{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JA5EOHOUZOUW5Y3QOP5CCXGJEQ","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":"2deed267f7d02a069bdc33e500a0d993e3716cb3c7e9dba1bd633e8fbfb18a14","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-11T23:35:51Z","title_canon_sha256":"2adbadcb8ba7b1ea0bb398061f2d0d59c06e7bd4c59816fe2a9610baddc4a70c"},"schema_version":"1.0","source":{"id":"1210.3394","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3394","created_at":"2026-05-18T03:43:20Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3394v1","created_at":"2026-05-18T03:43:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3394","created_at":"2026-05-18T03:43:20Z"},{"alias_kind":"pith_short_12","alias_value":"JA5EOHOUZOUW","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JA5EOHOUZOUW5Y3Q","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JA5EOHOU","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:ffcdf615bf4cf1bb26425e4907493ab1d7e4648f90f8f539e9ac3f2195bbb309","target":"graph","created_at":"2026-05-18T03:43:20Z","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 refine the construction and related estimates for complete Constant Mean Curvature surfaces in Euclidean three-space developed in Kapouleas (1990) by adopting the more precise and powerful version of the methodology which was developed in Kapouleas (1995). As a consequence we remove the severe restrictions in establishing embeddedness for complete Constant Mean Curvature surfaces in Kapouleas (1990) and we produce a very large class of new embedded examples of finite topology.","authors_text":"Christine Breiner, Nikolaos Kapouleas","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-11T23:35:51Z","title":"Embedded Constant Mean Curvature Surfaces in Euclidean Three Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3394","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:cafbf79a39a098ff2d99f27305994493d05b61f7d728f343bbf514e9dd6eab6b","target":"record","created_at":"2026-05-18T03:43:20Z","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":"2deed267f7d02a069bdc33e500a0d993e3716cb3c7e9dba1bd633e8fbfb18a14","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-11T23:35:51Z","title_canon_sha256":"2adbadcb8ba7b1ea0bb398061f2d0d59c06e7bd4c59816fe2a9610baddc4a70c"},"schema_version":"1.0","source":{"id":"1210.3394","kind":"arxiv","version":1}},"canonical_sha256":"483a471dd4cba96ee37073fa215cc9241fc9364a94e20a7d37ed7acc4506fce1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"483a471dd4cba96ee37073fa215cc9241fc9364a94e20a7d37ed7acc4506fce1","first_computed_at":"2026-05-18T03:43:20.004392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:20.004392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ld1bjzSq3e2hbzG89d2EW6jukjnxbcXv1ueinqPyP4IJnJhwiJKxOJx7TTrCWUTEnm7VovKxgT+aEForLWLMDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:20.005119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3394","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cafbf79a39a098ff2d99f27305994493d05b61f7d728f343bbf514e9dd6eab6b","sha256:ffcdf615bf4cf1bb26425e4907493ab1d7e4648f90f8f539e9ac3f2195bbb309"],"state_sha256":"88dea67d0c4ce9729f7fb44bb07e8582421e979a954bb469124c50ae3ce97102"}