{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:UHP4XP3M55N2OJWFZ72K5F7EZG","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":"1fb0041447cff7f69ce41d6c10f3cfe0e874869c8e4a4ce2996f49d1996d3d25","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-08-24T13:04:00Z","title_canon_sha256":"988251709b90d3c517609d7c415928d0871a3d82ae6fb8e1844855a043fef508"},"schema_version":"1.0","source":{"id":"2308.12758","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.12758","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"arxiv_version","alias_value":"2308.12758v3","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.12758","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"pith_short_12","alias_value":"UHP4XP3M55N2","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"pith_short_16","alias_value":"UHP4XP3M55N2OJWF","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"pith_short_8","alias_value":"UHP4XP3M","created_at":"2026-07-05T10:59:56Z"}],"graph_snapshots":[{"event_id":"sha256:f152b459a6baeb683b5e77d38a35cf6e6ae9d571c11f4f491eb4af81eed0d78e","target":"graph","created_at":"2026-07-05T10:59:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2308.12758/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Chenmin Sun, Nikolay Tzvetkov","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-08-24T13:04:00Z","title":"Quasi-invariance of Gaussian measures for the $3d$ energy critical nonlinear Schr\\\" odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.12758","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":"sha256:3867d7376d2ff51830f69f103f886067c13a73405abd9c5353de52a84a48d2f6","target":"record","created_at":"2026-07-05T10:59:56Z","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":"1fb0041447cff7f69ce41d6c10f3cfe0e874869c8e4a4ce2996f49d1996d3d25","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-08-24T13:04:00Z","title_canon_sha256":"988251709b90d3c517609d7c415928d0871a3d82ae6fb8e1844855a043fef508"},"schema_version":"1.0","source":{"id":"2308.12758","kind":"arxiv","version":3}},"canonical_sha256":"a1dfcbbf6cef5ba726c5cff4ae97e4c9b027aacbc76b122526621c10b52046ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1dfcbbf6cef5ba726c5cff4ae97e4c9b027aacbc76b122526621c10b52046ef","first_computed_at":"2026-07-05T10:59:56.385178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:59:56.385178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FuX/jZFJBZuGP50mqT/Ybenn7X+jOTHSJmhRTpWtee7hdOdcN3Wasl7nrqbbeJgmu2dP5KRCeGII+1pDua8pDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:59:56.385620Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.12758","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3867d7376d2ff51830f69f103f886067c13a73405abd9c5353de52a84a48d2f6","sha256:f152b459a6baeb683b5e77d38a35cf6e6ae9d571c11f4f491eb4af81eed0d78e"],"state_sha256":"f7fdaf7cba377999303e03708ea1132584df190e4a39aa4350f2596b10073e7f"}