{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:XHJRF2KVHJVV7BEJEJ2QJREH44","short_pith_number":"pith:XHJRF2KV","schema_version":"1.0","canonical_sha256":"b9d312e9553a6b5f8489227504c487e703fa8b7907300b0a3a9e2173d0e31fe3","source":{"kind":"arxiv","id":"2604.00252","version":2},"attestation_state":"computed","paper":{"title":"Applications of renormalisation to orthonormal Strichartz estimates and the NLS system on the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Andrew Rout, Sonae Hadama","submitted_at":"2026-03-31T21:24:41Z","abstract_excerpt":"In this paper, we introduce a renormalisation procedure for the density associated with the system of nonlinear Schr\\\"odinger equations (NLSS) on a circle. We show that this renormalised density satisfies better orthonormal Strichartz estimates than the non-renormalised density, which was considered in Nakamura (2020). As an application, we determine the critical Schatten exponent below which the cubic renormalised NLSS on the circle is globally well-posed and above which it is ill-posed. Finally, we show that the improvement for orthonormal Strichartz estimates satisfied by the renormalised d"},"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":"2604.00252","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-03-31T21:24:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"88132afdb49b6e297a5485cd1ecb5dfc3c04a0ba76fc7e1d900a90b4e7798a76","abstract_canon_sha256":"cc990559d77ac7c79176ee7d75623f91f58b82b14719ac06a4333f8718a39a7b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-23T01:24:25.572627Z","signature_b64":"YF0hwjJ7orMoGyCGUtnkWedgUvsZdB/8aSN+tlUq8aO7HE5IBbIUF8MTLwfbp2f1qmPCDImHjaAYhnUPR3FZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9d312e9553a6b5f8489227504c487e703fa8b7907300b0a3a9e2173d0e31fe3","last_reissued_at":"2026-07-23T01:24:25.571597Z","signature_status":"signed_v1","first_computed_at":"2026-07-23T01:24:25.571597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Applications of renormalisation to orthonormal Strichartz estimates and the NLS system on the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Andrew Rout, Sonae Hadama","submitted_at":"2026-03-31T21:24:41Z","abstract_excerpt":"In this paper, we introduce a renormalisation procedure for the density associated with the system of nonlinear Schr\\\"odinger equations (NLSS) on a circle. We show that this renormalised density satisfies better orthonormal Strichartz estimates than the non-renormalised density, which was considered in Nakamura (2020). As an application, we determine the critical Schatten exponent below which the cubic renormalised NLSS on the circle is globally well-posed and above which it is ill-posed. Finally, we show that the improvement for orthonormal Strichartz estimates satisfied by the renormalised d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.00252","kind":"arxiv","version":2},"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/2604.00252/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":"2604.00252","created_at":"2026-07-23T01:24:25.572109+00:00"},{"alias_kind":"arxiv_version","alias_value":"2604.00252v2","created_at":"2026-07-23T01:24:25.572109+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.00252","created_at":"2026-07-23T01:24:25.572109+00:00"},{"alias_kind":"pith_short_12","alias_value":"XHJRF2KVHJVV","created_at":"2026-07-23T01:24:25.572109+00:00"},{"alias_kind":"pith_short_16","alias_value":"XHJRF2KVHJVV7BEJ","created_at":"2026-07-23T01:24:25.572109+00:00"},{"alias_kind":"pith_short_8","alias_value":"XHJRF2KV","created_at":"2026-07-23T01:24:25.572109+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.16998","citing_title":"Global solutions for the Alber equation in $H^1\\mathfrak{S}^1(\\mathbb{T})$","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XHJRF2KVHJVV7BEJEJ2QJREH44","json":"https://pith.science/pith/XHJRF2KVHJVV7BEJEJ2QJREH44.json","graph_json":"https://pith.science/api/pith-number/XHJRF2KVHJVV7BEJEJ2QJREH44/graph.json","events_json":"https://pith.science/api/pith-number/XHJRF2KVHJVV7BEJEJ2QJREH44/events.json","paper":"https://pith.science/paper/XHJRF2KV"},"agent_actions":{"view_html":"https://pith.science/pith/XHJRF2KVHJVV7BEJEJ2QJREH44","download_json":"https://pith.science/pith/XHJRF2KVHJVV7BEJEJ2QJREH44.json","view_paper":"https://pith.science/paper/XHJRF2KV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2604.00252&json=true","fetch_graph":"https://pith.science/api/pith-number/XHJRF2KVHJVV7BEJEJ2QJREH44/graph.json","fetch_events":"https://pith.science/api/pith-number/XHJRF2KVHJVV7BEJEJ2QJREH44/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XHJRF2KVHJVV7BEJEJ2QJREH44/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XHJRF2KVHJVV7BEJEJ2QJREH44/action/storage_attestation","attest_author":"https://pith.science/pith/XHJRF2KVHJVV7BEJEJ2QJREH44/action/author_attestation","sign_citation":"https://pith.science/pith/XHJRF2KVHJVV7BEJEJ2QJREH44/action/citation_signature","submit_replication":"https://pith.science/pith/XHJRF2KVHJVV7BEJEJ2QJREH44/action/replication_record"}},"created_at":"2026-07-23T01:24:25.572109+00:00","updated_at":"2026-07-23T01:24:25.572109+00:00"}