{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:TYNHBFKLJAPSXSLMFMRH7POHHF","short_pith_number":"pith:TYNHBFKL","schema_version":"1.0","canonical_sha256":"9e1a70954b481f2bc96c2b227fbdc73978ef81d60881b64f31a8e4035c9eaf80","source":{"kind":"arxiv","id":"2501.11455","version":2},"attestation_state":"computed","paper":{"title":"Unconditional well-posendness for the fourth order nonlinear Schrodinger type equations on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Takamori Kato","submitted_at":"2025-01-20T12:42:00Z","abstract_excerpt":"We prove the unconditional well-posedness for the fourth order nonlinear Schrodinger type equations in H^s(\\mathbb{T}) when s \\geq 1, which includes the non-integrable case. This regularity threshold is optimal because the nonlinear terms cannot be defined in the space-time distribution framework for s<1. The main idea is to employ the normal form reduction and a kind of cancellation property to deal with derivative losses."},"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":"2501.11455","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-20T12:42:00Z","cross_cats_sorted":[],"title_canon_sha256":"bd9f595cf1b085f5f4c0817ef3180a8e534cfec2d9b71740ad3ebb251b872d82","abstract_canon_sha256":"0bd5ff792aa1d3c7a39af4c5f10e1e96c5b9b9fea1b4c00445d0c42940b8d2a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:15:24.606778Z","signature_b64":"Jyf5zfyfpscmo0GtHqlDGriNnhJ+tSLdrH5yvCenm7vFFp9cZ2O4VsvHMbS/qHAIVP5ToGuijiBp50523vo9Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e1a70954b481f2bc96c2b227fbdc73978ef81d60881b64f31a8e4035c9eaf80","last_reissued_at":"2026-07-05T10:15:24.606224Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:15:24.606224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unconditional well-posendness for the fourth order nonlinear Schrodinger type equations on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Takamori Kato","submitted_at":"2025-01-20T12:42:00Z","abstract_excerpt":"We prove the unconditional well-posedness for the fourth order nonlinear Schrodinger type equations in H^s(\\mathbb{T}) when s \\geq 1, which includes the non-integrable case. This regularity threshold is optimal because the nonlinear terms cannot be defined in the space-time distribution framework for s<1. The main idea is to employ the normal form reduction and a kind of cancellation property to deal with derivative losses."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.11455","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/2501.11455/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":"2501.11455","created_at":"2026-07-05T10:15:24.606297+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.11455v2","created_at":"2026-07-05T10:15:24.606297+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.11455","created_at":"2026-07-05T10:15:24.606297+00:00"},{"alias_kind":"pith_short_12","alias_value":"TYNHBFKLJAPS","created_at":"2026-07-05T10:15:24.606297+00:00"},{"alias_kind":"pith_short_16","alias_value":"TYNHBFKLJAPSXSLM","created_at":"2026-07-05T10:15:24.606297+00:00"},{"alias_kind":"pith_short_8","alias_value":"TYNHBFKL","created_at":"2026-07-05T10:15:24.606297+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/TYNHBFKLJAPSXSLMFMRH7POHHF","json":"https://pith.science/pith/TYNHBFKLJAPSXSLMFMRH7POHHF.json","graph_json":"https://pith.science/api/pith-number/TYNHBFKLJAPSXSLMFMRH7POHHF/graph.json","events_json":"https://pith.science/api/pith-number/TYNHBFKLJAPSXSLMFMRH7POHHF/events.json","paper":"https://pith.science/paper/TYNHBFKL"},"agent_actions":{"view_html":"https://pith.science/pith/TYNHBFKLJAPSXSLMFMRH7POHHF","download_json":"https://pith.science/pith/TYNHBFKLJAPSXSLMFMRH7POHHF.json","view_paper":"https://pith.science/paper/TYNHBFKL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.11455&json=true","fetch_graph":"https://pith.science/api/pith-number/TYNHBFKLJAPSXSLMFMRH7POHHF/graph.json","fetch_events":"https://pith.science/api/pith-number/TYNHBFKLJAPSXSLMFMRH7POHHF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TYNHBFKLJAPSXSLMFMRH7POHHF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TYNHBFKLJAPSXSLMFMRH7POHHF/action/storage_attestation","attest_author":"https://pith.science/pith/TYNHBFKLJAPSXSLMFMRH7POHHF/action/author_attestation","sign_citation":"https://pith.science/pith/TYNHBFKLJAPSXSLMFMRH7POHHF/action/citation_signature","submit_replication":"https://pith.science/pith/TYNHBFKLJAPSXSLMFMRH7POHHF/action/replication_record"}},"created_at":"2026-07-05T10:15:24.606297+00:00","updated_at":"2026-07-05T10:15:24.606297+00:00"}