{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:NSZRRZU44QTILF6BISB3DXDBSZ","short_pith_number":"pith:NSZRRZU4","schema_version":"1.0","canonical_sha256":"6cb318e69ce4268597c14483b1dc619649dbcfbb41b59930ce8e278a3b2401b0","source":{"kind":"arxiv","id":"2606.19309","version":1},"attestation_state":"computed","paper":{"title":"Norm inflation for the cubic hyperbolic NLS on $\\mathbb T^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shunlin Shen, Yuzhao Wang","submitted_at":"2026-06-17T17:31:21Z","abstract_excerpt":"We prove norm inflation for the cubic hyperbolic nonlinear Schr\\\"odinger equation in $H^s(\\mathbb T^2)$ for every $s\\in(-\\infty,0)\\cup(0,\\frac12]$. The scaling-critical point $s=0$ is excluded by conservation of the $L^2$ norm. The strong ill-posedness below and above the scaling-critical point arises from two completely different mechanisms. Particularly in the scaling-subcritical regime, this dynamical instability stems from the hyperbolic nature. Together with the local well-posedness result in \\cite{WangHNLS}, this gives a sharp dichotomy away from the mass space $L^2(\\mathbb T^2)$: local "},"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":"2606.19309","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-17T17:31:21Z","cross_cats_sorted":[],"title_canon_sha256":"91e6c6a878f4707ec6838f94854303d8851efce159adeafd2029a96664c847bf","abstract_canon_sha256":"1df9bb5397e43e875e8afc4eec083ad8f058d16d0b47ecb3642b6f84abda724b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:10.850699Z","signature_b64":"ebteruu521pf3TRv1/+kvSgpmLUKzmbxjf/QJqe/oZDNfs+p+cHApeODsj+yBTsHCzgrt7tI1R7BPMcrSHKKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cb318e69ce4268597c14483b1dc619649dbcfbb41b59930ce8e278a3b2401b0","last_reissued_at":"2026-06-19T16:12:10.850359Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:10.850359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Norm inflation for the cubic hyperbolic NLS on $\\mathbb T^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shunlin Shen, Yuzhao Wang","submitted_at":"2026-06-17T17:31:21Z","abstract_excerpt":"We prove norm inflation for the cubic hyperbolic nonlinear Schr\\\"odinger equation in $H^s(\\mathbb T^2)$ for every $s\\in(-\\infty,0)\\cup(0,\\frac12]$. The scaling-critical point $s=0$ is excluded by conservation of the $L^2$ norm. The strong ill-posedness below and above the scaling-critical point arises from two completely different mechanisms. Particularly in the scaling-subcritical regime, this dynamical instability stems from the hyperbolic nature. Together with the local well-posedness result in \\cite{WangHNLS}, this gives a sharp dichotomy away from the mass space $L^2(\\mathbb T^2)$: local "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19309","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/2606.19309/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":"2606.19309","created_at":"2026-06-19T16:12:10.850419+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.19309v1","created_at":"2026-06-19T16:12:10.850419+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19309","created_at":"2026-06-19T16:12:10.850419+00:00"},{"alias_kind":"pith_short_12","alias_value":"NSZRRZU44QTI","created_at":"2026-06-19T16:12:10.850419+00:00"},{"alias_kind":"pith_short_16","alias_value":"NSZRRZU44QTILF6B","created_at":"2026-06-19T16:12:10.850419+00:00"},{"alias_kind":"pith_short_8","alias_value":"NSZRRZU4","created_at":"2026-06-19T16:12:10.850419+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/NSZRRZU44QTILF6BISB3DXDBSZ","json":"https://pith.science/pith/NSZRRZU44QTILF6BISB3DXDBSZ.json","graph_json":"https://pith.science/api/pith-number/NSZRRZU44QTILF6BISB3DXDBSZ/graph.json","events_json":"https://pith.science/api/pith-number/NSZRRZU44QTILF6BISB3DXDBSZ/events.json","paper":"https://pith.science/paper/NSZRRZU4"},"agent_actions":{"view_html":"https://pith.science/pith/NSZRRZU44QTILF6BISB3DXDBSZ","download_json":"https://pith.science/pith/NSZRRZU44QTILF6BISB3DXDBSZ.json","view_paper":"https://pith.science/paper/NSZRRZU4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.19309&json=true","fetch_graph":"https://pith.science/api/pith-number/NSZRRZU44QTILF6BISB3DXDBSZ/graph.json","fetch_events":"https://pith.science/api/pith-number/NSZRRZU44QTILF6BISB3DXDBSZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NSZRRZU44QTILF6BISB3DXDBSZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NSZRRZU44QTILF6BISB3DXDBSZ/action/storage_attestation","attest_author":"https://pith.science/pith/NSZRRZU44QTILF6BISB3DXDBSZ/action/author_attestation","sign_citation":"https://pith.science/pith/NSZRRZU44QTILF6BISB3DXDBSZ/action/citation_signature","submit_replication":"https://pith.science/pith/NSZRRZU44QTILF6BISB3DXDBSZ/action/replication_record"}},"created_at":"2026-06-19T16:12:10.850419+00:00","updated_at":"2026-06-19T16:12:10.850419+00:00"}