{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HOQZ35WDSC2QKWKVZDIWK3Q26D","short_pith_number":"pith:HOQZ35WD","canonical_record":{"source":{"id":"1104.1259","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-07T07:41:45Z","cross_cats_sorted":[],"title_canon_sha256":"98f729fd0caa0de780ebebec15d3f96ac873eb3876e89afdad0783b99d7a2515","abstract_canon_sha256":"94cb8b611f7f8ba8de791d7355534be14c7651926d0307cde9235b8103a30a94"},"schema_version":"1.0"},"canonical_sha256":"3ba19df6c390b5055955c8d1656e1af0ffc12c66d6515ecd54479b09c6fe554c","source":{"kind":"arxiv","id":"1104.1259","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1259","created_at":"2026-05-18T02:31:27Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1259v4","created_at":"2026-05-18T02:31:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1259","created_at":"2026-05-18T02:31:27Z"},{"alias_kind":"pith_short_12","alias_value":"HOQZ35WDSC2Q","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HOQZ35WDSC2QKWKV","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HOQZ35WD","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HOQZ35WDSC2QKWKVZDIWK3Q26D","target":"record","payload":{"canonical_record":{"source":{"id":"1104.1259","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-07T07:41:45Z","cross_cats_sorted":[],"title_canon_sha256":"98f729fd0caa0de780ebebec15d3f96ac873eb3876e89afdad0783b99d7a2515","abstract_canon_sha256":"94cb8b611f7f8ba8de791d7355534be14c7651926d0307cde9235b8103a30a94"},"schema_version":"1.0"},"canonical_sha256":"3ba19df6c390b5055955c8d1656e1af0ffc12c66d6515ecd54479b09c6fe554c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:27.782859Z","signature_b64":"OcXAnfOWWzYPj8jCxsdvPkj9vmJM7I1KGzUHjWWp+SkRMEIAsqTh2OAPlYfhlLlXEheZfEdaUPa6WjP5cGDuDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ba19df6c390b5055955c8d1656e1af0ffc12c66d6515ecd54479b09c6fe554c","last_reissued_at":"2026-05-18T02:31:27.782299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:27.782299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.1259","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FNAqJbvo/4WVHqeD9Grh3xf3GtPz4p1e4kLS+QBRIGTSzHMdivo4xbUMjgFBD496sVmROjoLJEU8bSaZLetCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:37:22.182080Z"},"content_sha256":"12f307f8e497f7515c492c089cac83de019d149fb66d2ce2729ec1e6a048c616","schema_version":"1.0","event_id":"sha256:12f307f8e497f7515c492c089cac83de019d149fb66d2ce2729ec1e6a048c616"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HOQZ35WDSC2QKWKVZDIWK3Q26D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New examples of constant mean curvature surfaces in $\\mathbb{S}^2\\times\\mathbb{R}$ and $\\mathbb{H}^2\\times \\mathbb{R}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Francisco Torralbo, Jos\\'e M. Manzano","submitted_at":"2011-04-07T07:41:45Z","abstract_excerpt":"We construct non-zero constant mean curvature H surfaces in the product spaces $\\mathbb{S}^2 \\times \\mathbb{R}$ and $\\mathbb{H}^2\\times \\mathbb{R}$ by using suitable conjugate Plateau constructions. The resulting surfaces are complete, have bounded height and are invariant under a discrete group of horizontal translations. In $\\mathbb{S}^2\\times\\mathbb{R}$ (for any $H > 0$) or $\\mathbb{H}^2\\times\\mathbb{R}$ (for $H > 1/2$), a 1-parameter family of unduloid-type surfaces is obtained, some of which are shown to be compact in $\\mathbb{S}^2\\times\\mathbb{R}$. Finally, in the case of $H = 1/2$ in $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1259","kind":"arxiv","version":4},"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":"2026-05-18T02:31:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VwUjwgaIKLHyzc7Egqv4m/d9eaoCt2UjWz4mhRbGkbxQmCnT6ptTIrKwL3GJfDFKrDmZHS4MZVhl9ZkzBC0vBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:37:22.182771Z"},"content_sha256":"c0bd085799a53746af65a753d1f8749c64d37ec4dbe062546575b45ef121c682","schema_version":"1.0","event_id":"sha256:c0bd085799a53746af65a753d1f8749c64d37ec4dbe062546575b45ef121c682"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HOQZ35WDSC2QKWKVZDIWK3Q26D/bundle.json","state_url":"https://pith.science/pith/HOQZ35WDSC2QKWKVZDIWK3Q26D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HOQZ35WDSC2QKWKVZDIWK3Q26D/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":"2026-06-10T01:37:22Z","links":{"resolver":"https://pith.science/pith/HOQZ35WDSC2QKWKVZDIWK3Q26D","bundle":"https://pith.science/pith/HOQZ35WDSC2QKWKVZDIWK3Q26D/bundle.json","state":"https://pith.science/pith/HOQZ35WDSC2QKWKVZDIWK3Q26D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HOQZ35WDSC2QKWKVZDIWK3Q26D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HOQZ35WDSC2QKWKVZDIWK3Q26D","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":"94cb8b611f7f8ba8de791d7355534be14c7651926d0307cde9235b8103a30a94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-07T07:41:45Z","title_canon_sha256":"98f729fd0caa0de780ebebec15d3f96ac873eb3876e89afdad0783b99d7a2515"},"schema_version":"1.0","source":{"id":"1104.1259","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1259","created_at":"2026-05-18T02:31:27Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1259v4","created_at":"2026-05-18T02:31:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1259","created_at":"2026-05-18T02:31:27Z"},{"alias_kind":"pith_short_12","alias_value":"HOQZ35WDSC2Q","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HOQZ35WDSC2QKWKV","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HOQZ35WD","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:c0bd085799a53746af65a753d1f8749c64d37ec4dbe062546575b45ef121c682","target":"graph","created_at":"2026-05-18T02:31:27Z","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 construct non-zero constant mean curvature H surfaces in the product spaces $\\mathbb{S}^2 \\times \\mathbb{R}$ and $\\mathbb{H}^2\\times \\mathbb{R}$ by using suitable conjugate Plateau constructions. The resulting surfaces are complete, have bounded height and are invariant under a discrete group of horizontal translations. In $\\mathbb{S}^2\\times\\mathbb{R}$ (for any $H > 0$) or $\\mathbb{H}^2\\times\\mathbb{R}$ (for $H > 1/2$), a 1-parameter family of unduloid-type surfaces is obtained, some of which are shown to be compact in $\\mathbb{S}^2\\times\\mathbb{R}$. Finally, in the case of $H = 1/2$ in $\\","authors_text":"Francisco Torralbo, Jos\\'e M. Manzano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-07T07:41:45Z","title":"New examples of constant mean curvature surfaces in $\\mathbb{S}^2\\times\\mathbb{R}$ and $\\mathbb{H}^2\\times \\mathbb{R}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1259","kind":"arxiv","version":4},"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":"sha256:12f307f8e497f7515c492c089cac83de019d149fb66d2ce2729ec1e6a048c616","target":"record","created_at":"2026-05-18T02:31:27Z","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":"94cb8b611f7f8ba8de791d7355534be14c7651926d0307cde9235b8103a30a94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-07T07:41:45Z","title_canon_sha256":"98f729fd0caa0de780ebebec15d3f96ac873eb3876e89afdad0783b99d7a2515"},"schema_version":"1.0","source":{"id":"1104.1259","kind":"arxiv","version":4}},"canonical_sha256":"3ba19df6c390b5055955c8d1656e1af0ffc12c66d6515ecd54479b09c6fe554c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ba19df6c390b5055955c8d1656e1af0ffc12c66d6515ecd54479b09c6fe554c","first_computed_at":"2026-05-18T02:31:27.782299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:27.782299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OcXAnfOWWzYPj8jCxsdvPkj9vmJM7I1KGzUHjWWp+SkRMEIAsqTh2OAPlYfhlLlXEheZfEdaUPa6WjP5cGDuDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:27.782859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1259","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12f307f8e497f7515c492c089cac83de019d149fb66d2ce2729ec1e6a048c616","sha256:c0bd085799a53746af65a753d1f8749c64d37ec4dbe062546575b45ef121c682"],"state_sha256":"7e1caa5c2075fbf6539468a281fefd5552fd0f096c3a434b35a4a7c741423e78"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6czNKfl87nLhhxnzRD+SAr3k1dGnW9J0ISS3EyptWiix0NmkhtqLjziAk9paoxTe9cByCF0NhQrGYBz/j8rBBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T01:37:22.187408Z","bundle_sha256":"c7e7cc804a735e34a420ccb7b335860e6d06043962cccd0ec376ecf623ee9fb5"}}