{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YIBCWP3NGOZNPWJDOQIRDGNSDB","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":"02842da71ccd8017f2ca9df5e7b08db3d6aed13c31377f86fa76515435775bb2","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-01T09:59:59Z","title_canon_sha256":"7334334abf0324718172ac71ffcc8288275a0b6ed4fd3af8cd837d2481ea66f9"},"schema_version":"1.0","source":{"id":"1707.00131","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00131","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00131v1","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00131","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"YIBCWP3NGOZN","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YIBCWP3NGOZNPWJD","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YIBCWP3N","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:2e969d7fccb8c45c4d51e2ccb7c4208b7a27303686e2269e8ef77b1626cdb90c","target":"graph","created_at":"2026-05-18T00:41:06Z","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 a version of the fractional Sobolev inequality in domains and study whether the best constant in this inequality is attained. For the half-space and a large class of bounded domains we show that a minimizer exists, which is in contrast to the classical Sobolev inequalities in domains.","authors_text":"Jingang Xiong, Rupert L. Frank, Tianling Jin","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-01T09:59:59Z","title":"Minimizers for the fractional Sobolev inequality on domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00131","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":"sha256:69c152bbd490ee51f0af1b1ec65adb89a58c1995ae0fc908a5a0cabab6319b8b","target":"record","created_at":"2026-05-18T00:41:06Z","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":"02842da71ccd8017f2ca9df5e7b08db3d6aed13c31377f86fa76515435775bb2","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-01T09:59:59Z","title_canon_sha256":"7334334abf0324718172ac71ffcc8288275a0b6ed4fd3af8cd837d2481ea66f9"},"schema_version":"1.0","source":{"id":"1707.00131","kind":"arxiv","version":1}},"canonical_sha256":"c2022b3f6d33b2d7d92374111199b2186abc8a4bae4b19e02bfa12cca636cd13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2022b3f6d33b2d7d92374111199b2186abc8a4bae4b19e02bfa12cca636cd13","first_computed_at":"2026-05-18T00:41:06.380142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:06.380142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8HZBfSGx6nO4wMjcCRO3xx2AbieF4FCrCU6n87SlMwM9AaN/YDmy0s6mp00OLaDkkNAWeVvqAPBKRSRfyWBIDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:06.380790Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.00131","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69c152bbd490ee51f0af1b1ec65adb89a58c1995ae0fc908a5a0cabab6319b8b","sha256:2e969d7fccb8c45c4d51e2ccb7c4208b7a27303686e2269e8ef77b1626cdb90c"],"state_sha256":"e3ab30daa564dc0a0938bca07b19f92f7e0737ab8a8192ede93600fc66e6d3ce"}