{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OHQ5XCABHLNLNFIHEQ4WMCCMI7","short_pith_number":"pith:OHQ5XCAB","canonical_record":{"source":{"id":"1707.04008","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-13T07:44:40Z","cross_cats_sorted":[],"title_canon_sha256":"480f2b5b5de8660446a80933ea2bf5251dbc2ad819dc40d26553ff29222ba233","abstract_canon_sha256":"b3593a5b48986a68a510fb6beccd8ead95a570067789c931504e3f1c5f79b425"},"schema_version":"1.0"},"canonical_sha256":"71e1db88013adab69507243966084c47f670c2c2c309e52f5a68b20559b420ce","source":{"kind":"arxiv","id":"1707.04008","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.04008","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"arxiv_version","alias_value":"1707.04008v1","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04008","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"pith_short_12","alias_value":"OHQ5XCABHLNL","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OHQ5XCABHLNLNFIH","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OHQ5XCAB","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OHQ5XCABHLNLNFIHEQ4WMCCMI7","target":"record","payload":{"canonical_record":{"source":{"id":"1707.04008","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-13T07:44:40Z","cross_cats_sorted":[],"title_canon_sha256":"480f2b5b5de8660446a80933ea2bf5251dbc2ad819dc40d26553ff29222ba233","abstract_canon_sha256":"b3593a5b48986a68a510fb6beccd8ead95a570067789c931504e3f1c5f79b425"},"schema_version":"1.0"},"canonical_sha256":"71e1db88013adab69507243966084c47f670c2c2c309e52f5a68b20559b420ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:22.845601Z","signature_b64":"fXs3eZZ6l8xq7C0elHmQMiAOGZ48nD3PXEF/Y94ptDyiHwSx+uFFV0aQ/6RBI6bBrMNmjbuicnmlvfkg1UloDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71e1db88013adab69507243966084c47f670c2c2c309e52f5a68b20559b420ce","last_reissued_at":"2026-05-18T00:40:22.844925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:22.844925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.04008","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aLVXGEfzLgQaYd6q6VCOu3nMH29aC3BzOqyVZaIE3vqfYXkjH6IYvjZsYITpL7vAx40WvKqBqY7AMbdtRKV5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:25:37.610962Z"},"content_sha256":"9ad320664d9457c3f0da0022c5cd17706d6eaf5cdce48b7341626761d37a1fa9","schema_version":"1.0","event_id":"sha256:9ad320664d9457c3f0da0022c5cd17706d6eaf5cdce48b7341626761d37a1fa9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OHQ5XCABHLNLNFIHEQ4WMCCMI7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complete Constant Mean Curvature Hypersurfaces in Euclidean space of dimension four or higher","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Christine Breiner, Nikolaos Kapouleas","submitted_at":"2017-07-13T07:44:40Z","abstract_excerpt":"In this article we provide a general construction when $n\\ge3$ for immersed in Euclidean $(n+1)$-space, complete, smooth, constant mean curvature hypersurfaces of finite topological type (in short CMC $n$-hypersurfaces). More precisely our construction converts certain graphs in Euclidean $(n+1)$-space to CMC $n$-hypersurfaces with asymptotically Delaunay ends in two steps: First appropriate small perturbations of the given graph have their vertices replaced by round spherical regions and their edges and rays by Delaunay pieces so that a family of initial smooth hypersurfaces is constructed. O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04008","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DpC/si4LvvgKNEWax42Gka3F2tEbV8asGM6QSiINgg56IiAjKuFsG8tHZcm0otCsdaL/C8GF7WgmzjurPMzGCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:25:37.611308Z"},"content_sha256":"6eaef508c592f2300683e132be52b2e914f4d565288634613e9d7611c6982a49","schema_version":"1.0","event_id":"sha256:6eaef508c592f2300683e132be52b2e914f4d565288634613e9d7611c6982a49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OHQ5XCABHLNLNFIHEQ4WMCCMI7/bundle.json","state_url":"https://pith.science/pith/OHQ5XCABHLNLNFIHEQ4WMCCMI7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OHQ5XCABHLNLNFIHEQ4WMCCMI7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T18:25:37Z","links":{"resolver":"https://pith.science/pith/OHQ5XCABHLNLNFIHEQ4WMCCMI7","bundle":"https://pith.science/pith/OHQ5XCABHLNLNFIHEQ4WMCCMI7/bundle.json","state":"https://pith.science/pith/OHQ5XCABHLNLNFIHEQ4WMCCMI7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OHQ5XCABHLNLNFIHEQ4WMCCMI7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OHQ5XCABHLNLNFIHEQ4WMCCMI7","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":"b3593a5b48986a68a510fb6beccd8ead95a570067789c931504e3f1c5f79b425","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-13T07:44:40Z","title_canon_sha256":"480f2b5b5de8660446a80933ea2bf5251dbc2ad819dc40d26553ff29222ba233"},"schema_version":"1.0","source":{"id":"1707.04008","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.04008","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"arxiv_version","alias_value":"1707.04008v1","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04008","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"pith_short_12","alias_value":"OHQ5XCABHLNL","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OHQ5XCABHLNLNFIH","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OHQ5XCAB","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:6eaef508c592f2300683e132be52b2e914f4d565288634613e9d7611c6982a49","target":"graph","created_at":"2026-05-18T00:40:22Z","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 article we provide a general construction when $n\\ge3$ for immersed in Euclidean $(n+1)$-space, complete, smooth, constant mean curvature hypersurfaces of finite topological type (in short CMC $n$-hypersurfaces). More precisely our construction converts certain graphs in Euclidean $(n+1)$-space to CMC $n$-hypersurfaces with asymptotically Delaunay ends in two steps: First appropriate small perturbations of the given graph have their vertices replaced by round spherical regions and their edges and rays by Delaunay pieces so that a family of initial smooth hypersurfaces is constructed. O","authors_text":"Christine Breiner, Nikolaos Kapouleas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-13T07:44:40Z","title":"Complete Constant Mean Curvature Hypersurfaces in Euclidean space of dimension four or higher"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04008","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":"sha256:9ad320664d9457c3f0da0022c5cd17706d6eaf5cdce48b7341626761d37a1fa9","target":"record","created_at":"2026-05-18T00:40:22Z","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":"b3593a5b48986a68a510fb6beccd8ead95a570067789c931504e3f1c5f79b425","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-13T07:44:40Z","title_canon_sha256":"480f2b5b5de8660446a80933ea2bf5251dbc2ad819dc40d26553ff29222ba233"},"schema_version":"1.0","source":{"id":"1707.04008","kind":"arxiv","version":1}},"canonical_sha256":"71e1db88013adab69507243966084c47f670c2c2c309e52f5a68b20559b420ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71e1db88013adab69507243966084c47f670c2c2c309e52f5a68b20559b420ce","first_computed_at":"2026-05-18T00:40:22.844925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:22.844925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fXs3eZZ6l8xq7C0elHmQMiAOGZ48nD3PXEF/Y94ptDyiHwSx+uFFV0aQ/6RBI6bBrMNmjbuicnmlvfkg1UloDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:22.845601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.04008","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ad320664d9457c3f0da0022c5cd17706d6eaf5cdce48b7341626761d37a1fa9","sha256:6eaef508c592f2300683e132be52b2e914f4d565288634613e9d7611c6982a49"],"state_sha256":"11710e7fda6584a9b9e7d814ea5b53e3a7f5c48c0f42ad522bb2f66070b470a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A487e2bDyp9e9a9FlK1B0FkDf8vhLnMuYvbziUeajtsHonVL7UsbcCGKLiQBWRCbhSpDg6Z29qoXdIeTEPnEDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:25:37.613235Z","bundle_sha256":"3de3b81d36f3e4577b3fed21fb9ce4b8b84207aa17b64c77df151e97b77dbfe2"}}