{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EQSP2ESXW6KJFD46PYK5PSL2X7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"85f72127b4022de407358eb461a088ad0ccf3e9d4ed8081c340eca281367a46c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-27T08:17:34Z","title_canon_sha256":"9b6520a2989a58993d4b355ece3ad0e3b53d14453e490ca220da550e7e764441"},"schema_version":"1.0","source":{"id":"1009.5184","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5184","created_at":"2026-05-18T02:44:32Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5184v1","created_at":"2026-05-18T02:44:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5184","created_at":"2026-05-18T02:44:32Z"},{"alias_kind":"pith_short_12","alias_value":"EQSP2ESXW6KJ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EQSP2ESXW6KJFD46","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EQSP2ESX","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:ca3c8969e2d43b6337fd4933f8747fe52fa9e8b5d3bb60839546e8f5dac9f622","target":"graph","created_at":"2026-05-18T02:44:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the instability of standing waves for nonlinear Schr\\\"{o}dinger equations. Under a general assumption on nonlinearity, we prove that linear instability implies orbital instability in any dimension. For that purpose, we establish a Strichartz type estimate for the propagator generated by the linearized operator around standing wave.","authors_text":"Masahito Ohta, Vladimir Georgiev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-27T08:17:34Z","title":"Nonlinear instability of linearly unstable standing waves for nonlinear Schr\\\"{o}dinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5184","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d50ce5bf5198c38dbeb3f286925275d9f0eee6dc420621d321d4f42273b5e738","target":"record","created_at":"2026-05-18T02:44:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"85f72127b4022de407358eb461a088ad0ccf3e9d4ed8081c340eca281367a46c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-27T08:17:34Z","title_canon_sha256":"9b6520a2989a58993d4b355ece3ad0e3b53d14453e490ca220da550e7e764441"},"schema_version":"1.0","source":{"id":"1009.5184","kind":"arxiv","version":1}},"canonical_sha256":"2424fd1257b794928f9e7e15d7c97abfd779fcc441ac357da803da1d1f0b259c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2424fd1257b794928f9e7e15d7c97abfd779fcc441ac357da803da1d1f0b259c","first_computed_at":"2026-05-18T02:44:32.764170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:32.764170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BX7RYMH4vO7LhDQBBHtKraigeEf8ah7eb3nUY8vC/uIKErsofp46IK0WeJJZbW+kQkxC6n+IHYflACdqeEoDBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:32.764616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5184","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d50ce5bf5198c38dbeb3f286925275d9f0eee6dc420621d321d4f42273b5e738","sha256:ca3c8969e2d43b6337fd4933f8747fe52fa9e8b5d3bb60839546e8f5dac9f622"],"state_sha256":"f737a4b21f55021beb4b9959c050d99f91eeb404526555d58f092b64fe720ac9"}