{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:55XE5CESJPUBTYSKERRK5KD4ZN","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":"47d7bfce8e9c9cfa484026f22ce3c33974cb62e308f52f4dd48f9d828b53a651","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-30T13:39:16Z","title_canon_sha256":"d32768c1a1245c2af53682fc041e1721035993dee91dcc43cc287f63f4991aa1"},"schema_version":"1.0","source":{"id":"1212.6719","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6719","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6719v1","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6719","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"pith_short_12","alias_value":"55XE5CESJPUB","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"55XE5CESJPUBTYSK","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"55XE5CES","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:7d5ade4077c17350d695c9acbb22cdcc8de82308dc396bcd889a217fc9263da0","target":"graph","created_at":"2026-05-18T03:37:31Z","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 consider the energy critical focusing NLS in R^3 and prove, for any $\\nu$ sufficiently small, the existence of radial finite energy solutions that as $t\\to\\infty$ behave as a sum of a dynamically rescaled ground state plus a radiation, the scaling law being of the form $t^{\\nu}$.","authors_text":"Cecilia Ortoleva, Galina Perelman (LAMA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-30T13:39:16Z","title":"Non-dispersive vanishing and blow up at infinity for the energy critical nonlinear Schr\\\"odinger equation in R^3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6719","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":"sha256:214d859f8d7195055862e7aecc3c116c4bd5e44ec56ff91aa488c9a9fdab513f","target":"record","created_at":"2026-05-18T03:37:31Z","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":"47d7bfce8e9c9cfa484026f22ce3c33974cb62e308f52f4dd48f9d828b53a651","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-30T13:39:16Z","title_canon_sha256":"d32768c1a1245c2af53682fc041e1721035993dee91dcc43cc287f63f4991aa1"},"schema_version":"1.0","source":{"id":"1212.6719","kind":"arxiv","version":1}},"canonical_sha256":"ef6e4e88924be819e24a2462aea87ccb7100e6ce298d6a683a2ca9492849496b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef6e4e88924be819e24a2462aea87ccb7100e6ce298d6a683a2ca9492849496b","first_computed_at":"2026-05-18T03:37:31.092155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:31.092155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2wGlESp6cHQlI2ACtnsH4jLJ6j/b1ySLuhGHnSriQ2UE3ldnDvAVG+vkInXa2QpoSBlRPV7gkHq528sANeRHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:31.092841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6719","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:214d859f8d7195055862e7aecc3c116c4bd5e44ec56ff91aa488c9a9fdab513f","sha256:7d5ade4077c17350d695c9acbb22cdcc8de82308dc396bcd889a217fc9263da0"],"state_sha256":"09791d59a1c1570bc5d8c51170d3eb194785ab4b783479fc25e6554f395b8fb6"}