{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KQFHEDD7LGYKS2M3G3ID3CG5AT","short_pith_number":"pith:KQFHEDD7","canonical_record":{"source":{"id":"1703.07201","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-21T13:09:15Z","cross_cats_sorted":[],"title_canon_sha256":"338f05a3f581d57e84ef59f675c32ec745fe0bb0e37045161dbf92a9218b1e80","abstract_canon_sha256":"ce8c3932fa0f4fe1ab0082bc4996bc8fc8ed7fc30ba86f1555f58eb05bf167f7"},"schema_version":"1.0"},"canonical_sha256":"540a720c7f59b0a9699b36d03d88dd04c7e31b30bc02126973355123cbdf95e1","source":{"kind":"arxiv","id":"1703.07201","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07201","created_at":"2026-05-18T00:48:11Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07201v1","created_at":"2026-05-18T00:48:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07201","created_at":"2026-05-18T00:48:11Z"},{"alias_kind":"pith_short_12","alias_value":"KQFHEDD7LGYK","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KQFHEDD7LGYKS2M3","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KQFHEDD7","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KQFHEDD7LGYKS2M3G3ID3CG5AT","target":"record","payload":{"canonical_record":{"source":{"id":"1703.07201","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-21T13:09:15Z","cross_cats_sorted":[],"title_canon_sha256":"338f05a3f581d57e84ef59f675c32ec745fe0bb0e37045161dbf92a9218b1e80","abstract_canon_sha256":"ce8c3932fa0f4fe1ab0082bc4996bc8fc8ed7fc30ba86f1555f58eb05bf167f7"},"schema_version":"1.0"},"canonical_sha256":"540a720c7f59b0a9699b36d03d88dd04c7e31b30bc02126973355123cbdf95e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:11.017896Z","signature_b64":"SMyiyQm7h8jUD2RsIkuhNvjBmC9teLwU5ICLn3Nn6wibcXO+uQ6EFkZB/AblwmBI217x7enk43xeBR0DNfOuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"540a720c7f59b0a9699b36d03d88dd04c7e31b30bc02126973355123cbdf95e1","last_reissued_at":"2026-05-18T00:48:11.017224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:11.017224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.07201","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":"2026-05-18T00:48:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CovJlbwl5O44/dgDOP61buhjdmzn+xUol4qMTLH5M87uMlx6Xsro3OOYKtc9+TTFldmBHSmnyTQW4n6xVA0xCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:37:32.764794Z"},"content_sha256":"b3255dd4800bd3fdaca42c9659fff76d5baff31d277fd3aadade72cc0b1697e1","schema_version":"1.0","event_id":"sha256:b3255dd4800bd3fdaca42c9659fff76d5baff31d277fd3aadade72cc0b1697e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KQFHEDD7LGYKS2M3G3ID3CG5AT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Capillary Immersions in E($\\kappa$,${\\tau}$)","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Haimer A. Trejos","submitted_at":"2017-03-21T13:09:15Z","abstract_excerpt":"In [3] and [11] the authors showed the existence of a Codazzi pair defined on any constant mean curvature surface in the homogeneous spaces E($\\kappa$,$\\tau$) associated to the Abresch-Rosenberg differential. In this paper, we use the mentioned Codazzi pair to classify capillary disks in E($\\kappa$,$\\tau$). As a consequence, the results presented in this paper generalize the previous classification of constant mean curvature disks in the product spaces $\\mathbb{S}^2 \\times \\mathbb{R}$ and $\\mathbb{H}^2 \\times \\mathbb{R}$ in [4] and [5]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07201","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":"2026-05-18T00:48:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FBzPF3BjiDiYxmqK/Hs0OZAj16E/ZDwJCJr9UMuN/UJteIJZukoEHr8sc2VTFLonZjkvdtLTI1Ve6GRY6iLWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:37:32.765139Z"},"content_sha256":"6610c9116f07544fdd0ab0b39207101b33f3bdd63ca461aba4bb5541d457cd5b","schema_version":"1.0","event_id":"sha256:6610c9116f07544fdd0ab0b39207101b33f3bdd63ca461aba4bb5541d457cd5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KQFHEDD7LGYKS2M3G3ID3CG5AT/bundle.json","state_url":"https://pith.science/pith/KQFHEDD7LGYKS2M3G3ID3CG5AT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KQFHEDD7LGYKS2M3G3ID3CG5AT/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":"2026-06-22T10:37:32Z","links":{"resolver":"https://pith.science/pith/KQFHEDD7LGYKS2M3G3ID3CG5AT","bundle":"https://pith.science/pith/KQFHEDD7LGYKS2M3G3ID3CG5AT/bundle.json","state":"https://pith.science/pith/KQFHEDD7LGYKS2M3G3ID3CG5AT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KQFHEDD7LGYKS2M3G3ID3CG5AT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KQFHEDD7LGYKS2M3G3ID3CG5AT","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":"ce8c3932fa0f4fe1ab0082bc4996bc8fc8ed7fc30ba86f1555f58eb05bf167f7","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-21T13:09:15Z","title_canon_sha256":"338f05a3f581d57e84ef59f675c32ec745fe0bb0e37045161dbf92a9218b1e80"},"schema_version":"1.0","source":{"id":"1703.07201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07201","created_at":"2026-05-18T00:48:11Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07201v1","created_at":"2026-05-18T00:48:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07201","created_at":"2026-05-18T00:48:11Z"},{"alias_kind":"pith_short_12","alias_value":"KQFHEDD7LGYK","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KQFHEDD7LGYKS2M3","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KQFHEDD7","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:6610c9116f07544fdd0ab0b39207101b33f3bdd63ca461aba4bb5541d457cd5b","target":"graph","created_at":"2026-05-18T00:48:11Z","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 [3] and [11] the authors showed the existence of a Codazzi pair defined on any constant mean curvature surface in the homogeneous spaces E($\\kappa$,$\\tau$) associated to the Abresch-Rosenberg differential. In this paper, we use the mentioned Codazzi pair to classify capillary disks in E($\\kappa$,$\\tau$). As a consequence, the results presented in this paper generalize the previous classification of constant mean curvature disks in the product spaces $\\mathbb{S}^2 \\times \\mathbb{R}$ and $\\mathbb{H}^2 \\times \\mathbb{R}$ in [4] and [5].","authors_text":"Haimer A. Trejos","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-21T13:09:15Z","title":"Capillary Immersions in E($\\kappa$,${\\tau}$)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07201","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:b3255dd4800bd3fdaca42c9659fff76d5baff31d277fd3aadade72cc0b1697e1","target":"record","created_at":"2026-05-18T00:48:11Z","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":"ce8c3932fa0f4fe1ab0082bc4996bc8fc8ed7fc30ba86f1555f58eb05bf167f7","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-21T13:09:15Z","title_canon_sha256":"338f05a3f581d57e84ef59f675c32ec745fe0bb0e37045161dbf92a9218b1e80"},"schema_version":"1.0","source":{"id":"1703.07201","kind":"arxiv","version":1}},"canonical_sha256":"540a720c7f59b0a9699b36d03d88dd04c7e31b30bc02126973355123cbdf95e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"540a720c7f59b0a9699b36d03d88dd04c7e31b30bc02126973355123cbdf95e1","first_computed_at":"2026-05-18T00:48:11.017224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:11.017224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SMyiyQm7h8jUD2RsIkuhNvjBmC9teLwU5ICLn3Nn6wibcXO+uQ6EFkZB/AblwmBI217x7enk43xeBR0DNfOuCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:11.017896Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.07201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3255dd4800bd3fdaca42c9659fff76d5baff31d277fd3aadade72cc0b1697e1","sha256:6610c9116f07544fdd0ab0b39207101b33f3bdd63ca461aba4bb5541d457cd5b"],"state_sha256":"9e7a205176f8feb36073ef25966db12c25fe84034eac859e2ef195e76e88336a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qdFvDktmsFsYVJkLqCDkYoAYfRUl1RONeSfR+ShQa00d28JLFl7KdjPNnx93TcYxrbl5skw3cs65SkNUU4QIAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T10:37:32.767144Z","bundle_sha256":"9b6133e087bd1bca88fd4ff5369a70d820c03baaa8ac560c01e12b46372297a6"}}