{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:EPXEIHESBBLPKYT336ZFTPYZUE","short_pith_number":"pith:EPXEIHES","schema_version":"1.0","canonical_sha256":"23ee441c920856f5627bdfb259bf19a127b6e908ce2a4248983a83f1804b203f","source":{"kind":"arxiv","id":"1604.06957","version":1},"attestation_state":"computed","paper":{"title":"Strong instability of standing waves for nonlinear Schr\\\"odinger equations with harmonic potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masahito Ohta","submitted_at":"2016-04-23T21:35:00Z","abstract_excerpt":"We study strong instability of standing waves $e^{i\\omega t} \\phi_{\\omega}(x)$ for nonlinear Schr\\\"odinger equations with $L^2$-supercritical nonlinearity and a harmonic potential, where $\\phi_{\\omega}$ is a ground state of the corresponding stationary problem. We prove that $e^{i\\omega t} \\phi_{\\omega}(x)$ is strongly unstable if $\\partial_{\\lambda}^2 E(\\phi_{\\omega}^{\\lambda}) |_{\\lambda=1}\\le 0$, where $E$ is the energy and $v^{\\lambda}(x)=\\lambda^{N/2} v(\\lambda x)$ is the $L^2$-invariant scaling."},"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":"1604.06957","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-23T21:35:00Z","cross_cats_sorted":[],"title_canon_sha256":"6ee6723d3aa7bed5425d2cc87063d0d52c2bfc7b0d87b4434a47bf4ea453f1cf","abstract_canon_sha256":"586b41ea4c20db4a21ae79cc1f33ca335bc2198b350c6e315ccb456441377918"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:36.194141Z","signature_b64":"Yn1/mcrkKT9AsDO6mqBNyLgoBihlzTIOhfhfjDUtM/GAPQNg2rpZUor0aQK7/j/XnyzDKu7hL24OpwlWqKetAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23ee441c920856f5627bdfb259bf19a127b6e908ce2a4248983a83f1804b203f","last_reissued_at":"2026-05-18T00:19:36.193356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:36.193356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong instability of standing waves for nonlinear Schr\\\"odinger equations with harmonic potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masahito Ohta","submitted_at":"2016-04-23T21:35:00Z","abstract_excerpt":"We study strong instability of standing waves $e^{i\\omega t} \\phi_{\\omega}(x)$ for nonlinear Schr\\\"odinger equations with $L^2$-supercritical nonlinearity and a harmonic potential, where $\\phi_{\\omega}$ is a ground state of the corresponding stationary problem. We prove that $e^{i\\omega t} \\phi_{\\omega}(x)$ is strongly unstable if $\\partial_{\\lambda}^2 E(\\phi_{\\omega}^{\\lambda}) |_{\\lambda=1}\\le 0$, where $E$ is the energy and $v^{\\lambda}(x)=\\lambda^{N/2} v(\\lambda x)$ is the $L^2$-invariant scaling."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06957","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":""},"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":"1604.06957","created_at":"2026-05-18T00:19:36.193494+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.06957v1","created_at":"2026-05-18T00:19:36.193494+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06957","created_at":"2026-05-18T00:19:36.193494+00:00"},{"alias_kind":"pith_short_12","alias_value":"EPXEIHESBBLP","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"EPXEIHESBBLPKYT3","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"EPXEIHES","created_at":"2026-05-18T12:30:12.583610+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/EPXEIHESBBLPKYT336ZFTPYZUE","json":"https://pith.science/pith/EPXEIHESBBLPKYT336ZFTPYZUE.json","graph_json":"https://pith.science/api/pith-number/EPXEIHESBBLPKYT336ZFTPYZUE/graph.json","events_json":"https://pith.science/api/pith-number/EPXEIHESBBLPKYT336ZFTPYZUE/events.json","paper":"https://pith.science/paper/EPXEIHES"},"agent_actions":{"view_html":"https://pith.science/pith/EPXEIHESBBLPKYT336ZFTPYZUE","download_json":"https://pith.science/pith/EPXEIHESBBLPKYT336ZFTPYZUE.json","view_paper":"https://pith.science/paper/EPXEIHES","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.06957&json=true","fetch_graph":"https://pith.science/api/pith-number/EPXEIHESBBLPKYT336ZFTPYZUE/graph.json","fetch_events":"https://pith.science/api/pith-number/EPXEIHESBBLPKYT336ZFTPYZUE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EPXEIHESBBLPKYT336ZFTPYZUE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EPXEIHESBBLPKYT336ZFTPYZUE/action/storage_attestation","attest_author":"https://pith.science/pith/EPXEIHESBBLPKYT336ZFTPYZUE/action/author_attestation","sign_citation":"https://pith.science/pith/EPXEIHESBBLPKYT336ZFTPYZUE/action/citation_signature","submit_replication":"https://pith.science/pith/EPXEIHESBBLPKYT336ZFTPYZUE/action/replication_record"}},"created_at":"2026-05-18T00:19:36.193494+00:00","updated_at":"2026-05-18T00:19:36.193494+00:00"}