{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ZVDA44KPDVDBEQHIEOIYIJNN7F","short_pith_number":"pith:ZVDA44KP","schema_version":"1.0","canonical_sha256":"cd460e714f1d461240e823918425adf96ae0c80ef4a878c3b2a77f07db127e74","source":{"kind":"arxiv","id":"1606.01510","version":2},"attestation_state":"computed","paper":{"title":"Numerical Analysis on Ergodic Limit of Approximations for Stochastic NLS Equation via Multi-symplectic Scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jialin Hong, Liying Zhang, Xu Wang","submitted_at":"2016-06-05T13:56:49Z","abstract_excerpt":"We consider a finite dimensional approximation of the stochastic nonlinear Schr\\\"odinger equation driven by multiplicative noise, which is derived by applying a symplectic method to the original equation in spatial direction. Both the unique ergodicity and the charge conservation law for this finite dimensional approximation are obtained on the unit sphere. To simulate the ergodic limit over long time for the finite dimensional approximation, we discretize it further in temporal direction to obtain a fully discrete scheme, which inherits not only the stochastic multi-symplecticity and charge c"},"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":"1606.01510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-05T13:56:49Z","cross_cats_sorted":[],"title_canon_sha256":"d14dbc420cdaf7d131e018f6a059070938e624b4e7fd7e3a60f8420b62afdb33","abstract_canon_sha256":"eb429d4bf73e580f468c153e230d0d97dcba34f6cbf15a6e0d64d87df735bf49"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:37.839006Z","signature_b64":"BODhLiBHlwD25O1GdPoz8u4xoSN+Je800qudN0VDh+R/ZPOqUHTl0jy6y2ltH8M9P8C1Q3kyibYi9RNRBCSxAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd460e714f1d461240e823918425adf96ae0c80ef4a878c3b2a77f07db127e74","last_reissued_at":"2026-05-18T00:56:37.838186Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:37.838186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerical Analysis on Ergodic Limit of Approximations for Stochastic NLS Equation via Multi-symplectic Scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jialin Hong, Liying Zhang, Xu Wang","submitted_at":"2016-06-05T13:56:49Z","abstract_excerpt":"We consider a finite dimensional approximation of the stochastic nonlinear Schr\\\"odinger equation driven by multiplicative noise, which is derived by applying a symplectic method to the original equation in spatial direction. Both the unique ergodicity and the charge conservation law for this finite dimensional approximation are obtained on the unit sphere. To simulate the ergodic limit over long time for the finite dimensional approximation, we discretize it further in temporal direction to obtain a fully discrete scheme, which inherits not only the stochastic multi-symplecticity and charge c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01510","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.01510","created_at":"2026-05-18T00:56:37.838331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.01510v2","created_at":"2026-05-18T00:56:37.838331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01510","created_at":"2026-05-18T00:56:37.838331+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZVDA44KPDVDB","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZVDA44KPDVDBEQHI","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZVDA44KP","created_at":"2026-05-18T12:30:55.937587+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/ZVDA44KPDVDBEQHIEOIYIJNN7F","json":"https://pith.science/pith/ZVDA44KPDVDBEQHIEOIYIJNN7F.json","graph_json":"https://pith.science/api/pith-number/ZVDA44KPDVDBEQHIEOIYIJNN7F/graph.json","events_json":"https://pith.science/api/pith-number/ZVDA44KPDVDBEQHIEOIYIJNN7F/events.json","paper":"https://pith.science/paper/ZVDA44KP"},"agent_actions":{"view_html":"https://pith.science/pith/ZVDA44KPDVDBEQHIEOIYIJNN7F","download_json":"https://pith.science/pith/ZVDA44KPDVDBEQHIEOIYIJNN7F.json","view_paper":"https://pith.science/paper/ZVDA44KP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.01510&json=true","fetch_graph":"https://pith.science/api/pith-number/ZVDA44KPDVDBEQHIEOIYIJNN7F/graph.json","fetch_events":"https://pith.science/api/pith-number/ZVDA44KPDVDBEQHIEOIYIJNN7F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZVDA44KPDVDBEQHIEOIYIJNN7F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZVDA44KPDVDBEQHIEOIYIJNN7F/action/storage_attestation","attest_author":"https://pith.science/pith/ZVDA44KPDVDBEQHIEOIYIJNN7F/action/author_attestation","sign_citation":"https://pith.science/pith/ZVDA44KPDVDBEQHIEOIYIJNN7F/action/citation_signature","submit_replication":"https://pith.science/pith/ZVDA44KPDVDBEQHIEOIYIJNN7F/action/replication_record"}},"created_at":"2026-05-18T00:56:37.838331+00:00","updated_at":"2026-05-18T00:56:37.838331+00:00"}