{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:353KUJIZK64SDKHCI6IX6CZS3L","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":"1eff1d7e29beb1381a86e1dd719d345f54f2ca4f397783578c3e252465f45a03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-09T12:51:31Z","title_canon_sha256":"816e7c1d540bacd39c0b63d537ae63bde143a23ae1a8232b9c6ab5ed02dbf92d"},"schema_version":"1.0","source":{"id":"1803.03492","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03492","created_at":"2026-05-17T23:57:15Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03492v1","created_at":"2026-05-17T23:57:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03492","created_at":"2026-05-17T23:57:15Z"},{"alias_kind":"pith_short_12","alias_value":"353KUJIZK64S","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"353KUJIZK64SDKHC","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"353KUJIZ","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:0a2f71bc6be9243a22507df0b731ae9e099032a0e7629c9c6d8bdac4136c2912","target":"graph","created_at":"2026-05-17T23:57:15Z","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 $p$-Choquard equation in 3-dimensional case and establish existence and uniqueness of ground states for the corresponding Weinstein functional. For proving the uniqueness of ground states, we use the radial symmetry to transform the equation into an ordinary differential system, and applying the Pohozaev identities and Gronwall lemma we show that any two Weinstein minimizers coincide.","authors_text":"George Venkov, Mirko Tarulli, Vladimir Georgiev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-09T12:51:31Z","title":"Existence and uniqueness of ground states for $p$ - Choquard model in 3D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03492","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":"sha256:2fe5640eb2fc455c5af121990565a1630d5c344bfb947cbc1963e7d21afda839","target":"record","created_at":"2026-05-17T23:57:15Z","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":"1eff1d7e29beb1381a86e1dd719d345f54f2ca4f397783578c3e252465f45a03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-09T12:51:31Z","title_canon_sha256":"816e7c1d540bacd39c0b63d537ae63bde143a23ae1a8232b9c6ab5ed02dbf92d"},"schema_version":"1.0","source":{"id":"1803.03492","kind":"arxiv","version":1}},"canonical_sha256":"df76aa251957b921a8e247917f0b32daf0286a5e5065b6f870d260ee512ed040","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df76aa251957b921a8e247917f0b32daf0286a5e5065b6f870d260ee512ed040","first_computed_at":"2026-05-17T23:57:15.359411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:15.359411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Oczb6yWukAvlIqSK/VgeHyuE3qQzZ68am3ErzZU2PiXoWOLTwAknc6M2JCBriBQEsxFhRcjJzyDvnzEwauICDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:15.360001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03492","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fe5640eb2fc455c5af121990565a1630d5c344bfb947cbc1963e7d21afda839","sha256:0a2f71bc6be9243a22507df0b731ae9e099032a0e7629c9c6d8bdac4136c2912"],"state_sha256":"1e5b83910676c8f7621822f275d316210629f60d23fe2c1466757526f6fa532e"}