{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:UVXTEZHTRKYT6N36RUVXPZ5IFB","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":"d14873c4028bc66e893dbe8b4c65cbc4603f597ee2f8c11265c2c2e2664e3c7f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-10-01T15:24:28Z","title_canon_sha256":"1831bdfc0ff6cd784fc2004aba4b41b9799ab81ee14e6009316b7ebcdd9725ab"},"schema_version":"1.0","source":{"id":"0910.0199","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.0199","created_at":"2026-05-18T04:26:33Z"},{"alias_kind":"arxiv_version","alias_value":"0910.0199v2","created_at":"2026-05-18T04:26:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.0199","created_at":"2026-05-18T04:26:33Z"},{"alias_kind":"pith_short_12","alias_value":"UVXTEZHTRKYT","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"UVXTEZHTRKYT6N36","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"UVXTEZHT","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:064d2dc139a3c53d549c72a1d151618e303b4af4c0793ea1452399633a6c2d17","target":"graph","created_at":"2026-05-18T04:26:33Z","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":"Given a compact closed subset $M$ of a line segment in $\\mathbb{R}^3$, we construct a sequence of minimal surfaces $\\Sigma_k$ embedded in a neighborhood $C$ of the line segment that converge smoothly to a limit lamination of $C$ away from $M$. Moreover, the curvature of this sequence blows up precisely on $M$, and the limit lamination has non-removable singularities precisely on the boundary of $M$.","authors_text":"Stephen J. Kleene","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-10-01T15:24:28Z","title":"A Minimal Lamination with Cantor Set-Like Singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.0199","kind":"arxiv","version":2},"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":"sha256:3998e6ff53f523590c7519eb9b26cba7369ffdf35d1f5da347ba677567936ffe","target":"record","created_at":"2026-05-18T04:26:33Z","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":"d14873c4028bc66e893dbe8b4c65cbc4603f597ee2f8c11265c2c2e2664e3c7f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-10-01T15:24:28Z","title_canon_sha256":"1831bdfc0ff6cd784fc2004aba4b41b9799ab81ee14e6009316b7ebcdd9725ab"},"schema_version":"1.0","source":{"id":"0910.0199","kind":"arxiv","version":2}},"canonical_sha256":"a56f3264f38ab13f377e8d2b77e7a8287cac80dd0dc894b1106bdedc529e274d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a56f3264f38ab13f377e8d2b77e7a8287cac80dd0dc894b1106bdedc529e274d","first_computed_at":"2026-05-18T04:26:33.372134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:33.372134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mi4TmZ+H3zr5JGH0BJ1OP5EtNbCP4LhJN5CnmBOTvkVEkD2ROLHC8muoTGmVM1Q5d8rT9rCehZd/ozjpxzAMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:33.372896Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.0199","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3998e6ff53f523590c7519eb9b26cba7369ffdf35d1f5da347ba677567936ffe","sha256:064d2dc139a3c53d549c72a1d151618e303b4af4c0793ea1452399633a6c2d17"],"state_sha256":"669d5f3ada3a514a97e4430db15d89a751aa723fd820cafd473abf177e4950fc"}