{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:UHP4XP3M55N2OJWFZ72K5F7EZG","short_pith_number":"pith:UHP4XP3M","schema_version":"1.0","canonical_sha256":"a1dfcbbf6cef5ba726c5cff4ae97e4c9b027aacbc76b122526621c10b52046ef","source":{"kind":"arxiv","id":"2308.12758","version":3},"attestation_state":"computed","paper":{"title":"Quasi-invariance of Gaussian measures for the $3d$ energy critical nonlinear Schr\\\" odinger equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Chenmin Sun, Nikolay Tzvetkov","submitted_at":"2023-08-24T13:04:00Z","abstract_excerpt":"We consider the $3d$ energy critical nonlinear Schr\\\" odinger equation with data distributed according to the Gaussian measure with covariance operator $(1-\\Delta)^{-s}$, where $\\Delta$ is the Laplace operator and $s$ is sufficiently large. We prove that the flow sends full measure sets to full measure sets. We also discuss some simple applications. This extends a previous result by Planchon-Visciglia and the second author from $1d$ to higher dimensions."},"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":"2308.12758","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-08-24T13:04:00Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"988251709b90d3c517609d7c415928d0871a3d82ae6fb8e1844855a043fef508","abstract_canon_sha256":"1fb0041447cff7f69ce41d6c10f3cfe0e874869c8e4a4ce2996f49d1996d3d25"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:59:56.385620Z","signature_b64":"FuX/jZFJBZuGP50mqT/Ybenn7X+jOTHSJmhRTpWtee7hdOdcN3Wasl7nrqbbeJgmu2dP5KRCeGII+1pDua8pDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1dfcbbf6cef5ba726c5cff4ae97e4c9b027aacbc76b122526621c10b52046ef","last_reissued_at":"2026-07-05T10:59:56.385178Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:59:56.385178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasi-invariance of Gaussian measures for the $3d$ energy critical nonlinear Schr\\\" odinger equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Chenmin Sun, Nikolay Tzvetkov","submitted_at":"2023-08-24T13:04:00Z","abstract_excerpt":"We consider the $3d$ energy critical nonlinear Schr\\\" odinger equation with data distributed according to the Gaussian measure with covariance operator $(1-\\Delta)^{-s}$, where $\\Delta$ is the Laplace operator and $s$ is sufficiently large. We prove that the flow sends full measure sets to full measure sets. We also discuss some simple applications. This extends a previous result by Planchon-Visciglia and the second author from $1d$ to higher dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.12758","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.12758/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2308.12758","created_at":"2026-07-05T10:59:56.385237+00:00"},{"alias_kind":"arxiv_version","alias_value":"2308.12758v3","created_at":"2026-07-05T10:59:56.385237+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.12758","created_at":"2026-07-05T10:59:56.385237+00:00"},{"alias_kind":"pith_short_12","alias_value":"UHP4XP3M55N2","created_at":"2026-07-05T10:59:56.385237+00:00"},{"alias_kind":"pith_short_16","alias_value":"UHP4XP3M55N2OJWF","created_at":"2026-07-05T10:59:56.385237+00:00"},{"alias_kind":"pith_short_8","alias_value":"UHP4XP3M","created_at":"2026-07-05T10:59:56.385237+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.02162","citing_title":"New invariant surface measures for the cubic Schr\\\"odinger equation","ref_index":27,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UHP4XP3M55N2OJWFZ72K5F7EZG","json":"https://pith.science/pith/UHP4XP3M55N2OJWFZ72K5F7EZG.json","graph_json":"https://pith.science/api/pith-number/UHP4XP3M55N2OJWFZ72K5F7EZG/graph.json","events_json":"https://pith.science/api/pith-number/UHP4XP3M55N2OJWFZ72K5F7EZG/events.json","paper":"https://pith.science/paper/UHP4XP3M"},"agent_actions":{"view_html":"https://pith.science/pith/UHP4XP3M55N2OJWFZ72K5F7EZG","download_json":"https://pith.science/pith/UHP4XP3M55N2OJWFZ72K5F7EZG.json","view_paper":"https://pith.science/paper/UHP4XP3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2308.12758&json=true","fetch_graph":"https://pith.science/api/pith-number/UHP4XP3M55N2OJWFZ72K5F7EZG/graph.json","fetch_events":"https://pith.science/api/pith-number/UHP4XP3M55N2OJWFZ72K5F7EZG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UHP4XP3M55N2OJWFZ72K5F7EZG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UHP4XP3M55N2OJWFZ72K5F7EZG/action/storage_attestation","attest_author":"https://pith.science/pith/UHP4XP3M55N2OJWFZ72K5F7EZG/action/author_attestation","sign_citation":"https://pith.science/pith/UHP4XP3M55N2OJWFZ72K5F7EZG/action/citation_signature","submit_replication":"https://pith.science/pith/UHP4XP3M55N2OJWFZ72K5F7EZG/action/replication_record"}},"created_at":"2026-07-05T10:59:56.385237+00:00","updated_at":"2026-07-05T10:59:56.385237+00:00"}