{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:UY4WM7NMICG5X6KNSBTSOVFJS4","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":"089ac0c441c2038033ae137ee80576fccffb19a4f44f1a53e8b07a005b7ed482","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-12-26T12:23:52Z","title_canon_sha256":"625f366e73232b5992eef32c77ff3460c32a5459aea2f00135a16f305cf6208e"},"schema_version":"1.0","source":{"id":"2312.16022","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.16022","created_at":"2026-07-05T09:35:47Z"},{"alias_kind":"arxiv_version","alias_value":"2312.16022v2","created_at":"2026-07-05T09:35:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.16022","created_at":"2026-07-05T09:35:47Z"},{"alias_kind":"pith_short_12","alias_value":"UY4WM7NMICG5","created_at":"2026-07-05T09:35:47Z"},{"alias_kind":"pith_short_16","alias_value":"UY4WM7NMICG5X6KN","created_at":"2026-07-05T09:35:47Z"},{"alias_kind":"pith_short_8","alias_value":"UY4WM7NM","created_at":"2026-07-05T09:35:47Z"}],"graph_snapshots":[{"event_id":"sha256:bd1c14a91799e63b413b43503fa30f62884998a51fb56411350435f60ab33912","target":"graph","created_at":"2026-07-05T09:35:47Z","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/2312.16022/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In odd dimensions, we prove a scalar curvature rigidity for parabolic convex polytopes in hyperbolic space enclosed by linear planes in the Poincare upper half-space model and convex with respect to the conformally related flat metric. Our method is based on spinor techniques and relies on the recent smoothing constructions of Brendle-Wang. We also prove a Llarull type rigidity for bounded smooth parabolic convex domains and a dihedral rigidity for polytopal initial data sets with dominant energy conditions.","authors_text":"Xiaoxiang Chai (POSTECH), Xueyuan Wan (CQUT)","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-12-26T12:23:52Z","title":"Scalar curvature rigidity of parabolic convex polytopes in hyperbolic space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.16022","kind":"arxiv","version":2},"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":"sha256:495f8b3e651819e9d6e62956977b8a355a40017803b32ad7d3e27ecde14abf4e","target":"record","created_at":"2026-07-05T09:35:47Z","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":"089ac0c441c2038033ae137ee80576fccffb19a4f44f1a53e8b07a005b7ed482","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-12-26T12:23:52Z","title_canon_sha256":"625f366e73232b5992eef32c77ff3460c32a5459aea2f00135a16f305cf6208e"},"schema_version":"1.0","source":{"id":"2312.16022","kind":"arxiv","version":2}},"canonical_sha256":"a639667dac408ddbf94d90672754a9972fee8cb31f6e66bf2b732900a8d998f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a639667dac408ddbf94d90672754a9972fee8cb31f6e66bf2b732900a8d998f3","first_computed_at":"2026-07-05T09:35:47.239826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:35:47.239826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Mxg3rtI3SJTf75pzu7jDfm/ilBsYuFN8FMmwXdvYBuzxzx0yvVh8msKmSEwVwQ1qbOXAu0n9xG3Ubxu6m5fAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:35:47.240328Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.16022","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:495f8b3e651819e9d6e62956977b8a355a40017803b32ad7d3e27ecde14abf4e","sha256:bd1c14a91799e63b413b43503fa30f62884998a51fb56411350435f60ab33912"],"state_sha256":"2fd42e96e47bfa20e3976c13976e7b74b60c77e107a73919552a6d213e7190bc"}