{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ND4CTSHJOOOM2PWZP7LZUGGIVS","short_pith_number":"pith:ND4CTSHJ","canonical_record":{"source":{"id":"1701.05680","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-20T04:13:44Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"a03e60ea80c91ed09e08a2317683e55d47843fb767b5d42de898f530d137a828","abstract_canon_sha256":"9a189662659bd6ea979670fdc48237df8ccd523212a6622f4b17f02974481ead"},"schema_version":"1.0"},"canonical_sha256":"68f829c8e9739ccd3ed97fd79a18c8acaab8993cb8498aef0e57206cb177a630","source":{"kind":"arxiv","id":"1701.05680","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05680","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05680v3","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05680","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"pith_short_12","alias_value":"ND4CTSHJOOOM","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"ND4CTSHJOOOM2PWZ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"ND4CTSHJ","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ND4CTSHJOOOM2PWZP7LZUGGIVS","target":"record","payload":{"canonical_record":{"source":{"id":"1701.05680","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-20T04:13:44Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"a03e60ea80c91ed09e08a2317683e55d47843fb767b5d42de898f530d137a828","abstract_canon_sha256":"9a189662659bd6ea979670fdc48237df8ccd523212a6622f4b17f02974481ead"},"schema_version":"1.0"},"canonical_sha256":"68f829c8e9739ccd3ed97fd79a18c8acaab8993cb8498aef0e57206cb177a630","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:01.597644Z","signature_b64":"AlcyUSHDX7EcfLv6Lom9SPX4Bvc+ieGZyvdWV55lm0kCgvPCL5ll+bkmcgytnk7ucpHa/3iK7hE+N0Naiz9tCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68f829c8e9739ccd3ed97fd79a18c8acaab8993cb8498aef0e57206cb177a630","last_reissued_at":"2026-05-17T23:53:01.596997Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:01.596997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.05680","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LGgsqPRcm5MAiY6vvYz4EDZhLOpK08OwmsBwVn2sjCuFKgvG/lPUeHazlznEh69RWMAxu+OdXHCwX10kwpJACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T23:59:40.114196Z"},"content_sha256":"ba54121a41d397471f5be70dcda52791d0f0273161676f068fd9a158f6125745","schema_version":"1.0","event_id":"sha256:ba54121a41d397471f5be70dcda52791d0f0273161676f068fd9a158f6125745"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ND4CTSHJOOOM2PWZP7LZUGGIVS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strong Convergence Rate of Splitting Schemes for Stochastic Nonlinear Schr\\\"odinger Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NA","authors_text":"Jialin Hong, Jianbo Cui, Weien Zhou, Zhihui Liu","submitted_at":"2017-01-20T04:13:44Z","abstract_excerpt":"We prove the optimal strong convergence rate of a fully discrete scheme, based on a splitting approach, for a stochastic nonlinear Schr\\\"odinger (NLS) equation. The main novelty of our method lies on the uniform a priori estimate and exponential integrability of a sequence of splitting processes which are used to approximate the solution of the stochastic NLS equation. We show that the splitting processes converge to the solution with strong order $1/2$. Then we use the Crank--Nicolson scheme to temporally discretize the splitting process and get the temporal splitting scheme which also posses"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05680","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c2bC5maqzAE+Nb+FBbJ+NlM6qQNStifEYTmDdiWM3o+DVvns6az8BtOiZC5s0upaerTaoBWCOanENPS5QpiiCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T23:59:40.114582Z"},"content_sha256":"7bdb582fa97ad963877f43596b1055890b3244e1c3ef50e5dd6f148fbcd759a4","schema_version":"1.0","event_id":"sha256:7bdb582fa97ad963877f43596b1055890b3244e1c3ef50e5dd6f148fbcd759a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS/bundle.json","state_url":"https://pith.science/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS/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":"2026-05-29T23:59:40Z","links":{"resolver":"https://pith.science/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS","bundle":"https://pith.science/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS/bundle.json","state":"https://pith.science/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ND4CTSHJOOOM2PWZP7LZUGGIVS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ND4CTSHJOOOM2PWZP7LZUGGIVS","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":"9a189662659bd6ea979670fdc48237df8ccd523212a6622f4b17f02974481ead","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-20T04:13:44Z","title_canon_sha256":"a03e60ea80c91ed09e08a2317683e55d47843fb767b5d42de898f530d137a828"},"schema_version":"1.0","source":{"id":"1701.05680","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05680","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05680v3","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05680","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"pith_short_12","alias_value":"ND4CTSHJOOOM","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"ND4CTSHJOOOM2PWZ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"ND4CTSHJ","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:7bdb582fa97ad963877f43596b1055890b3244e1c3ef50e5dd6f148fbcd759a4","target":"graph","created_at":"2026-05-17T23:53:01Z","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":"We prove the optimal strong convergence rate of a fully discrete scheme, based on a splitting approach, for a stochastic nonlinear Schr\\\"odinger (NLS) equation. The main novelty of our method lies on the uniform a priori estimate and exponential integrability of a sequence of splitting processes which are used to approximate the solution of the stochastic NLS equation. We show that the splitting processes converge to the solution with strong order $1/2$. Then we use the Crank--Nicolson scheme to temporally discretize the splitting process and get the temporal splitting scheme which also posses","authors_text":"Jialin Hong, Jianbo Cui, Weien Zhou, Zhihui Liu","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-20T04:13:44Z","title":"Strong Convergence Rate of Splitting Schemes for Stochastic Nonlinear Schr\\\"odinger Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05680","kind":"arxiv","version":3},"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:ba54121a41d397471f5be70dcda52791d0f0273161676f068fd9a158f6125745","target":"record","created_at":"2026-05-17T23:53:01Z","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":"9a189662659bd6ea979670fdc48237df8ccd523212a6622f4b17f02974481ead","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-20T04:13:44Z","title_canon_sha256":"a03e60ea80c91ed09e08a2317683e55d47843fb767b5d42de898f530d137a828"},"schema_version":"1.0","source":{"id":"1701.05680","kind":"arxiv","version":3}},"canonical_sha256":"68f829c8e9739ccd3ed97fd79a18c8acaab8993cb8498aef0e57206cb177a630","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68f829c8e9739ccd3ed97fd79a18c8acaab8993cb8498aef0e57206cb177a630","first_computed_at":"2026-05-17T23:53:01.596997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:01.596997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AlcyUSHDX7EcfLv6Lom9SPX4Bvc+ieGZyvdWV55lm0kCgvPCL5ll+bkmcgytnk7ucpHa/3iK7hE+N0Naiz9tCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:01.597644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05680","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba54121a41d397471f5be70dcda52791d0f0273161676f068fd9a158f6125745","sha256:7bdb582fa97ad963877f43596b1055890b3244e1c3ef50e5dd6f148fbcd759a4"],"state_sha256":"0ccbc169c4c575001e99608462553318c90fb1859f3bfe5c7c49c56443cf82ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qsiked5Tvki64fmWNcHmH3FhvgA5lKhSVP1+4FhrLX70csMKnLhOZJvlCuZPx0bPNy50FMYhSg1GY5P3uWAmCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T23:59:40.116916Z","bundle_sha256":"1bcfa043bcc6ca1353eeabbd0c88680f2785aef2f0007e1a1e5ba33121d3645a"}}