{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:UNN7TWXSGTXVOWQRDNK3UXK4EY","short_pith_number":"pith:UNN7TWXS","schema_version":"1.0","canonical_sha256":"a35bf9daf234ef575a111b55ba5d5c2605c054f89b3c74696f3e161788f6b10d","source":{"kind":"arxiv","id":"2406.07116","version":1},"attestation_state":"computed","paper":{"title":"Transport of low regularity Gaussian measures for the 1d quintic nonlinear Schr\\\"odinger equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexis Knezevitch","submitted_at":"2024-06-11T10:01:51Z","abstract_excerpt":"We consider the 1d nonlinear Schr\\\"odinger equation (NLS) on the torus with initial data distributed according to the Gaussian measure with covariance operator $(1 - \\Delta)^{-s}$, where $\\Delta$ is the Laplace operator. We prove that the Gaussian measures are quasi-invariant along the flow of (NLS) for the full range $s > \\frac{3}{2}$. This improves a previous result obtained by Planchon, Tzvetkov and Visciglia (in 2019), where the quasi-invariance is proven for $s=2k$, for all integers $k\\geq 1$. In our approach, to prove the quasi-invariance, we directly establish an explicit formula for th"},"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":"2406.07116","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-11T10:01:51Z","cross_cats_sorted":[],"title_canon_sha256":"f6f06b770c8981d42459c884b6f7fcece5b6314c652b2f5b9993c5df091d4b8e","abstract_canon_sha256":"3f09a86214f9c9229efcd9f78ae201264e72f65b89180554fd3bf1d7d84ac16b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:51:22.918498Z","signature_b64":"Z9lrC4d95ZF6iTuxIus2Br9hcvDHrSRz/g9I6tDsRxWDkHwEbXQ+gdrSixTs/QLy3Hyq/8ER8Qf+IeIlH3o4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a35bf9daf234ef575a111b55ba5d5c2605c054f89b3c74696f3e161788f6b10d","last_reissued_at":"2026-07-05T10:51:22.917966Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:51:22.917966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transport of low regularity Gaussian measures for the 1d quintic nonlinear Schr\\\"odinger equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexis Knezevitch","submitted_at":"2024-06-11T10:01:51Z","abstract_excerpt":"We consider the 1d nonlinear Schr\\\"odinger equation (NLS) on the torus with initial data distributed according to the Gaussian measure with covariance operator $(1 - \\Delta)^{-s}$, where $\\Delta$ is the Laplace operator. We prove that the Gaussian measures are quasi-invariant along the flow of (NLS) for the full range $s > \\frac{3}{2}$. This improves a previous result obtained by Planchon, Tzvetkov and Visciglia (in 2019), where the quasi-invariance is proven for $s=2k$, for all integers $k\\geq 1$. In our approach, to prove the quasi-invariance, we directly establish an explicit formula for th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.07116","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.07116/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":"2406.07116","created_at":"2026-07-05T10:51:22.918034+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.07116v1","created_at":"2026-07-05T10:51:22.918034+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.07116","created_at":"2026-07-05T10:51:22.918034+00:00"},{"alias_kind":"pith_short_12","alias_value":"UNN7TWXSGTXV","created_at":"2026-07-05T10:51:22.918034+00:00"},{"alias_kind":"pith_short_16","alias_value":"UNN7TWXSGTXVOWQR","created_at":"2026-07-05T10:51:22.918034+00:00"},{"alias_kind":"pith_short_8","alias_value":"UNN7TWXS","created_at":"2026-07-05T10:51:22.918034+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.17180","citing_title":"Improved quasi-invariance result for the periodic Benjamin-Ono-BBM equation","ref_index":24,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UNN7TWXSGTXVOWQRDNK3UXK4EY","json":"https://pith.science/pith/UNN7TWXSGTXVOWQRDNK3UXK4EY.json","graph_json":"https://pith.science/api/pith-number/UNN7TWXSGTXVOWQRDNK3UXK4EY/graph.json","events_json":"https://pith.science/api/pith-number/UNN7TWXSGTXVOWQRDNK3UXK4EY/events.json","paper":"https://pith.science/paper/UNN7TWXS"},"agent_actions":{"view_html":"https://pith.science/pith/UNN7TWXSGTXVOWQRDNK3UXK4EY","download_json":"https://pith.science/pith/UNN7TWXSGTXVOWQRDNK3UXK4EY.json","view_paper":"https://pith.science/paper/UNN7TWXS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.07116&json=true","fetch_graph":"https://pith.science/api/pith-number/UNN7TWXSGTXVOWQRDNK3UXK4EY/graph.json","fetch_events":"https://pith.science/api/pith-number/UNN7TWXSGTXVOWQRDNK3UXK4EY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UNN7TWXSGTXVOWQRDNK3UXK4EY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UNN7TWXSGTXVOWQRDNK3UXK4EY/action/storage_attestation","attest_author":"https://pith.science/pith/UNN7TWXSGTXVOWQRDNK3UXK4EY/action/author_attestation","sign_citation":"https://pith.science/pith/UNN7TWXSGTXVOWQRDNK3UXK4EY/action/citation_signature","submit_replication":"https://pith.science/pith/UNN7TWXSGTXVOWQRDNK3UXK4EY/action/replication_record"}},"created_at":"2026-07-05T10:51:22.918034+00:00","updated_at":"2026-07-05T10:51:22.918034+00:00"}