{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OTTGITFULDIECIDWAZKLBDHVZQ","short_pith_number":"pith:OTTGITFU","canonical_record":{"source":{"id":"1202.5167","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-23T13:05:12Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"638977abf5afa41aa145725de5f301a6e0b1f57528622e434a1e845e701e7066","abstract_canon_sha256":"7785a5f4a38a8dab9da7ea4bb76345b82b4041c0f6005eef26e1e6b4ec302c10"},"schema_version":"1.0"},"canonical_sha256":"74e6644cb458d04120760654b08cf5cc103241c235ac594a5c19a3bebe7d6b2a","source":{"kind":"arxiv","id":"1202.5167","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5167","created_at":"2026-05-18T03:10:37Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5167v3","created_at":"2026-05-18T03:10:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5167","created_at":"2026-05-18T03:10:37Z"},{"alias_kind":"pith_short_12","alias_value":"OTTGITFULDIE","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OTTGITFULDIECIDW","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OTTGITFU","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OTTGITFULDIECIDWAZKLBDHVZQ","target":"record","payload":{"canonical_record":{"source":{"id":"1202.5167","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-23T13:05:12Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"638977abf5afa41aa145725de5f301a6e0b1f57528622e434a1e845e701e7066","abstract_canon_sha256":"7785a5f4a38a8dab9da7ea4bb76345b82b4041c0f6005eef26e1e6b4ec302c10"},"schema_version":"1.0"},"canonical_sha256":"74e6644cb458d04120760654b08cf5cc103241c235ac594a5c19a3bebe7d6b2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:37.532664Z","signature_b64":"2QYrC3ISVq2eptICK2WUJW0ndaRkkH8WadXXIZILBCLQr18DXhF5piPttO4f472kN+JMHmUi9FKDXqHbXJYPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74e6644cb458d04120760654b08cf5cc103241c235ac594a5c19a3bebe7d6b2a","last_reissued_at":"2026-05-18T03:10:37.531971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:37.531971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.5167","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:10:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"satwQjSAAu4aoXdR4QPb6GJzRyNz5CfUa22YCoX6xrCRKIspIbFlIwUU6sdEURxctUTQEWiHInhmYCMTkYdRDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:01:17.450824Z"},"content_sha256":"ee5086fbf536614bdc4f42919bb9ae7f956272645f9cae9452684042ef29ac9d","schema_version":"1.0","event_id":"sha256:ee5086fbf536614bdc4f42919bb9ae7f956272645f9cae9452684042ef29ac9d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OTTGITFULDIECIDWAZKLBDHVZQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometry and Topology of some overdetermined elliptic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Antonio Ros, Pieralberto Sicbaldi","submitted_at":"2012-02-23T13:05:12Z","abstract_excerpt":"We study necessary conditions on the geometry and the topology of domains in $\\mathbb{R}^2$ that support a positive solution to a classical overdetermined elliptic problem. The ideas and tools we use come from constant mean curvature surface theory. In particular, we obtain a partial answer to a question posed by H. Berestycki, L. Caffarelli and L. Nirenberg in 1997. We investigate also some boundedness properties of the solution $u$. Some of our results generalize to higher dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5167","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:10:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O7ifUa9b0F/QQgQ2Mg9YGyTxGC0iMk++93cDkVFraPnG70r/acCNCzweTBAQ1QFDh4jfAdO5jHvYqGDsdlE1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:01:17.451162Z"},"content_sha256":"4218c331a26d896a10afa8cff01d0c136e32774e2e9460ad47a8e8cecdd205a8","schema_version":"1.0","event_id":"sha256:4218c331a26d896a10afa8cff01d0c136e32774e2e9460ad47a8e8cecdd205a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OTTGITFULDIECIDWAZKLBDHVZQ/bundle.json","state_url":"https://pith.science/pith/OTTGITFULDIECIDWAZKLBDHVZQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OTTGITFULDIECIDWAZKLBDHVZQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T07:01:17Z","links":{"resolver":"https://pith.science/pith/OTTGITFULDIECIDWAZKLBDHVZQ","bundle":"https://pith.science/pith/OTTGITFULDIECIDWAZKLBDHVZQ/bundle.json","state":"https://pith.science/pith/OTTGITFULDIECIDWAZKLBDHVZQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OTTGITFULDIECIDWAZKLBDHVZQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OTTGITFULDIECIDWAZKLBDHVZQ","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":"7785a5f4a38a8dab9da7ea4bb76345b82b4041c0f6005eef26e1e6b4ec302c10","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-23T13:05:12Z","title_canon_sha256":"638977abf5afa41aa145725de5f301a6e0b1f57528622e434a1e845e701e7066"},"schema_version":"1.0","source":{"id":"1202.5167","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5167","created_at":"2026-05-18T03:10:37Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5167v3","created_at":"2026-05-18T03:10:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5167","created_at":"2026-05-18T03:10:37Z"},{"alias_kind":"pith_short_12","alias_value":"OTTGITFULDIE","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OTTGITFULDIECIDW","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OTTGITFU","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:4218c331a26d896a10afa8cff01d0c136e32774e2e9460ad47a8e8cecdd205a8","target":"graph","created_at":"2026-05-18T03:10:37Z","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 study necessary conditions on the geometry and the topology of domains in $\\mathbb{R}^2$ that support a positive solution to a classical overdetermined elliptic problem. The ideas and tools we use come from constant mean curvature surface theory. In particular, we obtain a partial answer to a question posed by H. Berestycki, L. Caffarelli and L. Nirenberg in 1997. We investigate also some boundedness properties of the solution $u$. Some of our results generalize to higher dimensions.","authors_text":"Antonio Ros, Pieralberto Sicbaldi","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-23T13:05:12Z","title":"Geometry and Topology of some overdetermined elliptic problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5167","kind":"arxiv","version":3},"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:ee5086fbf536614bdc4f42919bb9ae7f956272645f9cae9452684042ef29ac9d","target":"record","created_at":"2026-05-18T03:10:37Z","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":"7785a5f4a38a8dab9da7ea4bb76345b82b4041c0f6005eef26e1e6b4ec302c10","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-23T13:05:12Z","title_canon_sha256":"638977abf5afa41aa145725de5f301a6e0b1f57528622e434a1e845e701e7066"},"schema_version":"1.0","source":{"id":"1202.5167","kind":"arxiv","version":3}},"canonical_sha256":"74e6644cb458d04120760654b08cf5cc103241c235ac594a5c19a3bebe7d6b2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74e6644cb458d04120760654b08cf5cc103241c235ac594a5c19a3bebe7d6b2a","first_computed_at":"2026-05-18T03:10:37.531971Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:37.531971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2QYrC3ISVq2eptICK2WUJW0ndaRkkH8WadXXIZILBCLQr18DXhF5piPttO4f472kN+JMHmUi9FKDXqHbXJYPDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:37.532664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5167","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee5086fbf536614bdc4f42919bb9ae7f956272645f9cae9452684042ef29ac9d","sha256:4218c331a26d896a10afa8cff01d0c136e32774e2e9460ad47a8e8cecdd205a8"],"state_sha256":"068b0d69de57ac247c7e2c26fd8bd006a6a2fdb48de4add83c71072ec815f603"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1jeOyKiI+9kOp+rswCyOBF04I9mjpjseivKQph/QWLusrZLhDjArsU+MVZfn9ByYs76PC9GJMM11KzcnrfR4AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T07:01:17.453543Z","bundle_sha256":"f9045434a46013d069cbb2fb09cf76c5a4a3dfca87c6599511bf28b8d760f238"}}