{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3SRD56Z2ALSCKV5QDTRNA55LER","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":"17b85d072a38af211390d4208d146d0ef090e004dcd4be77f5f6a3c386f3013d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-26T11:51:25Z","title_canon_sha256":"0cb181a86f074f7e9768f9ed6455194cd9cf4e7813b5333732dc697e8277699b"},"schema_version":"1.0","source":{"id":"1109.5530","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5530","created_at":"2026-05-18T03:42:32Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5530v4","created_at":"2026-05-18T03:42:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5530","created_at":"2026-05-18T03:42:32Z"},{"alias_kind":"pith_short_12","alias_value":"3SRD56Z2ALSC","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3SRD56Z2ALSCKV5Q","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3SRD56Z2","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:82a2d7a7f614eae68b752e289148d4f07f92a92b2c70f0d598a246491a0147c5","target":"graph","created_at":"2026-05-18T03:42:32Z","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 existence and nonexistence of nonnegative distributional solutions for a class of semilinear fractional elliptic equations involving the Hardy potential.","authors_text":"Mouhamed Moustapha Fall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-26T11:51:25Z","title":"Semilinear elliptic equations for the fractional Laplacian with Hardy potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5530","kind":"arxiv","version":4},"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":"sha256:51d33a344ad3c7d1a556ed2ed28edaa0635f3e46baf08648493ebe31f85985bf","target":"record","created_at":"2026-05-18T03:42:32Z","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":"17b85d072a38af211390d4208d146d0ef090e004dcd4be77f5f6a3c386f3013d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-26T11:51:25Z","title_canon_sha256":"0cb181a86f074f7e9768f9ed6455194cd9cf4e7813b5333732dc697e8277699b"},"schema_version":"1.0","source":{"id":"1109.5530","kind":"arxiv","version":4}},"canonical_sha256":"dca23efb3a02e42557b01ce2d077ab245ce5105fe24e6e2f95bd1eee6bd4523d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dca23efb3a02e42557b01ce2d077ab245ce5105fe24e6e2f95bd1eee6bd4523d","first_computed_at":"2026-05-18T03:42:32.262176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:32.262176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gQRYw/ToNqzXR/3jzNu/Zn0RKg/hiuBeAvTQdd/Tqo2lKNIni3v/PKBgYHNVtlsQ5EMRyV9TVrdZySP8TXB5Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:32.262615Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5530","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51d33a344ad3c7d1a556ed2ed28edaa0635f3e46baf08648493ebe31f85985bf","sha256:82a2d7a7f614eae68b752e289148d4f07f92a92b2c70f0d598a246491a0147c5"],"state_sha256":"b682d1af446f9e1bcf43c84b015c0e220a1f90bb9b52fb2fca5c07a0af24ea15"}