{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AD4L5YT3KJD24RY2BFQ6CUCDQL","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":"a0ed8d30784ebb423c7316e59201b3a844f58e4f1b5c2fc4e6dfbb8d9a151a96","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-24T15:57:47Z","title_canon_sha256":"3eca50320d46d2a15839e7d54f6ac9065f1c965690ab59d3a7af46b1ada995cd"},"schema_version":"1.0","source":{"id":"1801.08049","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08049","created_at":"2026-05-18T00:15:36Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08049v2","created_at":"2026-05-18T00:15:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08049","created_at":"2026-05-18T00:15:36Z"},{"alias_kind":"pith_short_12","alias_value":"AD4L5YT3KJD2","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AD4L5YT3KJD24RY2","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AD4L5YT3","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:e6320b75974e58988a64ca7def4a4fcd02b527b6adc5137ad2f7dda67068adc5","target":"graph","created_at":"2026-05-18T00:15:36Z","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":"In this paper we study dynamical properties of blowup solutions to the focusing mass-critical nonlinear fractional Schr\\\"odinger equation. We establish a profile decomposition and a compactness lemma related to the equation. As a result, we obtain the $L^2$-concentration and the limiting profile with minimal mass of blowup solutions.","authors_text":"Van Duong Dinh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-24T15:57:47Z","title":"On Blowup solutions to the focusing mass-critical nonlinear fractional Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08049","kind":"arxiv","version":2},"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:b8b9165c970bd541c2acb261785a1a39ffac76e7d158c9f9a86cd4880089b5d5","target":"record","created_at":"2026-05-18T00:15:36Z","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":"a0ed8d30784ebb423c7316e59201b3a844f58e4f1b5c2fc4e6dfbb8d9a151a96","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-24T15:57:47Z","title_canon_sha256":"3eca50320d46d2a15839e7d54f6ac9065f1c965690ab59d3a7af46b1ada995cd"},"schema_version":"1.0","source":{"id":"1801.08049","kind":"arxiv","version":2}},"canonical_sha256":"00f8bee27b5247ae471a0961e1504382e8af6ce2b26eaa40ef976093be0dedf6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00f8bee27b5247ae471a0961e1504382e8af6ce2b26eaa40ef976093be0dedf6","first_computed_at":"2026-05-18T00:15:36.781761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:36.781761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RJC4MD2qwY0PwANiyvbSWWOsVlpxkDtAmzAA+3TK5Wd6NRaO5zoVYxM3+K8pRcoJeJ6REc6fm6poCUZR7bxOBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:36.782528Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.08049","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8b9165c970bd541c2acb261785a1a39ffac76e7d158c9f9a86cd4880089b5d5","sha256:e6320b75974e58988a64ca7def4a4fcd02b527b6adc5137ad2f7dda67068adc5"],"state_sha256":"38f69f1391b25bf9a288b5af43cf4693191c72344840da69610201a3386a2fee"}