{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:2KNC3ITSJOFY62W4Y7AEP7X7NI","short_pith_number":"pith:2KNC3ITS","schema_version":"1.0","canonical_sha256":"d29a2da2724b8b8f6adcc7c047feff6a119b3e3ae82038da4ec40fd2d22f8530","source":{"kind":"arxiv","id":"2505.14966","version":1},"attestation_state":"computed","paper":{"title":"On the optimal Sobolev threshold for evolution equations with rough nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ben Pineau, Mitchell A. Taylor","submitted_at":"2025-05-20T23:10:35Z","abstract_excerpt":"In this article we are concerned with evolution equations of the form \\begin{equation*} \\partial_tu-A(D)u=F(u,\\overline{u},\\nabla u, \\nabla \\overline{u}) \\end{equation*} where $A(D)$ is a Fourier multiplier of either dispersive or parabolic type and the nonlinear term $F$ is of limited regularity. Our objective is to develop a robust set of principles which can be used in many cases to predict the \\emph{highest} Sobolev exponent $s=s(q,d)$ for which the above evolution is well-posed in $W_x^{s,q}(\\mathbb{R}^d)$ (necessarily restricting to $q=2$ for dispersive problems). We will confirm the val"},"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":"2505.14966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-20T23:10:35Z","cross_cats_sorted":[],"title_canon_sha256":"2410ee7db65b9ea9473f69ff749a3ef80736c31c0495a6cff11035e40620075b","abstract_canon_sha256":"c7e953c67a72b397477dc08506d1342eb11fb8315fce5de895c18dd0443b2ae8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:06:38.477701Z","signature_b64":"C+aJQOl/J5ux3zY+gpLbspU5fT/mKgBo9PBwCV2aDIWjS1P7z9KxZ1K9WJA7waosQqu+OtlJ8w/JMlnUYNKyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d29a2da2724b8b8f6adcc7c047feff6a119b3e3ae82038da4ec40fd2d22f8530","last_reissued_at":"2026-07-05T11:06:38.477226Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:06:38.477226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the optimal Sobolev threshold for evolution equations with rough nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ben Pineau, Mitchell A. Taylor","submitted_at":"2025-05-20T23:10:35Z","abstract_excerpt":"In this article we are concerned with evolution equations of the form \\begin{equation*} \\partial_tu-A(D)u=F(u,\\overline{u},\\nabla u, \\nabla \\overline{u}) \\end{equation*} where $A(D)$ is a Fourier multiplier of either dispersive or parabolic type and the nonlinear term $F$ is of limited regularity. Our objective is to develop a robust set of principles which can be used in many cases to predict the \\emph{highest} Sobolev exponent $s=s(q,d)$ for which the above evolution is well-posed in $W_x^{s,q}(\\mathbb{R}^d)$ (necessarily restricting to $q=2$ for dispersive problems). We will confirm the val"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.14966","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/2505.14966/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":"2505.14966","created_at":"2026-07-05T11:06:38.477283+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.14966v1","created_at":"2026-07-05T11:06:38.477283+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.14966","created_at":"2026-07-05T11:06:38.477283+00:00"},{"alias_kind":"pith_short_12","alias_value":"2KNC3ITSJOFY","created_at":"2026-07-05T11:06:38.477283+00:00"},{"alias_kind":"pith_short_16","alias_value":"2KNC3ITSJOFY62W4","created_at":"2026-07-05T11:06:38.477283+00:00"},{"alias_kind":"pith_short_8","alias_value":"2KNC3ITS","created_at":"2026-07-05T11:06:38.477283+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2KNC3ITSJOFY62W4Y7AEP7X7NI","json":"https://pith.science/pith/2KNC3ITSJOFY62W4Y7AEP7X7NI.json","graph_json":"https://pith.science/api/pith-number/2KNC3ITSJOFY62W4Y7AEP7X7NI/graph.json","events_json":"https://pith.science/api/pith-number/2KNC3ITSJOFY62W4Y7AEP7X7NI/events.json","paper":"https://pith.science/paper/2KNC3ITS"},"agent_actions":{"view_html":"https://pith.science/pith/2KNC3ITSJOFY62W4Y7AEP7X7NI","download_json":"https://pith.science/pith/2KNC3ITSJOFY62W4Y7AEP7X7NI.json","view_paper":"https://pith.science/paper/2KNC3ITS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.14966&json=true","fetch_graph":"https://pith.science/api/pith-number/2KNC3ITSJOFY62W4Y7AEP7X7NI/graph.json","fetch_events":"https://pith.science/api/pith-number/2KNC3ITSJOFY62W4Y7AEP7X7NI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2KNC3ITSJOFY62W4Y7AEP7X7NI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2KNC3ITSJOFY62W4Y7AEP7X7NI/action/storage_attestation","attest_author":"https://pith.science/pith/2KNC3ITSJOFY62W4Y7AEP7X7NI/action/author_attestation","sign_citation":"https://pith.science/pith/2KNC3ITSJOFY62W4Y7AEP7X7NI/action/citation_signature","submit_replication":"https://pith.science/pith/2KNC3ITSJOFY62W4Y7AEP7X7NI/action/replication_record"}},"created_at":"2026-07-05T11:06:38.477283+00:00","updated_at":"2026-07-05T11:06:38.477283+00:00"}