{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:AG3DBFA4MXFOGBGDEKTAYWMISV","short_pith_number":"pith:AG3DBFA4","canonical_record":{"source":{"id":"2606.24686","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-23T15:16:03Z","cross_cats_sorted":[],"title_canon_sha256":"503c16741e5cb262824c5b781aff3502351311cceab2781f0380edb26e65024e","abstract_canon_sha256":"d86dfc3fafe0bd5d7a641b1a4a7530fdfa34df3470463380a0d03a131c9e6cec"},"schema_version":"1.0"},"canonical_sha256":"01b630941c65cae304c322a60c5988956788acdaabd282c353e0d11f15d832fa","source":{"kind":"arxiv","id":"2606.24686","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24686","created_at":"2026-06-24T01:15:39Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24686v1","created_at":"2026-06-24T01:15:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24686","created_at":"2026-06-24T01:15:39Z"},{"alias_kind":"pith_short_12","alias_value":"AG3DBFA4MXFO","created_at":"2026-06-24T01:15:39Z"},{"alias_kind":"pith_short_16","alias_value":"AG3DBFA4MXFOGBGD","created_at":"2026-06-24T01:15:39Z"},{"alias_kind":"pith_short_8","alias_value":"AG3DBFA4","created_at":"2026-06-24T01:15:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:AG3DBFA4MXFOGBGDEKTAYWMISV","target":"record","payload":{"canonical_record":{"source":{"id":"2606.24686","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-23T15:16:03Z","cross_cats_sorted":[],"title_canon_sha256":"503c16741e5cb262824c5b781aff3502351311cceab2781f0380edb26e65024e","abstract_canon_sha256":"d86dfc3fafe0bd5d7a641b1a4a7530fdfa34df3470463380a0d03a131c9e6cec"},"schema_version":"1.0"},"canonical_sha256":"01b630941c65cae304c322a60c5988956788acdaabd282c353e0d11f15d832fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:15:39.220243Z","signature_b64":"xfrHVszJI73NLskG5rBQBDfuQcXU/Nxtj7OiZbJI9Z6eCcetGvqdEXrZmAFBuNjoCb9rzzTffQBMd+JZe1dFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01b630941c65cae304c322a60c5988956788acdaabd282c353e0d11f15d832fa","last_reissued_at":"2026-06-24T01:15:39.219853Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:15:39.219853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.24686","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":"2026-06-24T01:15:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"91EIWz4NJrQ/Z4jCpRvqbKg294WXEGDYaN5ieW1rrFfhxTVgZl3r+xBsEIkxZuS8h680XCHYMk9lXVGI3I3sBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:50:13.170077Z"},"content_sha256":"590d203af0ac45e56048277f5933d0d89071af79afc15002ab4f803aadbf06a0","schema_version":"1.0","event_id":"sha256:590d203af0ac45e56048277f5933d0d89071af79afc15002ab4f803aadbf06a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:AG3DBFA4MXFOGBGDEKTAYWMISV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hypersurfaces of $\\mathbb{H}^2\\times\\mathbb{H}^2$ with constant sectional curvature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Haizhong Li, Luc Vrancken, Xianfeng Wang, Zeke Yao","submitted_at":"2026-06-23T15:16:03Z","abstract_excerpt":"In this paper, we classify the hypersurfaces of $\\mathbb{H}^2\\times\\mathbb{H}^2$ with constant sectional curvature. In contrast to $\\mathbb{S}^2\\times\\mathbb{S}^2$, the resulting examples for $\\mathbb{H}^2\\times\\mathbb{H}^2$ exhibit more diversity, and we construct a special example with non-constant product angle function. For $\\mathbb{S}^2\\times\\mathbb{S}^2$, however, the product angle function of any constant sectional curvature hypersurface is identically zero. As a byproduct, we classify the hypersurfaces of $\\mathbb{H}^2\\times\\mathbb{H}^2$ with constant product angle function and constan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24686","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/2606.24686/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":"2026-06-24T01:15:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"40EygsCb056rScWrXTq0ZrZEnV4ek31gb8Iqa+MA+ZEVb6CuscOHr8WdhWZRTDh7Ca4lBVKtZkkRE+mzWQ9WCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:50:13.170462Z"},"content_sha256":"85dc94688e02dc6a271e0441fadf646158782c88f0eb0b1edfd3e51f855f6200","schema_version":"1.0","event_id":"sha256:85dc94688e02dc6a271e0441fadf646158782c88f0eb0b1edfd3e51f855f6200"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AG3DBFA4MXFOGBGDEKTAYWMISV/bundle.json","state_url":"https://pith.science/pith/AG3DBFA4MXFOGBGDEKTAYWMISV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AG3DBFA4MXFOGBGDEKTAYWMISV/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":"2026-06-27T04:50:13Z","links":{"resolver":"https://pith.science/pith/AG3DBFA4MXFOGBGDEKTAYWMISV","bundle":"https://pith.science/pith/AG3DBFA4MXFOGBGDEKTAYWMISV/bundle.json","state":"https://pith.science/pith/AG3DBFA4MXFOGBGDEKTAYWMISV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AG3DBFA4MXFOGBGDEKTAYWMISV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AG3DBFA4MXFOGBGDEKTAYWMISV","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":"d86dfc3fafe0bd5d7a641b1a4a7530fdfa34df3470463380a0d03a131c9e6cec","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-23T15:16:03Z","title_canon_sha256":"503c16741e5cb262824c5b781aff3502351311cceab2781f0380edb26e65024e"},"schema_version":"1.0","source":{"id":"2606.24686","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24686","created_at":"2026-06-24T01:15:39Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24686v1","created_at":"2026-06-24T01:15:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24686","created_at":"2026-06-24T01:15:39Z"},{"alias_kind":"pith_short_12","alias_value":"AG3DBFA4MXFO","created_at":"2026-06-24T01:15:39Z"},{"alias_kind":"pith_short_16","alias_value":"AG3DBFA4MXFOGBGD","created_at":"2026-06-24T01:15:39Z"},{"alias_kind":"pith_short_8","alias_value":"AG3DBFA4","created_at":"2026-06-24T01:15:39Z"}],"graph_snapshots":[{"event_id":"sha256:85dc94688e02dc6a271e0441fadf646158782c88f0eb0b1edfd3e51f855f6200","target":"graph","created_at":"2026-06-24T01:15:39Z","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/2606.24686/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we classify the hypersurfaces of $\\mathbb{H}^2\\times\\mathbb{H}^2$ with constant sectional curvature. In contrast to $\\mathbb{S}^2\\times\\mathbb{S}^2$, the resulting examples for $\\mathbb{H}^2\\times\\mathbb{H}^2$ exhibit more diversity, and we construct a special example with non-constant product angle function. For $\\mathbb{S}^2\\times\\mathbb{S}^2$, however, the product angle function of any constant sectional curvature hypersurface is identically zero. As a byproduct, we classify the hypersurfaces of $\\mathbb{H}^2\\times\\mathbb{H}^2$ with constant product angle function and constan","authors_text":"Haizhong Li, Luc Vrancken, Xianfeng Wang, Zeke Yao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-23T15:16:03Z","title":"Hypersurfaces of $\\mathbb{H}^2\\times\\mathbb{H}^2$ with constant sectional curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24686","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":"sha256:590d203af0ac45e56048277f5933d0d89071af79afc15002ab4f803aadbf06a0","target":"record","created_at":"2026-06-24T01:15:39Z","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":"d86dfc3fafe0bd5d7a641b1a4a7530fdfa34df3470463380a0d03a131c9e6cec","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-23T15:16:03Z","title_canon_sha256":"503c16741e5cb262824c5b781aff3502351311cceab2781f0380edb26e65024e"},"schema_version":"1.0","source":{"id":"2606.24686","kind":"arxiv","version":1}},"canonical_sha256":"01b630941c65cae304c322a60c5988956788acdaabd282c353e0d11f15d832fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01b630941c65cae304c322a60c5988956788acdaabd282c353e0d11f15d832fa","first_computed_at":"2026-06-24T01:15:39.219853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:15:39.219853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xfrHVszJI73NLskG5rBQBDfuQcXU/Nxtj7OiZbJI9Z6eCcetGvqdEXrZmAFBuNjoCb9rzzTffQBMd+JZe1dFCw==","signature_status":"signed_v1","signed_at":"2026-06-24T01:15:39.220243Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.24686","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:590d203af0ac45e56048277f5933d0d89071af79afc15002ab4f803aadbf06a0","sha256:85dc94688e02dc6a271e0441fadf646158782c88f0eb0b1edfd3e51f855f6200"],"state_sha256":"6ddafc53f22a20f81968ddc25111608115cd29f638fe209efd2d24479d12505f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"02kEbMidhD48OJsaiTTXdUSgPqLLgi6YYF0MJWdli3gsmnm+E8Her5upEQRZFqcxoyQ6T8xNf19tJdQAiqBuCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T04:50:13.172550Z","bundle_sha256":"8cbec169957372f00c8ec76cd56aa761d9f3e3bf7ccce2b395109b430d623e55"}}