI resulting from iterative implementation of implicit conservative SRK methods with fixed-point and Newton's iterations. Finally, numerical experiments are performed to test the behavior of the methods in preserving QI.","authors_text":"Dongsheng Xu, Jialin Hong, Lijin Wang, Liying Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-23T08:54:23Z","title":"Near Preservation of Quadratic Invariants by Stochastic Runge-Kutta Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6293","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":"sha256:8bd9d9466beceab8d4ff431828a92158c6c453c0939db1ffc9907f9244e15916","target":"record","created_at":"2026-05-18T02:39:31Z","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":"f093454827d6480e9d84a68b13f159380a2ee70b116ded0fd041d95715782752","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-23T08:54:23Z","title_canon_sha256":"0c761f61bcbd9d5fa693eca4beb14d54006682da7673317a47a08acb0a093fa7"},"schema_version":"1.0","source":{"id":"1410.6293","kind":"arxiv","version":1}},"canonical_sha256":"944682ada193f50b0d2cd940f05aa41542262aac9858682f66fe71f73796f16b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"944682ada193f50b0d2cd940f05aa41542262aac9858682f66fe71f73796f16b","first_computed_at":"2026-05-18T02:39:31.177169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:31.177169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yJriJjHTsoDpIKeGUJBPTiVV76zkAHL2P/7ksZQcI5HCjCn4EQWKVENfEYLvajjKsyQQaCzcupmXDeUJ577WCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:31.177849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6293","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bd9d9466beceab8d4ff431828a92158c6c453c0939db1ffc9907f9244e15916","sha256:5834d84690d16febcdee440de84dce6865a1d71515d34edae758347af813d0db"],"state_sha256":"97f43ea05ee881ff541a709962c2250420448bf4468dbe7952ecdb1a638dfea8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cCPsrtkzjQUpyMV0awKIo1sEqdigHfrT9NrcZWpjwMphxousAnX0mFhAtaPWbwOV2eolAXHA+lwRP1ekPSU6BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:22:48.924710Z","bundle_sha256":"6c5aa6a3ea6af9f334510a942d3fb71de31e50d101122773acccd2542f03c346"}}