{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3AND7QBCUPNXMLZMXXT7MYSXWJ","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":"f2ce5c9c6caf92f2e9b2a51186f29fa491648ba85b45547474e3c5749766be24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-24T15:46:54Z","title_canon_sha256":"49003217c8a30775fc97a28787e52f89e8a58521b022767de4380ce52dada2d1"},"schema_version":"1.0","source":{"id":"1010.4974","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4974","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4974v1","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4974","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"pith_short_12","alias_value":"3AND7QBCUPNX","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3AND7QBCUPNXMLZM","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3AND7QBC","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:dc4fa15c60ed553638b4e3716acda08967b5a0c5b1945e39088700229c661891","target":"graph","created_at":"2026-05-18T04:38:49Z","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":"For all $m \\in \\mathbb N - \\{0\\}$, we prove the existence of a one dimensional family of genus $m$, constant mean curvature (equal to 1) surfaces which are complete, immersed in $\\mathbb R^3$ and have two Delaunay ends asymptotic to nodo\\\"{\\i}dal ends. Moreover, these surfaces are invariant under the group of isometries of $\\mathbb R^3$ leaving a horizontal regular polygon with $m+1$ sides fixed.","authors_text":"Frank Pacard, Harold Rosenberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-24T15:46:54Z","title":"Attaching handles to Delaunay nodo\\\"{\\i}ds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4974","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":"sha256:8a1d5e8854cc78ca4429f2f30404d99a07c5d75c85f961ad4eaa232d6e50a8b3","target":"record","created_at":"2026-05-18T04:38:49Z","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":"f2ce5c9c6caf92f2e9b2a51186f29fa491648ba85b45547474e3c5749766be24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-24T15:46:54Z","title_canon_sha256":"49003217c8a30775fc97a28787e52f89e8a58521b022767de4380ce52dada2d1"},"schema_version":"1.0","source":{"id":"1010.4974","kind":"arxiv","version":1}},"canonical_sha256":"d81a3fc022a3db762f2cbde7f66257b25206d7349431183a670a0f272962c322","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d81a3fc022a3db762f2cbde7f66257b25206d7349431183a670a0f272962c322","first_computed_at":"2026-05-18T04:38:49.678281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:49.678281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yxrgNPxG4/WVcDCbLMSE2zb/Ot7dwDwpYpVpAEZiPYrNBg4ixPuxwWGFfIMaflb4uUnz2+wrK5FrPr3/KfE2CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:49.678840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.4974","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a1d5e8854cc78ca4429f2f30404d99a07c5d75c85f961ad4eaa232d6e50a8b3","sha256:dc4fa15c60ed553638b4e3716acda08967b5a0c5b1945e39088700229c661891"],"state_sha256":"1694c192833dc90b518669c691fa279cdcfe77f5eb82528c63468ee92e8170aa"}