{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:3TRC5KLNM25F6P54SPRZP42DSI","short_pith_number":"pith:3TRC5KLN","schema_version":"1.0","canonical_sha256":"dce22ea96d66ba5f3fbc93e397f343923adc1cbb00301e0bc59c777e3e902129","source":{"kind":"arxiv","id":"2302.01604","version":2},"attestation_state":"computed","paper":{"title":"Convex hypersurfaces of prescribed curvatures in hyperbolic space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Li Chen","submitted_at":"2023-02-03T09:01:16Z","abstract_excerpt":"For a smooth, closed and uniformly $h$-convex hypersurface $M$ in $\\mathbb{H}^{n+1}$, the horospherical Gauss map $G: M \\rightarrow \\mathbb{S}^n$ is a diffeomorphism. We consider the problem of finding a smooth, closed and uniformly $h$-convex hypersurface $M\\subset \\mathbb{H}^{n+1}$ whose $k$-th shifted mean curvature $\\widetilde{H}_{k}$ ($1\\leq k\\leq n$) is prescribed as a positive function $\\tilde{f}(x)$ defined on $\\mathbb{S}^n$, i.e. \\begin{eqnarray*} \\widetilde{H}_{k}(G^{-1}(x))=\\tilde{f}(x). \\end{eqnarray*} We can prove the existence of solution to this problem if the given function $\\t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2302.01604","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-02-03T09:01:16Z","cross_cats_sorted":[],"title_canon_sha256":"0df247f7b25c428d4823aeb62e2677cac19d6f2b51a47e09f163524d7524cb86","abstract_canon_sha256":"9092f226570729b2fec792cbcd42dbfe8c5c704e66d250dfcf8aa1f5de3ba244"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:43:19.535895Z","signature_b64":"EQuSMgqdc4Ir/fPWu6dJkKJCRvhYWgH5ypJFbPegaRLEMCBbZ8xAXie8sLRFg7qzk+os03ohu6iwBsKKW7d8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dce22ea96d66ba5f3fbc93e397f343923adc1cbb00301e0bc59c777e3e902129","last_reissued_at":"2026-07-05T05:43:19.535409Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:43:19.535409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convex hypersurfaces of prescribed curvatures in hyperbolic space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Li Chen","submitted_at":"2023-02-03T09:01:16Z","abstract_excerpt":"For a smooth, closed and uniformly $h$-convex hypersurface $M$ in $\\mathbb{H}^{n+1}$, the horospherical Gauss map $G: M \\rightarrow \\mathbb{S}^n$ is a diffeomorphism. We consider the problem of finding a smooth, closed and uniformly $h$-convex hypersurface $M\\subset \\mathbb{H}^{n+1}$ whose $k$-th shifted mean curvature $\\widetilde{H}_{k}$ ($1\\leq k\\leq n$) is prescribed as a positive function $\\tilde{f}(x)$ defined on $\\mathbb{S}^n$, i.e. \\begin{eqnarray*} \\widetilde{H}_{k}(G^{-1}(x))=\\tilde{f}(x). \\end{eqnarray*} We can prove the existence of solution to this problem if the given function $\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.01604","kind":"arxiv","version":2},"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/2302.01604/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2302.01604","created_at":"2026-07-05T05:43:19.535470+00:00"},{"alias_kind":"arxiv_version","alias_value":"2302.01604v2","created_at":"2026-07-05T05:43:19.535470+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.01604","created_at":"2026-07-05T05:43:19.535470+00:00"},{"alias_kind":"pith_short_12","alias_value":"3TRC5KLNM25F","created_at":"2026-07-05T05:43:19.535470+00:00"},{"alias_kind":"pith_short_16","alias_value":"3TRC5KLNM25F6P54","created_at":"2026-07-05T05:43:19.535470+00:00"},{"alias_kind":"pith_short_8","alias_value":"3TRC5KLN","created_at":"2026-07-05T05:43:19.535470+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.17345","citing_title":"The horospherical $p$-Christoffel-Minkowski and prescribed $p$-shifted Weingarten curvature problems in hyperbolic space","ref_index":13,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3TRC5KLNM25F6P54SPRZP42DSI","json":"https://pith.science/pith/3TRC5KLNM25F6P54SPRZP42DSI.json","graph_json":"https://pith.science/api/pith-number/3TRC5KLNM25F6P54SPRZP42DSI/graph.json","events_json":"https://pith.science/api/pith-number/3TRC5KLNM25F6P54SPRZP42DSI/events.json","paper":"https://pith.science/paper/3TRC5KLN"},"agent_actions":{"view_html":"https://pith.science/pith/3TRC5KLNM25F6P54SPRZP42DSI","download_json":"https://pith.science/pith/3TRC5KLNM25F6P54SPRZP42DSI.json","view_paper":"https://pith.science/paper/3TRC5KLN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2302.01604&json=true","fetch_graph":"https://pith.science/api/pith-number/3TRC5KLNM25F6P54SPRZP42DSI/graph.json","fetch_events":"https://pith.science/api/pith-number/3TRC5KLNM25F6P54SPRZP42DSI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3TRC5KLNM25F6P54SPRZP42DSI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3TRC5KLNM25F6P54SPRZP42DSI/action/storage_attestation","attest_author":"https://pith.science/pith/3TRC5KLNM25F6P54SPRZP42DSI/action/author_attestation","sign_citation":"https://pith.science/pith/3TRC5KLNM25F6P54SPRZP42DSI/action/citation_signature","submit_replication":"https://pith.science/pith/3TRC5KLNM25F6P54SPRZP42DSI/action/replication_record"}},"created_at":"2026-07-05T05:43:19.535470+00:00","updated_at":"2026-07-05T05:43:19.535470+00:00"}