{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LWAUR2FJOL2X2KO7SOLONJJLIJ","short_pith_number":"pith:LWAUR2FJ","canonical_record":{"source":{"id":"1705.00313","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-30T13:29:35Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"70a74472b03bddb2c777fbf1ab9bc90c40f7106f4ca99023f3e2566a96cc41fa","abstract_canon_sha256":"fff9dab5f9b9f288fb01631f72275d3dda3a79bbc1244b5ac9bd4913e93c8626"},"schema_version":"1.0"},"canonical_sha256":"5d8148e8a972f57d29df9396e6a52b4260034513cde10810ebb6ac19fc1bc241","source":{"kind":"arxiv","id":"1705.00313","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00313","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00313v1","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00313","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"pith_short_12","alias_value":"LWAUR2FJOL2X","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LWAUR2FJOL2X2KO7","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LWAUR2FJ","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LWAUR2FJOL2X2KO7SOLONJJLIJ","target":"record","payload":{"canonical_record":{"source":{"id":"1705.00313","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-30T13:29:35Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"70a74472b03bddb2c777fbf1ab9bc90c40f7106f4ca99023f3e2566a96cc41fa","abstract_canon_sha256":"fff9dab5f9b9f288fb01631f72275d3dda3a79bbc1244b5ac9bd4913e93c8626"},"schema_version":"1.0"},"canonical_sha256":"5d8148e8a972f57d29df9396e6a52b4260034513cde10810ebb6ac19fc1bc241","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:20.817715Z","signature_b64":"qelpsKKFcqDtBGFt14hJlk7NuCshTIuaHwp2CQjeq9v5rya7CpI6vfjPZZ3i6fCK0m1VjDVGQSZE7zz4qvoPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d8148e8a972f57d29df9396e6a52b4260034513cde10810ebb6ac19fc1bc241","last_reissued_at":"2026-05-18T00:45:20.816989Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:20.816989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.00313","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":"2026-05-18T00:45:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Q3lX1RhLMd2NDPH/41iLLygUbXAmWRa0RFmhJ8RSwNU4+gzhNGJihI26UHlbUTio9d4wAHbpSTi4Vx6tkYqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T12:15:29.020402Z"},"content_sha256":"f27eccedca1c6012098c9d299659872e8180be94504385a5e17aec43487d520d","schema_version":"1.0","event_id":"sha256:f27eccedca1c6012098c9d299659872e8180be94504385a5e17aec43487d520d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LWAUR2FJOL2X2KO7SOLONJJLIJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Starshaped compact hypersurfaces with prescirbed Weingarten curvature in warped product manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Daguang Chen, Haizhong Li, Zhizhang Wang","submitted_at":"2017-04-30T13:29:35Z","abstract_excerpt":"Given a compact Riemannian manifold $M$, we consider a warped product $\\bar M = I \\times_h M$ where $I$ is an open interval in $\\Bbb R$. For a positive function $\\psi$ defined on $\\bar M$, we generalized the arguments in \\cite{GRW2015} and \\cite{RW16}, to obtain the curvature estimates for Hessian equations $\\sigma_k(\\kappa)=\\psi(V,\\nu(V))$. We also obtain some existence results for the starshaped compact hypersurface $\\Sigma$ satisfying the above equation with various assumptions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00313","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":""},"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":"2026-05-18T00:45:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Af7kXbkC8GfgZYyul7uIu5UWMorx3gh5OFbrh2Im4ooOhtlC2TBBKTR9Mk2pADvLyQV/lZRhq23tPiWN5R6LAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T12:15:29.020758Z"},"content_sha256":"810eca971e74bdae29d8f4690d0d7873518e82bbb2abd0fc692b46bb12c8abe9","schema_version":"1.0","event_id":"sha256:810eca971e74bdae29d8f4690d0d7873518e82bbb2abd0fc692b46bb12c8abe9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LWAUR2FJOL2X2KO7SOLONJJLIJ/bundle.json","state_url":"https://pith.science/pith/LWAUR2FJOL2X2KO7SOLONJJLIJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LWAUR2FJOL2X2KO7SOLONJJLIJ/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":"2026-07-01T12:15:29Z","links":{"resolver":"https://pith.science/pith/LWAUR2FJOL2X2KO7SOLONJJLIJ","bundle":"https://pith.science/pith/LWAUR2FJOL2X2KO7SOLONJJLIJ/bundle.json","state":"https://pith.science/pith/LWAUR2FJOL2X2KO7SOLONJJLIJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LWAUR2FJOL2X2KO7SOLONJJLIJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LWAUR2FJOL2X2KO7SOLONJJLIJ","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":"fff9dab5f9b9f288fb01631f72275d3dda3a79bbc1244b5ac9bd4913e93c8626","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-30T13:29:35Z","title_canon_sha256":"70a74472b03bddb2c777fbf1ab9bc90c40f7106f4ca99023f3e2566a96cc41fa"},"schema_version":"1.0","source":{"id":"1705.00313","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00313","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00313v1","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00313","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"pith_short_12","alias_value":"LWAUR2FJOL2X","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LWAUR2FJOL2X2KO7","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LWAUR2FJ","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:810eca971e74bdae29d8f4690d0d7873518e82bbb2abd0fc692b46bb12c8abe9","target":"graph","created_at":"2026-05-18T00:45:20Z","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"},"paper":{"abstract_excerpt":"Given a compact Riemannian manifold $M$, we consider a warped product $\\bar M = I \\times_h M$ where $I$ is an open interval in $\\Bbb R$. For a positive function $\\psi$ defined on $\\bar M$, we generalized the arguments in \\cite{GRW2015} and \\cite{RW16}, to obtain the curvature estimates for Hessian equations $\\sigma_k(\\kappa)=\\psi(V,\\nu(V))$. We also obtain some existence results for the starshaped compact hypersurface $\\Sigma$ satisfying the above equation with various assumptions.","authors_text":"Daguang Chen, Haizhong Li, Zhizhang Wang","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-30T13:29:35Z","title":"Starshaped compact hypersurfaces with prescirbed Weingarten curvature in warped product manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00313","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:f27eccedca1c6012098c9d299659872e8180be94504385a5e17aec43487d520d","target":"record","created_at":"2026-05-18T00:45:20Z","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":"fff9dab5f9b9f288fb01631f72275d3dda3a79bbc1244b5ac9bd4913e93c8626","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-30T13:29:35Z","title_canon_sha256":"70a74472b03bddb2c777fbf1ab9bc90c40f7106f4ca99023f3e2566a96cc41fa"},"schema_version":"1.0","source":{"id":"1705.00313","kind":"arxiv","version":1}},"canonical_sha256":"5d8148e8a972f57d29df9396e6a52b4260034513cde10810ebb6ac19fc1bc241","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d8148e8a972f57d29df9396e6a52b4260034513cde10810ebb6ac19fc1bc241","first_computed_at":"2026-05-18T00:45:20.816989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:20.816989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qelpsKKFcqDtBGFt14hJlk7NuCshTIuaHwp2CQjeq9v5rya7CpI6vfjPZZ3i6fCK0m1VjDVGQSZE7zz4qvoPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:20.817715Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00313","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f27eccedca1c6012098c9d299659872e8180be94504385a5e17aec43487d520d","sha256:810eca971e74bdae29d8f4690d0d7873518e82bbb2abd0fc692b46bb12c8abe9"],"state_sha256":"04e9a32e5268e7708ea0cda9f4b5f690278627631100694bcadc592ed6c9f27b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zgk2o/HL5NvK9irUjSKMF2OMjs6Il1DNQ3yyDSm00dFGJl5wh+ekM89sEv33X46YhRKwvjDPUD7K273p6IcUBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T12:15:29.022744Z","bundle_sha256":"0bb3ed485da0f06d24faf1f28187548d0e66e5e12240220d9e67fd239e4fcb3c"}}