{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7ARNHVUNRMXFT6Y7K7CWAKRL3O","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":"ebc143c0976c634bb12da413196265297f81520753c2b6869c6fa7e1bc51dd9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-24T20:19:06Z","title_canon_sha256":"67e507380e53b2c18d131cdd85a6ab60d322d32657e24c6f43b360c5d2b5695f"},"schema_version":"1.0","source":{"id":"1401.6443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6443","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6443v1","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6443","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"7ARNHVUNRMXF","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7ARNHVUNRMXFT6Y7","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7ARNHVUN","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:6eadb5ab112780dcf054671bf4179ce0a02f538dc0a1e9e946b74145ba0b8bf8","target":"graph","created_at":"2026-05-18T03:01:11Z","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 one-phase free boundary problem involving a fractional Laplacian $(-\\Delta)^\\alpha$, $0<\\alpha <1,$ and we prove that ``flat free boundaries\" are $C^{1,\\gamma}$. We thus extend the known result for the case $\\alpha=1/2.$","authors_text":"Daniela De Silva, Ovidiu Savin, Yannick Sire","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-24T20:19:06Z","title":"A one-phase problem for the fractional Laplacian: regularity of flat free boundaries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6443","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:d9aae8faf44f0ee70a08314b754ac3d00603ff00d71c6a8a9765c79da8c311a7","target":"record","created_at":"2026-05-18T03:01:11Z","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":"ebc143c0976c634bb12da413196265297f81520753c2b6869c6fa7e1bc51dd9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-24T20:19:06Z","title_canon_sha256":"67e507380e53b2c18d131cdd85a6ab60d322d32657e24c6f43b360c5d2b5695f"},"schema_version":"1.0","source":{"id":"1401.6443","kind":"arxiv","version":1}},"canonical_sha256":"f822d3d68d8b2e59fb1f57c5602a2bdbbcb9f129a6ac815d935ee137212378d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f822d3d68d8b2e59fb1f57c5602a2bdbbcb9f129a6ac815d935ee137212378d8","first_computed_at":"2026-05-18T03:01:11.964029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:11.964029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6bviwrifLDz5s8k2ioiaXwjcfQXtZaql+niD3e185/swn7TZwx+J+1w3P28jL6Mj02zC88dJpa97fOFysVXyAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:11.965159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9aae8faf44f0ee70a08314b754ac3d00603ff00d71c6a8a9765c79da8c311a7","sha256:6eadb5ab112780dcf054671bf4179ce0a02f538dc0a1e9e946b74145ba0b8bf8"],"state_sha256":"c5e130cba0ff35797980be9ed6b69df81df78843259197de5225eff5a89a966a"}