{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ODVUBL4253JD3ADDT3MRBVVMUR","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":"863033c6018298cf213138261796c7cd0f947028f76e7b5eca728e40ba8a6103","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2016-10-28T02:45:40Z","title_canon_sha256":"396b4542016cdbc7a947b2ead7e4b3fffb87628af6d1ef4768bcd0b40bebeccc"},"schema_version":"1.0","source":{"id":"1610.09062","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09062","created_at":"2026-05-18T00:49:23Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09062v2","created_at":"2026-05-18T00:49:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09062","created_at":"2026-05-18T00:49:23Z"},{"alias_kind":"pith_short_12","alias_value":"ODVUBL4253JD","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"ODVUBL4253JD3ADD","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"ODVUBL42","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:77af739847935d8c9a75ae8963d3e47f4fbdae0c8bcb317c4e21f6013a826ef6","target":"graph","created_at":"2026-05-18T00:49:23Z","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":"Our purpose of this paper is to study the isolated singularities of positive solutions to Choquard equation in the sublinear case $q \\in (0,1)$\n  $$\\displaystyle \\ \\ -\\Delta u+ u =I_\\alpha[u^p] u^q\\;\\;\n  {\\rm in}\\; \\mathbb{R}^N\\setminus\\{0\\},\n  % [2mm] \\phantom{ }\n  \\;\\; \\displaystyle \\lim_{|x|\\to+\\infty}u(x)=0, $$ where $p >0, N \\geq 3, \\alpha \\in (0,N)$ and $I_{\\alpha}[u^p](x) = \\int_{\\mathbb{R}^N} \\frac{u^p(y)}{|x-y|^{N-\\alpha}}dy$ is the Riesz potential, which appears as a nonlocal term in the equation. We investigate the nonexistence and existence of isolated singular solutions of Choquar","authors_text":"Feng Zhou, Huyuan Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2016-10-28T02:45:40Z","title":"Isolated singularities of positive solutions for Choquard equations in sublinear case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09062","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":"sha256:8a36508984b7adfe2c09e76f49d86327bbf70c2ee4fc062bfbf3125036a1a56c","target":"record","created_at":"2026-05-18T00:49:23Z","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":"863033c6018298cf213138261796c7cd0f947028f76e7b5eca728e40ba8a6103","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2016-10-28T02:45:40Z","title_canon_sha256":"396b4542016cdbc7a947b2ead7e4b3fffb87628af6d1ef4768bcd0b40bebeccc"},"schema_version":"1.0","source":{"id":"1610.09062","kind":"arxiv","version":2}},"canonical_sha256":"70eb40af9aeed23d80639ed910d6aca443617a7fadba9dbd89377da0ad733d61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70eb40af9aeed23d80639ed910d6aca443617a7fadba9dbd89377da0ad733d61","first_computed_at":"2026-05-18T00:49:23.560876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:23.560876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zCNRr4sbTWRyUhobw8RCLe4+mhRuw7STd/2yXSQwH8zeSyPwmiPLDlqIOy1QMbBPVHzp90Lv/ndIuhM6L/IpCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:23.561301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09062","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a36508984b7adfe2c09e76f49d86327bbf70c2ee4fc062bfbf3125036a1a56c","sha256:77af739847935d8c9a75ae8963d3e47f4fbdae0c8bcb317c4e21f6013a826ef6"],"state_sha256":"ada44bd4962e250d6f9e05bf315af1dbc773c9566bfe1bcc93df390a35acd992"}