{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FQMIGF2C56IXDUMNTH5T5XENPD","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":"d3adf06ba3f4a47ff57c648ed42736a4db3d80020d78d547c3fe2e1db92f95e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-14T07:00:13Z","title_canon_sha256":"7475253d8b625a6ac5a28310a0fc970c9007c535d25f27f5f503e0fa6a8a2046"},"schema_version":"1.0","source":{"id":"1207.3398","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3398","created_at":"2026-05-18T03:51:01Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3398v1","created_at":"2026-05-18T03:51:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3398","created_at":"2026-05-18T03:51:01Z"},{"alias_kind":"pith_short_12","alias_value":"FQMIGF2C56IX","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FQMIGF2C56IXDUMN","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FQMIGF2C","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:545ad340d18b866a3a9fe3f9cfbca45c60a85a42d032d8e32437ffaccc4de720","target":"graph","created_at":"2026-05-18T03:51:01Z","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 will investigate the singular points of the following unstable free boundary problem: {equation}\\label{Eq} \\Delta u= -\\chi_{\\{u>0\\}} \\quad\\quad\\textrm{in} B_1(0) {equation} where $\\chi_{\\{u>0\\}}$ is the characteristic function of the set $\\{u>0\\}$.","authors_text":"Georg Weiss, Henrik Shahgholian, John Andersson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-14T07:00:13Z","title":"The Singular Set of Higher Dimensional Unstable Obstacle Type Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3398","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":"sha256:8b07dac68261932b274909a43296b7c7c49981dafa1f35e75f661954fe5b4bdb","target":"record","created_at":"2026-05-18T03:51:01Z","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":"d3adf06ba3f4a47ff57c648ed42736a4db3d80020d78d547c3fe2e1db92f95e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-14T07:00:13Z","title_canon_sha256":"7475253d8b625a6ac5a28310a0fc970c9007c535d25f27f5f503e0fa6a8a2046"},"schema_version":"1.0","source":{"id":"1207.3398","kind":"arxiv","version":1}},"canonical_sha256":"2c18831742ef9171d18d99fb3edc8d78cd08948ce95a78c7392b39ed392ec803","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c18831742ef9171d18d99fb3edc8d78cd08948ce95a78c7392b39ed392ec803","first_computed_at":"2026-05-18T03:51:01.292134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:01.292134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KdXMEBzpPryoHJuvUlbMw9rP+Kav0A5DFbdFHSvs0Fphom1pRpM400p2IRyPjF0UleqDtBrRleo/NmVhxw9jDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:01.292967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3398","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b07dac68261932b274909a43296b7c7c49981dafa1f35e75f661954fe5b4bdb","sha256:545ad340d18b866a3a9fe3f9cfbca45c60a85a42d032d8e32437ffaccc4de720"],"state_sha256":"ba5fd33de65dd18a786e18688c90cd37dc1031f5d5e8dc588eee6079d6a64b3a"}