{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:WS3O7KZP3Y4WZVNHDXEE76WIJI","short_pith_number":"pith:WS3O7KZP","schema_version":"1.0","canonical_sha256":"b4b6efab2fde396cd5a71dc84ffac84a2dd8f967ac9cd0530a1900e165479f3e","source":{"kind":"arxiv","id":"2605.23229","version":1},"attestation_state":"computed","paper":{"title":"Strichartz estimates for Schr\\\"odinger equations with nonlinear boundary interactions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gigliola Staffilani, Nicola Garofalo","submitted_at":"2026-05-22T04:42:00Z","abstract_excerpt":"We study a Schr\\\"odinger equation in the upper half-space with a nonlinear Neumann boundary interaction driven by the Bessel operator $\\Ba$, $a>-1$. The problem arises naturally as an extension formulation for a nonlocal NLS with memory and can also be interpreted as a Schr\\\"odinger evolution with a nonlinear singular source concentrated on a codimension-one interface.\n  We first develop a complete linear theory for the associated inhomogeneous problem with nonhomogeneous Neumann data. A central ingredient is a new Duhamel representation formula that separates bulk and boundary dynamics and id"},"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":"2605.23229","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-22T04:42:00Z","cross_cats_sorted":[],"title_canon_sha256":"afe2fbec4c65e1e63edc85849a0505d0a0cb2aa26f21c19b993e5b828e9aca10","abstract_canon_sha256":"e074801cea676e6bae319601afef19c7d7b9f54a7590393451602ff3ccefefe3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:44.672658Z","signature_b64":"OykJQD3syhjyPH93hozzXGqk/OrzjArx8XsWEcBiXCaecvotsWnvruojqsvsnz9KGA689YQOOL92g3T/ISwFCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4b6efab2fde396cd5a71dc84ffac84a2dd8f967ac9cd0530a1900e165479f3e","last_reissued_at":"2026-05-25T02:01:44.672051Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:44.672051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strichartz estimates for Schr\\\"odinger equations with nonlinear boundary interactions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gigliola Staffilani, Nicola Garofalo","submitted_at":"2026-05-22T04:42:00Z","abstract_excerpt":"We study a Schr\\\"odinger equation in the upper half-space with a nonlinear Neumann boundary interaction driven by the Bessel operator $\\Ba$, $a>-1$. The problem arises naturally as an extension formulation for a nonlocal NLS with memory and can also be interpreted as a Schr\\\"odinger evolution with a nonlinear singular source concentrated on a codimension-one interface.\n  We first develop a complete linear theory for the associated inhomogeneous problem with nonhomogeneous Neumann data. A central ingredient is a new Duhamel representation formula that separates bulk and boundary dynamics and id"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23229","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/2605.23229/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":"2605.23229","created_at":"2026-05-25T02:01:44.672136+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.23229v1","created_at":"2026-05-25T02:01:44.672136+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23229","created_at":"2026-05-25T02:01:44.672136+00:00"},{"alias_kind":"pith_short_12","alias_value":"WS3O7KZP3Y4W","created_at":"2026-05-25T02:01:44.672136+00:00"},{"alias_kind":"pith_short_16","alias_value":"WS3O7KZP3Y4WZVNH","created_at":"2026-05-25T02:01:44.672136+00:00"},{"alias_kind":"pith_short_8","alias_value":"WS3O7KZP","created_at":"2026-05-25T02:01:44.672136+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/WS3O7KZP3Y4WZVNHDXEE76WIJI","json":"https://pith.science/pith/WS3O7KZP3Y4WZVNHDXEE76WIJI.json","graph_json":"https://pith.science/api/pith-number/WS3O7KZP3Y4WZVNHDXEE76WIJI/graph.json","events_json":"https://pith.science/api/pith-number/WS3O7KZP3Y4WZVNHDXEE76WIJI/events.json","paper":"https://pith.science/paper/WS3O7KZP"},"agent_actions":{"view_html":"https://pith.science/pith/WS3O7KZP3Y4WZVNHDXEE76WIJI","download_json":"https://pith.science/pith/WS3O7KZP3Y4WZVNHDXEE76WIJI.json","view_paper":"https://pith.science/paper/WS3O7KZP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.23229&json=true","fetch_graph":"https://pith.science/api/pith-number/WS3O7KZP3Y4WZVNHDXEE76WIJI/graph.json","fetch_events":"https://pith.science/api/pith-number/WS3O7KZP3Y4WZVNHDXEE76WIJI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WS3O7KZP3Y4WZVNHDXEE76WIJI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WS3O7KZP3Y4WZVNHDXEE76WIJI/action/storage_attestation","attest_author":"https://pith.science/pith/WS3O7KZP3Y4WZVNHDXEE76WIJI/action/author_attestation","sign_citation":"https://pith.science/pith/WS3O7KZP3Y4WZVNHDXEE76WIJI/action/citation_signature","submit_replication":"https://pith.science/pith/WS3O7KZP3Y4WZVNHDXEE76WIJI/action/replication_record"}},"created_at":"2026-05-25T02:01:44.672136+00:00","updated_at":"2026-05-25T02:01:44.672136+00:00"}