{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:4VCBCIV237KLDIM42EUZETFOUI","short_pith_number":"pith:4VCBCIV2","canonical_record":{"source":{"id":"2410.08915","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-10-11T15:43:44Z","cross_cats_sorted":[],"title_canon_sha256":"c9b49bf3021dac2b0cea969d23cfa8879526b9ea85d72562bb36387699176e90","abstract_canon_sha256":"2c754d430660cf62e0033f18464e40e7f8f2885f87989bbde7f8721baa4c955d"},"schema_version":"1.0"},"canonical_sha256":"e5441122badfd4b1a19cd129924caea2309b112b40d15c0af90ee6df6067bbfe","source":{"kind":"arxiv","id":"2410.08915","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.08915","created_at":"2026-07-05T09:19:19Z"},{"alias_kind":"arxiv_version","alias_value":"2410.08915v1","created_at":"2026-07-05T09:19:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.08915","created_at":"2026-07-05T09:19:19Z"},{"alias_kind":"pith_short_12","alias_value":"4VCBCIV237KL","created_at":"2026-07-05T09:19:19Z"},{"alias_kind":"pith_short_16","alias_value":"4VCBCIV237KLDIM4","created_at":"2026-07-05T09:19:19Z"},{"alias_kind":"pith_short_8","alias_value":"4VCBCIV2","created_at":"2026-07-05T09:19:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:4VCBCIV237KLDIM42EUZETFOUI","target":"record","payload":{"canonical_record":{"source":{"id":"2410.08915","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-10-11T15:43:44Z","cross_cats_sorted":[],"title_canon_sha256":"c9b49bf3021dac2b0cea969d23cfa8879526b9ea85d72562bb36387699176e90","abstract_canon_sha256":"2c754d430660cf62e0033f18464e40e7f8f2885f87989bbde7f8721baa4c955d"},"schema_version":"1.0"},"canonical_sha256":"e5441122badfd4b1a19cd129924caea2309b112b40d15c0af90ee6df6067bbfe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:19:19.531945Z","signature_b64":"1HRQjvAYHHlfE+k7VofvAMJfyzTluBmrXsYaNC5WHLDR4P9nVuv4eq4yQ3rHvEzeUJH9NMqdtoYhUfjWDafqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5441122badfd4b1a19cd129924caea2309b112b40d15c0af90ee6df6067bbfe","last_reissued_at":"2026-07-05T09:19:19.531468Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:19:19.531468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.08915","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":"2026-07-05T09:19:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2upD5H/Nfvcfv/dZhp3oqADiTmSOf4iEp2SFjNgxtSibtdpcTQRkFt/Eu1fiWJ+gk8aIoaZuDI3yq7rVNqYXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T15:03:15.294652Z"},"content_sha256":"2cc19b348028a5f6413543c0966066b642b83b6afd11207cb3101ff6e40c3f1b","schema_version":"1.0","event_id":"sha256:2cc19b348028a5f6413543c0966066b642b83b6afd11207cb3101ff6e40c3f1b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:4VCBCIV237KLDIM42EUZETFOUI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constant mean curvature surfaces from ring patterns: Geometry from combinatorics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alexander I. Bobenko, Nina Smeenk, Tim Hoffmann","submitted_at":"2024-10-11T15:43:44Z","abstract_excerpt":"We define discrete constant mean curvature (cmc) surfaces in the three-dimensional Euclidean and Lorentz spaces in terms of sphere packings with orthogonally intersecting circles. These discrete cmc surfaces can be constructed from orthogonal ring patterns in the two-sphere and the hyperbolic plane. We present a variational principle that allows us to solve boundary value problems and to construct discrete analogues of some classical cmc surfaces. The data used for the construction is purely combinatorial - the combinatorics of the curvature line pattern. In the limit of orthogonal circle patt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.08915","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.08915/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:19:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DGvufX5WAOZdbwcIYyLowpzozXYMipjVOIJYwyWi/LJh/8tlbGdFIpthfqPYF4D94YAcxXPGuqYEF0N+kg7IBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T15:03:15.295608Z"},"content_sha256":"585282b2c97c4dad72195b94a4753a74d08aad242a04f6dc1215531d76de9db2","schema_version":"1.0","event_id":"sha256:585282b2c97c4dad72195b94a4753a74d08aad242a04f6dc1215531d76de9db2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4VCBCIV237KLDIM42EUZETFOUI/bundle.json","state_url":"https://pith.science/pith/4VCBCIV237KLDIM42EUZETFOUI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4VCBCIV237KLDIM42EUZETFOUI/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":"2026-08-14T15:03:15Z","links":{"resolver":"https://pith.science/pith/4VCBCIV237KLDIM42EUZETFOUI","bundle":"https://pith.science/pith/4VCBCIV237KLDIM42EUZETFOUI/bundle.json","state":"https://pith.science/pith/4VCBCIV237KLDIM42EUZETFOUI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4VCBCIV237KLDIM42EUZETFOUI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4VCBCIV237KLDIM42EUZETFOUI","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":"2c754d430660cf62e0033f18464e40e7f8f2885f87989bbde7f8721baa4c955d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-10-11T15:43:44Z","title_canon_sha256":"c9b49bf3021dac2b0cea969d23cfa8879526b9ea85d72562bb36387699176e90"},"schema_version":"1.0","source":{"id":"2410.08915","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.08915","created_at":"2026-07-05T09:19:19Z"},{"alias_kind":"arxiv_version","alias_value":"2410.08915v1","created_at":"2026-07-05T09:19:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.08915","created_at":"2026-07-05T09:19:19Z"},{"alias_kind":"pith_short_12","alias_value":"4VCBCIV237KL","created_at":"2026-07-05T09:19:19Z"},{"alias_kind":"pith_short_16","alias_value":"4VCBCIV237KLDIM4","created_at":"2026-07-05T09:19:19Z"},{"alias_kind":"pith_short_8","alias_value":"4VCBCIV2","created_at":"2026-07-05T09:19:19Z"}],"graph_snapshots":[{"event_id":"sha256:585282b2c97c4dad72195b94a4753a74d08aad242a04f6dc1215531d76de9db2","target":"graph","created_at":"2026-07-05T09:19:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.08915/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define discrete constant mean curvature (cmc) surfaces in the three-dimensional Euclidean and Lorentz spaces in terms of sphere packings with orthogonally intersecting circles. These discrete cmc surfaces can be constructed from orthogonal ring patterns in the two-sphere and the hyperbolic plane. We present a variational principle that allows us to solve boundary value problems and to construct discrete analogues of some classical cmc surfaces. The data used for the construction is purely combinatorial - the combinatorics of the curvature line pattern. In the limit of orthogonal circle patt","authors_text":"Alexander I. Bobenko, Nina Smeenk, Tim Hoffmann","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-10-11T15:43:44Z","title":"Constant mean curvature surfaces from ring patterns: Geometry from combinatorics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.08915","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":"sha256:2cc19b348028a5f6413543c0966066b642b83b6afd11207cb3101ff6e40c3f1b","target":"record","created_at":"2026-07-05T09:19:19Z","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":"2c754d430660cf62e0033f18464e40e7f8f2885f87989bbde7f8721baa4c955d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-10-11T15:43:44Z","title_canon_sha256":"c9b49bf3021dac2b0cea969d23cfa8879526b9ea85d72562bb36387699176e90"},"schema_version":"1.0","source":{"id":"2410.08915","kind":"arxiv","version":1}},"canonical_sha256":"e5441122badfd4b1a19cd129924caea2309b112b40d15c0af90ee6df6067bbfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5441122badfd4b1a19cd129924caea2309b112b40d15c0af90ee6df6067bbfe","first_computed_at":"2026-07-05T09:19:19.531468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:19:19.531468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1HRQjvAYHHlfE+k7VofvAMJfyzTluBmrXsYaNC5WHLDR4P9nVuv4eq4yQ3rHvEzeUJH9NMqdtoYhUfjWDafqBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:19:19.531945Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.08915","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cc19b348028a5f6413543c0966066b642b83b6afd11207cb3101ff6e40c3f1b","sha256:585282b2c97c4dad72195b94a4753a74d08aad242a04f6dc1215531d76de9db2"],"state_sha256":"bfb9fbeb98c240330554ca7cab4f0bc79d94079791b9b3c1c02fa57b40beaffc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dG3CWWXHHbUCXyHK8Rd1yw0GytFrlxa9vW8MpJQUSikloTRHCuEF8eG+kdb52u9TbHW4GM7jBEAT5FR4y+jOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T15:03:15.301756Z","bundle_sha256":"bc65fe6b3221105bb972bbb1ae26316fe90f8cf67a3d5c01d61b4d4e0c33be9d"}}