{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EXOAEERTNDBPUFS2K24LFPILPU","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":"62abfd643810e3e24212763907cb1567f2f88bb78287a934b2b091b017e7c8dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-26T09:53:15Z","title_canon_sha256":"16f9aff72cb6da41f48b1d7d5afae2f5b58faf2a0ccf331e922e347b8778d448"},"schema_version":"1.0","source":{"id":"1302.6374","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6374","created_at":"2026-05-18T02:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6374v4","created_at":"2026-05-18T02:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6374","created_at":"2026-05-18T02:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"EXOAEERTNDBP","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EXOAEERTNDBPUFS2","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EXOAEERT","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:6b59a9a764ba346cdc098fb18880665ff12194a4b3e0916ced7a9f6519d13bdc","target":"graph","created_at":"2026-05-18T02:51:34Z","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 strongly indefinite systems involving the fractional Laplacian on bounded domains. We obtain existence and non-existence results, $a priori$ estimates of Gidas-Spruck type, and the symmetric property.","authors_text":"Woocheol Choi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-26T09:53:15Z","title":"On strongly indefinite systems involving the fractional Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6374","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":"sha256:64313fcd8d088f5adbd6647d631cc6b9d552ea0b97fc4f05cf754419e18be56b","target":"record","created_at":"2026-05-18T02:51:34Z","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":"62abfd643810e3e24212763907cb1567f2f88bb78287a934b2b091b017e7c8dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-26T09:53:15Z","title_canon_sha256":"16f9aff72cb6da41f48b1d7d5afae2f5b58faf2a0ccf331e922e347b8778d448"},"schema_version":"1.0","source":{"id":"1302.6374","kind":"arxiv","version":4}},"canonical_sha256":"25dc02123368c2fa165a56b8b2bd0b7d03abadc10a6fcccc817a3e463bb19076","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25dc02123368c2fa165a56b8b2bd0b7d03abadc10a6fcccc817a3e463bb19076","first_computed_at":"2026-05-18T02:51:34.301067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:34.301067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f4WU7GvxsSquWE2iUBSgqM76LzpJrD4IK5wrVr9zA9a1Z5LHXKfz6pHTmKwlD+DcDrSZnEmLbvy8EHcssEEOCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:34.301733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6374","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64313fcd8d088f5adbd6647d631cc6b9d552ea0b97fc4f05cf754419e18be56b","sha256:6b59a9a764ba346cdc098fb18880665ff12194a4b3e0916ced7a9f6519d13bdc"],"state_sha256":"ac758ed036006116b62222a3e06ac0fd2f6c11336e2b86f45626bbd534359fda"}