{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OLS7KKJRWBJDNGBKVFZ5SVXA5X","short_pith_number":"pith:OLS7KKJR","canonical_record":{"source":{"id":"1409.4007","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-14T02:58:46Z","cross_cats_sorted":[],"title_canon_sha256":"e62adca537d38eca6310f92c50eaef288d3e345acaf8acf278c4d6b42b9e28a2","abstract_canon_sha256":"e1e6602ba6ccc7dda2331599ddf6a1400320d95628ce9bbbd66f2cdf15a1db4e"},"schema_version":"1.0"},"canonical_sha256":"72e5f52931b05236982aa973d956e0edd2b3873b70220a6560aace805de7e52b","source":{"kind":"arxiv","id":"1409.4007","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4007","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4007v1","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4007","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"OLS7KKJRWBJD","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OLS7KKJRWBJDNGBK","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OLS7KKJR","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OLS7KKJRWBJDNGBKVFZ5SVXA5X","target":"record","payload":{"canonical_record":{"source":{"id":"1409.4007","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-14T02:58:46Z","cross_cats_sorted":[],"title_canon_sha256":"e62adca537d38eca6310f92c50eaef288d3e345acaf8acf278c4d6b42b9e28a2","abstract_canon_sha256":"e1e6602ba6ccc7dda2331599ddf6a1400320d95628ce9bbbd66f2cdf15a1db4e"},"schema_version":"1.0"},"canonical_sha256":"72e5f52931b05236982aa973d956e0edd2b3873b70220a6560aace805de7e52b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:53.247631Z","signature_b64":"gVmJ0n08MHBMynz6xlhfiN8sDDDpgM0OdQu3MmbpmLwNaFTvwljEsY8xe+2WvfQnl32qb05wqO91T5eLS9PkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72e5f52931b05236982aa973d956e0edd2b3873b70220a6560aace805de7e52b","last_reissued_at":"2026-05-18T02:42:53.247267Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:53.247267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.4007","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":"2026-05-18T02:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CUqSTPmLXlThYsVrIuE4TBinBcUTNocW7uq/1vqhWOcNc2iuPeuRwzyMOM8VwYOlHtSKXoezmfzDOQIVw3aaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:12:35.089890Z"},"content_sha256":"7cf33f926df349f5519c7d4995e42b5c43c789538b45187dadddccd4103bcc21","schema_version":"1.0","event_id":"sha256:7cf33f926df349f5519c7d4995e42b5c43c789538b45187dadddccd4103bcc21"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OLS7KKJRWBJDNGBKVFZ5SVXA5X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic nonlinear Schr\\\"odinger equations: no blow-up in the non-conservative case","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":"2014-09-14T02:58:46Z","abstract_excerpt":"This paper is devoted to the study of noise effects on blow-up solutions to stochastic nonlinear Schr\\\"odinger equations. It is a continuation of our recent work \\cite{BRZ14}, where the (local) well-posedness is established in $H^1$, also in the non-conservative critical case. Here we prove that in the non-conservative focusing mass-(super)critical case, by adding a large multiplicative Gaussian noise, with high probability one can prevent the blow-up on any given bounded time interval $[0,T]$, $0<T<\\9$. Moreover, in the case of spatially independent noise, the explosion even can be prevented "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4007","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":"2026-05-18T02:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MpM4pKae9OyVswADDgsgxUuKi36oPnke3zYvsD53gvJHVrR8AGpFVHVDNbbZ8sTl+sax5MpmkZCY4wixYt7xAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:12:35.090244Z"},"content_sha256":"3681426cd276751d66e39b8cf6acf781274fecdb6089e7be6cb290893ecb6143","schema_version":"1.0","event_id":"sha256:3681426cd276751d66e39b8cf6acf781274fecdb6089e7be6cb290893ecb6143"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OLS7KKJRWBJDNGBKVFZ5SVXA5X/bundle.json","state_url":"https://pith.science/pith/OLS7KKJRWBJDNGBKVFZ5SVXA5X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OLS7KKJRWBJDNGBKVFZ5SVXA5X/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":"2026-06-23T20:12:35Z","links":{"resolver":"https://pith.science/pith/OLS7KKJRWBJDNGBKVFZ5SVXA5X","bundle":"https://pith.science/pith/OLS7KKJRWBJDNGBKVFZ5SVXA5X/bundle.json","state":"https://pith.science/pith/OLS7KKJRWBJDNGBKVFZ5SVXA5X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OLS7KKJRWBJDNGBKVFZ5SVXA5X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OLS7KKJRWBJDNGBKVFZ5SVXA5X","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":"e1e6602ba6ccc7dda2331599ddf6a1400320d95628ce9bbbd66f2cdf15a1db4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-14T02:58:46Z","title_canon_sha256":"e62adca537d38eca6310f92c50eaef288d3e345acaf8acf278c4d6b42b9e28a2"},"schema_version":"1.0","source":{"id":"1409.4007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4007","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4007v1","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4007","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"OLS7KKJRWBJD","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OLS7KKJRWBJDNGBK","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OLS7KKJR","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:3681426cd276751d66e39b8cf6acf781274fecdb6089e7be6cb290893ecb6143","target":"graph","created_at":"2026-05-18T02:42:53Z","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":"This paper is devoted to the study of noise effects on blow-up solutions to stochastic nonlinear Schr\\\"odinger equations. It is a continuation of our recent work \\cite{BRZ14}, where the (local) well-posedness is established in $H^1$, also in the non-conservative critical case. Here we prove that in the non-conservative focusing mass-(super)critical case, by adding a large multiplicative Gaussian noise, with high probability one can prevent the blow-up on any given bounded time interval $[0,T]$, $0<T<\\9$. Moreover, in the case of spatially independent noise, the explosion even can be prevented ","authors_text":"Deng Zhang, Michael R\\\"ockner, Viorel Barbu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-14T02:58:46Z","title":"Stochastic nonlinear Schr\\\"odinger equations: no blow-up in the non-conservative case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4007","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":"sha256:7cf33f926df349f5519c7d4995e42b5c43c789538b45187dadddccd4103bcc21","target":"record","created_at":"2026-05-18T02:42:53Z","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":"e1e6602ba6ccc7dda2331599ddf6a1400320d95628ce9bbbd66f2cdf15a1db4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-14T02:58:46Z","title_canon_sha256":"e62adca537d38eca6310f92c50eaef288d3e345acaf8acf278c4d6b42b9e28a2"},"schema_version":"1.0","source":{"id":"1409.4007","kind":"arxiv","version":1}},"canonical_sha256":"72e5f52931b05236982aa973d956e0edd2b3873b70220a6560aace805de7e52b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72e5f52931b05236982aa973d956e0edd2b3873b70220a6560aace805de7e52b","first_computed_at":"2026-05-18T02:42:53.247267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:53.247267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gVmJ0n08MHBMynz6xlhfiN8sDDDpgM0OdQu3MmbpmLwNaFTvwljEsY8xe+2WvfQnl32qb05wqO91T5eLS9PkBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:53.247631Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.4007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cf33f926df349f5519c7d4995e42b5c43c789538b45187dadddccd4103bcc21","sha256:3681426cd276751d66e39b8cf6acf781274fecdb6089e7be6cb290893ecb6143"],"state_sha256":"5226d512a81710bd51b8ec80b34b79bf2c7ae79907b89533d14bf67a5c207788"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D5OvLiZesErNuVeoY/EJ/17isfpZDzeqBJyEU0GkHpzGrfe2RajWASqzO4wkmkL917I9JvQHL9Daj/sf0sfcDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T20:12:35.092177Z","bundle_sha256":"4b055864e345f24a6185bbbb638ab5ecd39fa51cb27684fef8b450414cdc3a06"}}