{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:7QBVQQSXJZECFMA64NPSRPZVC7","short_pith_number":"pith:7QBVQQSX","canonical_record":{"source":{"id":"2607.00108","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-30T19:48:40Z","cross_cats_sorted":[],"title_canon_sha256":"e84d3e4f5bf61c7086e4495fb181765fc233c8478f336d19b5be7a3edf02115d","abstract_canon_sha256":"98e7465891f3c4816529128df852830030afea71317411621e5ec1af87966aa7"},"schema_version":"1.0"},"canonical_sha256":"fc035842574e4822b01ee35f28bf3517ff542e6729179dc5a45ae61ff94a32a3","source":{"kind":"arxiv","id":"2607.00108","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00108","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00108v1","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00108","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"7QBVQQSXJZEC","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"pith_short_16","alias_value":"7QBVQQSXJZECFMA6","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"pith_short_8","alias_value":"7QBVQQSX","created_at":"2026-07-02T00:18:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:7QBVQQSXJZECFMA64NPSRPZVC7","target":"record","payload":{"canonical_record":{"source":{"id":"2607.00108","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-30T19:48:40Z","cross_cats_sorted":[],"title_canon_sha256":"e84d3e4f5bf61c7086e4495fb181765fc233c8478f336d19b5be7a3edf02115d","abstract_canon_sha256":"98e7465891f3c4816529128df852830030afea71317411621e5ec1af87966aa7"},"schema_version":"1.0"},"canonical_sha256":"fc035842574e4822b01ee35f28bf3517ff542e6729179dc5a45ae61ff94a32a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T00:18:34.735523Z","signature_b64":"wVapj6xcBO35nKvrKb8QSXAZsV8LJ74gMv6X7rJkiUwrLJpoiwO7+hAVIbEP0MVp4bhPkfUF1qWjYn40vZ5UAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc035842574e4822b01ee35f28bf3517ff542e6729179dc5a45ae61ff94a32a3","last_reissued_at":"2026-07-02T00:18:34.734958Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T00:18:34.734958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.00108","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":"2026-07-02T00:18:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jsF+u29SZY6zP23cWdzlJDz4S2UwldOQ5/FV75Wox87NmW4CbL8DGQ9W60vugF6PIdRUk3qK+oGYmh3RcRS+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T02:48:21.779476Z"},"content_sha256":"1ff7f4d922236bc8936f60259c1a4080a5372ae6265021dc719a3b7e13e12265","schema_version":"1.0","event_id":"sha256:1ff7f4d922236bc8936f60259c1a4080a5372ae6265021dc719a3b7e13e12265"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:7QBVQQSXJZECFMA64NPSRPZVC7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constant mean curvature hypersurfaces in $\\mathbb{H}^2\\times\\mathbb{H}^2$ with double horocyclic symmetry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Julio Cesar Mohnsam","submitted_at":"2026-06-30T19:48:40Z","abstract_excerpt":"We study constant mean curvature hypersurfaces in $\\mathbb{H}^2\\times\\mathbb{H}^2$ invariant under a double horocyclic action. We show that the CMC condition reduces to a single autonomous ordinary differential equation for an angular function. From this reduction, we obtain three distinct regimes and solve the ODE explicitly in each case, obtaining an existence and uniqueness result for double horocyclic CMC hypersurfaces in $\\mathbb{H}^2\\times\\mathbb{H}^2$. Finally, we classify the equilibrium solutions and identify the corresponding homogeneous models: $\\mathbb{H}^3$, $\\mathbb{H}^2\\times\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00108","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/2607.00108/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":"2026-07-02T00:18:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iTBOwd6gTPZBJVBqO964SEf8uOjMkgrJCa/apXXKsAu98UFqrZ075Rx782AvxhZcfuQqF/T103ZPfhIE/2HtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T02:48:21.779844Z"},"content_sha256":"a4a4b0b7ef1c0290e7db7ac9c043eae921f6f54e5908b45afa1e1f3c16e0aba4","schema_version":"1.0","event_id":"sha256:a4a4b0b7ef1c0290e7db7ac9c043eae921f6f54e5908b45afa1e1f3c16e0aba4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7QBVQQSXJZECFMA64NPSRPZVC7/bundle.json","state_url":"https://pith.science/pith/7QBVQQSXJZECFMA64NPSRPZVC7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7QBVQQSXJZECFMA64NPSRPZVC7/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":"2026-07-04T02:48:21Z","links":{"resolver":"https://pith.science/pith/7QBVQQSXJZECFMA64NPSRPZVC7","bundle":"https://pith.science/pith/7QBVQQSXJZECFMA64NPSRPZVC7/bundle.json","state":"https://pith.science/pith/7QBVQQSXJZECFMA64NPSRPZVC7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7QBVQQSXJZECFMA64NPSRPZVC7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7QBVQQSXJZECFMA64NPSRPZVC7","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":"98e7465891f3c4816529128df852830030afea71317411621e5ec1af87966aa7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-30T19:48:40Z","title_canon_sha256":"e84d3e4f5bf61c7086e4495fb181765fc233c8478f336d19b5be7a3edf02115d"},"schema_version":"1.0","source":{"id":"2607.00108","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00108","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00108v1","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00108","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"7QBVQQSXJZEC","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"pith_short_16","alias_value":"7QBVQQSXJZECFMA6","created_at":"2026-07-02T00:18:34Z"},{"alias_kind":"pith_short_8","alias_value":"7QBVQQSX","created_at":"2026-07-02T00:18:34Z"}],"graph_snapshots":[{"event_id":"sha256:a4a4b0b7ef1c0290e7db7ac9c043eae921f6f54e5908b45afa1e1f3c16e0aba4","target":"graph","created_at":"2026-07-02T00:18:34Z","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/2607.00108/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study constant mean curvature hypersurfaces in $\\mathbb{H}^2\\times\\mathbb{H}^2$ invariant under a double horocyclic action. We show that the CMC condition reduces to a single autonomous ordinary differential equation for an angular function. From this reduction, we obtain three distinct regimes and solve the ODE explicitly in each case, obtaining an existence and uniqueness result for double horocyclic CMC hypersurfaces in $\\mathbb{H}^2\\times\\mathbb{H}^2$. Finally, we classify the equilibrium solutions and identify the corresponding homogeneous models: $\\mathbb{H}^3$, $\\mathbb{H}^2\\times\\ma","authors_text":"Julio Cesar Mohnsam","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-30T19:48:40Z","title":"Constant mean curvature hypersurfaces in $\\mathbb{H}^2\\times\\mathbb{H}^2$ with double horocyclic symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00108","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":"sha256:1ff7f4d922236bc8936f60259c1a4080a5372ae6265021dc719a3b7e13e12265","target":"record","created_at":"2026-07-02T00:18:34Z","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":"98e7465891f3c4816529128df852830030afea71317411621e5ec1af87966aa7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-30T19:48:40Z","title_canon_sha256":"e84d3e4f5bf61c7086e4495fb181765fc233c8478f336d19b5be7a3edf02115d"},"schema_version":"1.0","source":{"id":"2607.00108","kind":"arxiv","version":1}},"canonical_sha256":"fc035842574e4822b01ee35f28bf3517ff542e6729179dc5a45ae61ff94a32a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc035842574e4822b01ee35f28bf3517ff542e6729179dc5a45ae61ff94a32a3","first_computed_at":"2026-07-02T00:18:34.734958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T00:18:34.734958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wVapj6xcBO35nKvrKb8QSXAZsV8LJ74gMv6X7rJkiUwrLJpoiwO7+hAVIbEP0MVp4bhPkfUF1qWjYn40vZ5UAA==","signature_status":"signed_v1","signed_at":"2026-07-02T00:18:34.735523Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.00108","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ff7f4d922236bc8936f60259c1a4080a5372ae6265021dc719a3b7e13e12265","sha256:a4a4b0b7ef1c0290e7db7ac9c043eae921f6f54e5908b45afa1e1f3c16e0aba4"],"state_sha256":"f92a321e6fae51e751fbf1b6d6907cb0f6c776d706fee4c247005b53f98b779e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O3DrES5h5TZDCILHQ5leHvAfLf/KlzrBtKDftelhDLn56ZSnur8TRBJDEGNhyvMhP8j7GFagSjMqusMJ0kodDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T02:48:21.781761Z","bundle_sha256":"97def18cd0d62ee977782c939209eb118b105bf58f06238c84f8ee8ecd31c46e"}}