{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PL37H25D7RWSC5QM727G7LYWSH","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":"01591e02ab4c141eff04fa5de5d8436362d6a064441e482108bbcbdc5649c681","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-21T04:44:52Z","title_canon_sha256":"3bf2b00e514a612dadb396172a89aa9a77ec28a850d8815934f7409db9a1237f"},"schema_version":"1.0","source":{"id":"1812.08943","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08943","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08943v1","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08943","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"PL37H25D7RWS","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PL37H25D7RWSC5QM","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PL37H25D","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:0f98b736b93ddba68819a94230bfe77d0e344debb25f7cdbb2ce8f717acbfa61","target":"graph","created_at":"2026-05-17T23:57:45Z","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 establish a connection between free boundary minimal surfaces in a ball in $\\mathbb{R}^3$ and free boundary cones arising in a one-phase problem. We prove that a doubly connected minimal surface with free boundary in a ball is a catenoid.","authors_text":"Alexei V. Penskoi, Nikolai Nadirashvili","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-21T04:44:52Z","title":"Free boundary minimal surfaces and overdetermined boundary value problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08943","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":"sha256:339ba324432658b1704bcdf91f8deb0e0c4e6e62490adf560fbe95eb49184853","target":"record","created_at":"2026-05-17T23:57:45Z","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":"01591e02ab4c141eff04fa5de5d8436362d6a064441e482108bbcbdc5649c681","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-21T04:44:52Z","title_canon_sha256":"3bf2b00e514a612dadb396172a89aa9a77ec28a850d8815934f7409db9a1237f"},"schema_version":"1.0","source":{"id":"1812.08943","kind":"arxiv","version":1}},"canonical_sha256":"7af7f3eba3fc6d21760cfebe6faf1691f488e5251a2a2ac444ed6c32c3bcf4f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7af7f3eba3fc6d21760cfebe6faf1691f488e5251a2a2ac444ed6c32c3bcf4f0","first_computed_at":"2026-05-17T23:57:45.832763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:45.832763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bpaxYyQD1xBsw9JFEB3Vx5XdTaKrLrmi8Q5hlGzdls87tjXmgXhVHXbtKrkJbyJiUPeBhhIlg0EsoH5qEdCRAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:45.833417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.08943","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:339ba324432658b1704bcdf91f8deb0e0c4e6e62490adf560fbe95eb49184853","sha256:0f98b736b93ddba68819a94230bfe77d0e344debb25f7cdbb2ce8f717acbfa61"],"state_sha256":"93f3c6149104532df2168f6b351f685093a6138e6a5962df7e89666b177f7120"}