{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ECC7J54WN2X7WN3QQ5F2N4QMFB","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":"ea09bc00e87f0e436dc29aecc036cf5b081aa5e410736b1ee4c210f9e24a6cec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-19T14:40:01Z","title_canon_sha256":"7063ae6fbce5bf6dda4668ef0586a85240464041068ac3a9a8a132313b326075"},"schema_version":"1.0","source":{"id":"1307.5236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5236","created_at":"2026-05-18T03:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5236v1","created_at":"2026-05-18T03:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5236","created_at":"2026-05-18T03:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"ECC7J54WN2X7","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"ECC7J54WN2X7WN3Q","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"ECC7J54W","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:ce46e4c9be46a111992ecd73e20906046f1d18b259eaeb5224ccdafa7ddb5822","target":"graph","created_at":"2026-05-18T03:18:05Z","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 extend a Poincar\\'{e}-type inequality for functions with large zero-sets by Jiang and Lin to fractional Sobolev spaces. As a consequence, we obtain a Hausdorff dimension estimate on the size of zero sets for fractional Sobolev functions whose inverse is integrable. Also, for a suboptimal Hausdorff dimension estimate, we give a completely elementary proof based on a pointwise Poincar\\'{e}-style inequality.","authors_text":"Armin Schikorra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-19T14:40:01Z","title":"A note on zero sets of fractional sobolev functions with negative power of integrability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5236","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":"sha256:9aaa7f779840eadc34546f0e2b2dca233126715a8a5e6fc7131d2d2dc939ad32","target":"record","created_at":"2026-05-18T03:18:05Z","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":"ea09bc00e87f0e436dc29aecc036cf5b081aa5e410736b1ee4c210f9e24a6cec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-19T14:40:01Z","title_canon_sha256":"7063ae6fbce5bf6dda4668ef0586a85240464041068ac3a9a8a132313b326075"},"schema_version":"1.0","source":{"id":"1307.5236","kind":"arxiv","version":1}},"canonical_sha256":"2085f4f7966eaffb3770874ba6f20c2874d123209ded7db5de8fc753e1fe786c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2085f4f7966eaffb3770874ba6f20c2874d123209ded7db5de8fc753e1fe786c","first_computed_at":"2026-05-18T03:18:05.368648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:05.368648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FNUjfxL671eJ0ddv7ZBkS8AcnO6UqaIs8g8qVByuroVjoMGmz8WNkN7171q2g3AtsX31m9XoPZFToAdFE/SDAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:05.369281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9aaa7f779840eadc34546f0e2b2dca233126715a8a5e6fc7131d2d2dc939ad32","sha256:ce46e4c9be46a111992ecd73e20906046f1d18b259eaeb5224ccdafa7ddb5822"],"state_sha256":"23262b01bb9608752f48999fe3268d54dd7c1eeb63b73a9c36b93310d65a2eb5"}