{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ET5OKHCKEWYNXFOSYVLJZKE4FT","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":"86d3f3052b921614c6c12ce65a3d5c6dba3c8b6ae47515b86e2b7a6eb528017a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-05T16:05:53Z","title_canon_sha256":"9277e112b05786b719a53c3af2fec37d25b223e634fb8693d35d14be53e6e0ca"},"schema_version":"1.0","source":{"id":"1701.01363","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01363","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01363v3","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01363","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"ET5OKHCKEWYN","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ET5OKHCKEWYNXFOS","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ET5OKHCK","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:2e4fef62b3b3d2bbe09f094602a815546985bb4dfe99f8e0b499c3ddab8f8b5d","target":"graph","created_at":"2026-05-18T00:31:36Z","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 consider the nonlinear fractional logarithmic Schr\\\"{o}dinger equation. By using a compactness method, we construct a unique global solution of the associated Cauchy problem in a suitable functional framework. We also prove the existence of ground states as minimizers of the action on the Nehari manifold. Finally, we prove that the set of minimizers is a stable set for the initial value problem, that is, a solution whose initial data is near the set will remain near it for all time.","authors_text":"Alex Hernandez Ardila","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-05T16:05:53Z","title":"Existence and stability of standing waves for nonlinear fractional Schr\\\"odinger equation with logarithmic nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01363","kind":"arxiv","version":3},"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:dacb9e2dae1714e25546e6e7fad00f5417cdc31f1176d9a0b8be41e19e413d58","target":"record","created_at":"2026-05-18T00:31:36Z","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":"86d3f3052b921614c6c12ce65a3d5c6dba3c8b6ae47515b86e2b7a6eb528017a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-05T16:05:53Z","title_canon_sha256":"9277e112b05786b719a53c3af2fec37d25b223e634fb8693d35d14be53e6e0ca"},"schema_version":"1.0","source":{"id":"1701.01363","kind":"arxiv","version":3}},"canonical_sha256":"24fae51c4a25b0db95d2c5569ca89c2ccfc528f8c252e25cb1aec123d8d51aea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24fae51c4a25b0db95d2c5569ca89c2ccfc528f8c252e25cb1aec123d8d51aea","first_computed_at":"2026-05-18T00:31:36.238656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:36.238656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XLgoYlAXuXUYoIn5AdeXP+N+xmwV57mkV8ILm9OzEuQXkief0MJiQNJ6yCy6fi5wiwjMKSeo2qj8UrhD/PLQAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:36.239063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01363","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dacb9e2dae1714e25546e6e7fad00f5417cdc31f1176d9a0b8be41e19e413d58","sha256:2e4fef62b3b3d2bbe09f094602a815546985bb4dfe99f8e0b499c3ddab8f8b5d"],"state_sha256":"e36bc77b94d04b164a82d466e2d08710bec1eb7bcc2a45c806fc717f0bc2482a"}