{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DN2CKJB5BLLDOJFWSWXSENY64D","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":"0c1c52fdcae29ca2052f805d83fc782c8dd4be6b46b6b2532b648b8a2166ab90","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-30T14:19:30Z","title_canon_sha256":"00d4c1a91ed53346c7be0762e2eb212aab7c366399121c2680d0058de8a2dec0"},"schema_version":"1.0","source":{"id":"2410.23051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.23051","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"arxiv_version","alias_value":"2410.23051v1","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.23051","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"pith_short_12","alias_value":"DN2CKJB5BLLD","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"pith_short_16","alias_value":"DN2CKJB5BLLDOJFW","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"pith_short_8","alias_value":"DN2CKJB5","created_at":"2026-07-05T09:28:40Z"}],"graph_snapshots":[{"event_id":"sha256:d3bb4c2f723aff3879537f653ecfdc7d93afe04ea90db4626d063d3188126936","target":"graph","created_at":"2026-07-05T09:28:40Z","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/2410.23051/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we pursue our investigations on the Cauchy problem for a class of dispersive PDEs where a rough time coefficient is present in front of the dispersion. We show that if the PDE satisfies a strong non-resonance condition (Theorem 1.6), eventually up to a completely resonant term (Theorem 1.9), then the modulated PDE is well-posed at any regularity index provided that the noise term in front of the dispersion is irregular enough. This extends earlier pioneering work of Chouk-Gubinelli and Chouk-Gubinelli-Li-Li-Oh to a more general context. We quantify the irregularity of the noise r","authors_text":"Tristan Robert","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-30T14:19:30Z","title":"Regularization by noise for some strongly non-resonant modulated dispersive PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.23051","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":"sha256:0267b9f47aa723dd5d33ecb29d59ecbfedb726818d17122ab39fab53354bbf2b","target":"record","created_at":"2026-07-05T09:28:40Z","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":"0c1c52fdcae29ca2052f805d83fc782c8dd4be6b46b6b2532b648b8a2166ab90","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-30T14:19:30Z","title_canon_sha256":"00d4c1a91ed53346c7be0762e2eb212aab7c366399121c2680d0058de8a2dec0"},"schema_version":"1.0","source":{"id":"2410.23051","kind":"arxiv","version":1}},"canonical_sha256":"1b7425243d0ad63724b695af22371ee0c6e6efe18e714bd7171986239db81121","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b7425243d0ad63724b695af22371ee0c6e6efe18e714bd7171986239db81121","first_computed_at":"2026-07-05T09:28:40.530524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:28:40.530524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u8aZN2IuVMrHn8ALfz3t3vFEUK6QRcGvugTMA+e5ylNusS7QRg3nxgIr7pHdrTYd2RjeEGuQUjm02nsoBkIqDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:28:40.531010Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.23051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0267b9f47aa723dd5d33ecb29d59ecbfedb726818d17122ab39fab53354bbf2b","sha256:d3bb4c2f723aff3879537f653ecfdc7d93afe04ea90db4626d063d3188126936"],"state_sha256":"d053987154750e22f1dd27ca6cf60af93bf2afc0a807c848389c337165fb5b47"}