{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:G4OEAN2BCCP7BRM5BZRLDD6O5N","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":"81ec4d439afd9306a6b2eeb1852deffaf6ae45bfa0985a7e309602a65efe269b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-25T21:40:57Z","title_canon_sha256":"f3ba8c653d6fea7764d74ffac32d01550f29371cf05e1b8ef66441d00164b3be"},"schema_version":"1.0","source":{"id":"1505.06764","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06764","created_at":"2026-05-18T01:02:05Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06764v3","created_at":"2026-05-18T01:02:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06764","created_at":"2026-05-18T01:02:05Z"},{"alias_kind":"pith_short_12","alias_value":"G4OEAN2BCCP7","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"G4OEAN2BCCP7BRM5","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"G4OEAN2B","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:93c34f0065ffd0515b480752b0e9d9caadc77a33473ac76efec469938ddca793","target":"graph","created_at":"2026-05-18T01:02:05Z","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 prove that any complete, embedded minimal surface $M$ with finite topology in a homogeneous three-manifold $N$ has positive injectivity radius. When one relaxes the condition that $N$ be homogeneous to that of being locally homogeneous, then we show that the closure of $M$ has the structure of a minimal lamination of $N$. As an application of this general result we prove that any complete, embedded minimal surface with finite genus and a countable number of ends is compact when the ambient space is $\\mathbb{S}^3$ equipped with a homogeneous metric of nonnegative scalar curvature.","authors_text":"Joaquin Perez, William H. Meeks III","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-25T21:40:57Z","title":"Finite topology minimal surfaces in homogeneous three-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06764","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:faf6ee0f77659cdc31a3f5ea78b494d5a6688ada658364525134a5b838ec475d","target":"record","created_at":"2026-05-18T01:02:05Z","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":"81ec4d439afd9306a6b2eeb1852deffaf6ae45bfa0985a7e309602a65efe269b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-25T21:40:57Z","title_canon_sha256":"f3ba8c653d6fea7764d74ffac32d01550f29371cf05e1b8ef66441d00164b3be"},"schema_version":"1.0","source":{"id":"1505.06764","kind":"arxiv","version":3}},"canonical_sha256":"371c403741109ff0c59d0e62b18fceeb60fc6069e70057d8c29c29ab8df1dc88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"371c403741109ff0c59d0e62b18fceeb60fc6069e70057d8c29c29ab8df1dc88","first_computed_at":"2026-05-18T01:02:05.100658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:05.100658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/kGvVv+aEAEw0jNKqykTuwQozZemkZ3m79E8vJ3LosmdUDRkl9L7GAelQ4RbZIR3wM/XQxxiln4Aq896c8BCCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:05.101201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06764","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:faf6ee0f77659cdc31a3f5ea78b494d5a6688ada658364525134a5b838ec475d","sha256:93c34f0065ffd0515b480752b0e9d9caadc77a33473ac76efec469938ddca793"],"state_sha256":"a4eed66c5774a43d0ced0d46d4ddbc2197bd469aabba173a3fea80e4ba864f95"}