{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KULXJL6GUGRDZYIFUUR3XESB5X","short_pith_number":"pith:KULXJL6G","schema_version":"1.0","canonical_sha256":"551774afc6a1a23ce105a523bb9241edfc1e3aeded5b3398de3f486371731f1c","source":{"kind":"arxiv","id":"1404.5039","version":1},"attestation_state":"computed","paper":{"title":"Stochastic nonlinear Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Deng Zhang, Michael R\\\"ockner, Viorel Barbu","submitted_at":"2014-04-20T13:56:18Z","abstract_excerpt":"This paper is devoted to the well-posedness of stochastic nonlinear Schr\\\"odinger equations in the energy space H1(Rd), which is a natural continuation of our recent work [1]. We consider both focusing and defocusing nonlinearities and prove global well-posedness in H1(Rd), including also the pathwise continuous dependence on initial conditions, with exponents exactly the same as in the deterministic case. In particular, this work improves earlier results in [4]. Moreover, the local existence, uniqueness and blowup alternative are also established for the energy-critical case. The approach pre"},"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":"1404.5039","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-20T13:56:18Z","cross_cats_sorted":[],"title_canon_sha256":"9dc331588e316a940bcdc385e12832f5d31ac19e5a6656257f56813f1293537d","abstract_canon_sha256":"c64c43945481a518355210b6ff996d3dcd8fcffcd7245e6b4b59afb448d43b90"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:52.100608Z","signature_b64":"WJz3aHD62dGU1YAik0xXf5iuRfxhsErKwBKO/4seAm7vZ26d2XwW56EPGFWLkz6Iddryi2nTUFBfXtx0txDGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"551774afc6a1a23ce105a523bb9241edfc1e3aeded5b3398de3f486371731f1c","last_reissued_at":"2026-05-18T02:53:52.099704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:52.099704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic nonlinear Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Deng Zhang, Michael R\\\"ockner, Viorel Barbu","submitted_at":"2014-04-20T13:56:18Z","abstract_excerpt":"This paper is devoted to the well-posedness of stochastic nonlinear Schr\\\"odinger equations in the energy space H1(Rd), which is a natural continuation of our recent work [1]. We consider both focusing and defocusing nonlinearities and prove global well-posedness in H1(Rd), including also the pathwise continuous dependence on initial conditions, with exponents exactly the same as in the deterministic case. In particular, this work improves earlier results in [4]. Moreover, the local existence, uniqueness and blowup alternative are also established for the energy-critical case. The approach pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5039","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1404.5039","created_at":"2026-05-18T02:53:52.099861+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.5039v1","created_at":"2026-05-18T02:53:52.099861+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5039","created_at":"2026-05-18T02:53:52.099861+00:00"},{"alias_kind":"pith_short_12","alias_value":"KULXJL6GUGRD","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KULXJL6GUGRDZYIF","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KULXJL6G","created_at":"2026-05-18T12:28:35.611951+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/KULXJL6GUGRDZYIFUUR3XESB5X","json":"https://pith.science/pith/KULXJL6GUGRDZYIFUUR3XESB5X.json","graph_json":"https://pith.science/api/pith-number/KULXJL6GUGRDZYIFUUR3XESB5X/graph.json","events_json":"https://pith.science/api/pith-number/KULXJL6GUGRDZYIFUUR3XESB5X/events.json","paper":"https://pith.science/paper/KULXJL6G"},"agent_actions":{"view_html":"https://pith.science/pith/KULXJL6GUGRDZYIFUUR3XESB5X","download_json":"https://pith.science/pith/KULXJL6GUGRDZYIFUUR3XESB5X.json","view_paper":"https://pith.science/paper/KULXJL6G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.5039&json=true","fetch_graph":"https://pith.science/api/pith-number/KULXJL6GUGRDZYIFUUR3XESB5X/graph.json","fetch_events":"https://pith.science/api/pith-number/KULXJL6GUGRDZYIFUUR3XESB5X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KULXJL6GUGRDZYIFUUR3XESB5X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KULXJL6GUGRDZYIFUUR3XESB5X/action/storage_attestation","attest_author":"https://pith.science/pith/KULXJL6GUGRDZYIFUUR3XESB5X/action/author_attestation","sign_citation":"https://pith.science/pith/KULXJL6GUGRDZYIFUUR3XESB5X/action/citation_signature","submit_replication":"https://pith.science/pith/KULXJL6GUGRDZYIFUUR3XESB5X/action/replication_record"}},"created_at":"2026-05-18T02:53:52.099861+00:00","updated_at":"2026-05-18T02:53:52.099861+00:00"}