{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:WMV7SFTYR7DI6SMOD5IERO7HHG","short_pith_number":"pith:WMV7SFTY","schema_version":"1.0","canonical_sha256":"b32bf916788fc68f498e1f5048bbe739b7b05dc241aaab1b4e06a5ead7faa287","source":{"kind":"arxiv","id":"2309.14276","version":1},"attestation_state":"computed","paper":{"title":"Almost-periodic solutions to the NLS equation with smooth convolution potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Guido Gentile, Livia Corsi, Michela Procesi","submitted_at":"2023-09-25T16:39:38Z","abstract_excerpt":"We consider the one-dimensional NLS equation with a convolution potential and a quintic nonlinearity. We prove that, for most choices of potentials with polynomially decreasing Fourier coefficients, there exist almost-periodic solutions in the Gevrey class with frequency satisfying a Bryuno non-resonance condition. This allows convolution potentials of class $C^p$, for any integer $p$: as far as we know this is the first result where the regularity of the potential is arbitrarily large and not compensated by a corresponding smoothing of the nonlinearity."},"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":"2309.14276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-09-25T16:39:38Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"bf081fb9361f25a0c41354a4e2ac38607be3dd3b735a49fed417013d961712d9","abstract_canon_sha256":"d79e186b71d2e7467268c6912930face9e693a2f540ff9c0cb5b24e6659a9ae6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:54:03.535857Z","signature_b64":"oa92jmsCA6TykDIK2JL0k7FlWsUUOSghxF0vtbTLHvHhfjtBwrKW/LdPpyyVZiGSbFvVIX1lp1r9JNIUZyzHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b32bf916788fc68f498e1f5048bbe739b7b05dc241aaab1b4e06a5ead7faa287","last_reissued_at":"2026-07-05T06:54:03.535400Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:54:03.535400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost-periodic solutions to the NLS equation with smooth convolution potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Guido Gentile, Livia Corsi, Michela Procesi","submitted_at":"2023-09-25T16:39:38Z","abstract_excerpt":"We consider the one-dimensional NLS equation with a convolution potential and a quintic nonlinearity. We prove that, for most choices of potentials with polynomially decreasing Fourier coefficients, there exist almost-periodic solutions in the Gevrey class with frequency satisfying a Bryuno non-resonance condition. This allows convolution potentials of class $C^p$, for any integer $p$: as far as we know this is the first result where the regularity of the potential is arbitrarily large and not compensated by a corresponding smoothing of the nonlinearity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.14276","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/2309.14276/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":"2309.14276","created_at":"2026-07-05T06:54:03.535460+00:00"},{"alias_kind":"arxiv_version","alias_value":"2309.14276v1","created_at":"2026-07-05T06:54:03.535460+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.14276","created_at":"2026-07-05T06:54:03.535460+00:00"},{"alias_kind":"pith_short_12","alias_value":"WMV7SFTYR7DI","created_at":"2026-07-05T06:54:03.535460+00:00"},{"alias_kind":"pith_short_16","alias_value":"WMV7SFTYR7DI6SMO","created_at":"2026-07-05T06:54:03.535460+00:00"},{"alias_kind":"pith_short_8","alias_value":"WMV7SFTY","created_at":"2026-07-05T06:54:03.535460+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/WMV7SFTYR7DI6SMOD5IERO7HHG","json":"https://pith.science/pith/WMV7SFTYR7DI6SMOD5IERO7HHG.json","graph_json":"https://pith.science/api/pith-number/WMV7SFTYR7DI6SMOD5IERO7HHG/graph.json","events_json":"https://pith.science/api/pith-number/WMV7SFTYR7DI6SMOD5IERO7HHG/events.json","paper":"https://pith.science/paper/WMV7SFTY"},"agent_actions":{"view_html":"https://pith.science/pith/WMV7SFTYR7DI6SMOD5IERO7HHG","download_json":"https://pith.science/pith/WMV7SFTYR7DI6SMOD5IERO7HHG.json","view_paper":"https://pith.science/paper/WMV7SFTY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2309.14276&json=true","fetch_graph":"https://pith.science/api/pith-number/WMV7SFTYR7DI6SMOD5IERO7HHG/graph.json","fetch_events":"https://pith.science/api/pith-number/WMV7SFTYR7DI6SMOD5IERO7HHG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WMV7SFTYR7DI6SMOD5IERO7HHG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WMV7SFTYR7DI6SMOD5IERO7HHG/action/storage_attestation","attest_author":"https://pith.science/pith/WMV7SFTYR7DI6SMOD5IERO7HHG/action/author_attestation","sign_citation":"https://pith.science/pith/WMV7SFTYR7DI6SMOD5IERO7HHG/action/citation_signature","submit_replication":"https://pith.science/pith/WMV7SFTYR7DI6SMOD5IERO7HHG/action/replication_record"}},"created_at":"2026-07-05T06:54:03.535460+00:00","updated_at":"2026-07-05T06:54:03.535460+00:00"}