{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ON2VULP2T4CA4W5ZWU6B2YM4UT","short_pith_number":"pith:ON2VULP2","canonical_record":{"source":{"id":"2504.15109","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-04-21T14:02:09Z","cross_cats_sorted":[],"title_canon_sha256":"14ad7da3dc708b862f3d2adf40dc3118b796f8a353bbeafdb2b7bcb63fc8ec6c","abstract_canon_sha256":"e930ec80b2e7ef3463197a0f714b31862de60947719088548843387f4138b6c6"},"schema_version":"1.0"},"canonical_sha256":"73755a2dfa9f040e5bb9b53c1d619ca4d33357a7b95da104cba7452607110807","source":{"kind":"arxiv","id":"2504.15109","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.15109","created_at":"2026-07-05T10:51:56Z"},{"alias_kind":"arxiv_version","alias_value":"2504.15109v1","created_at":"2026-07-05T10:51:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.15109","created_at":"2026-07-05T10:51:56Z"},{"alias_kind":"pith_short_12","alias_value":"ON2VULP2T4CA","created_at":"2026-07-05T10:51:56Z"},{"alias_kind":"pith_short_16","alias_value":"ON2VULP2T4CA4W5Z","created_at":"2026-07-05T10:51:56Z"},{"alias_kind":"pith_short_8","alias_value":"ON2VULP2","created_at":"2026-07-05T10:51:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ON2VULP2T4CA4W5ZWU6B2YM4UT","target":"record","payload":{"canonical_record":{"source":{"id":"2504.15109","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-04-21T14:02:09Z","cross_cats_sorted":[],"title_canon_sha256":"14ad7da3dc708b862f3d2adf40dc3118b796f8a353bbeafdb2b7bcb63fc8ec6c","abstract_canon_sha256":"e930ec80b2e7ef3463197a0f714b31862de60947719088548843387f4138b6c6"},"schema_version":"1.0"},"canonical_sha256":"73755a2dfa9f040e5bb9b53c1d619ca4d33357a7b95da104cba7452607110807","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:51:56.419733Z","signature_b64":"9O5Rhkz0LWduFPmnGecki2WwZwN6JjTG1Mcs0sSDcJIwffX/sN3UXvp5xGA7aeg4fbgIuJv9E0OO8eMSW7GQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73755a2dfa9f040e5bb9b53c1d619ca4d33357a7b95da104cba7452607110807","last_reissued_at":"2026-07-05T10:51:56.419273Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:51:56.419273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.15109","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":"2026-07-05T10:51:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zz59Xsns+fg+9YYwaptJW/Fao+nuwgU9pkaTOOWePlIabeq98ragSd5JAQlFQU+igQRIvtQzLprE/QcTN6XOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:54:27.587613Z"},"content_sha256":"0901e7cb4b7c650367f87f9a5ef4e85820835b826c5b19fa702450a5f5fb2b27","schema_version":"1.0","event_id":"sha256:0901e7cb4b7c650367f87f9a5ef4e85820835b826c5b19fa702450a5f5fb2b27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ON2VULP2T4CA4W5ZWU6B2YM4UT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Heintze-Karcher type inequalities in sub-static warped product manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Botong Xu, Haizhong Li, Yong Wei","submitted_at":"2025-04-21T14:02:09Z","abstract_excerpt":"In this paper, we prove Heintze-Karcher type inequalities involving the shifted mean curvature for smooth bounded domains in certain sub-static warped product manifolds. In particular, we prove a Heintze-Karcher-type inequality for non mean-convex domains in the hyperbolic space. As applications, we obtain uniqueness results for hypersurfaces satisfying a class of curvature equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.15109","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/2504.15109/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":"2026-07-05T10:51:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bNtS8m9uWqA4KFxFNaNCO4ssgJVHtmHMGrBCb+EcYoeBdiolnvntyyKi8ZWESFooXyf/mkCM/nFxt0FAmsRwBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:54:27.588101Z"},"content_sha256":"580bd705b35c6d9e618bd55f7052f826eac29d857ebe144a4cd63ed0c6ba4f17","schema_version":"1.0","event_id":"sha256:580bd705b35c6d9e618bd55f7052f826eac29d857ebe144a4cd63ed0c6ba4f17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ON2VULP2T4CA4W5ZWU6B2YM4UT/bundle.json","state_url":"https://pith.science/pith/ON2VULP2T4CA4W5ZWU6B2YM4UT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ON2VULP2T4CA4W5ZWU6B2YM4UT/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":"2026-08-14T08:54:27Z","links":{"resolver":"https://pith.science/pith/ON2VULP2T4CA4W5ZWU6B2YM4UT","bundle":"https://pith.science/pith/ON2VULP2T4CA4W5ZWU6B2YM4UT/bundle.json","state":"https://pith.science/pith/ON2VULP2T4CA4W5ZWU6B2YM4UT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ON2VULP2T4CA4W5ZWU6B2YM4UT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ON2VULP2T4CA4W5ZWU6B2YM4UT","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":"e930ec80b2e7ef3463197a0f714b31862de60947719088548843387f4138b6c6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-04-21T14:02:09Z","title_canon_sha256":"14ad7da3dc708b862f3d2adf40dc3118b796f8a353bbeafdb2b7bcb63fc8ec6c"},"schema_version":"1.0","source":{"id":"2504.15109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.15109","created_at":"2026-07-05T10:51:56Z"},{"alias_kind":"arxiv_version","alias_value":"2504.15109v1","created_at":"2026-07-05T10:51:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.15109","created_at":"2026-07-05T10:51:56Z"},{"alias_kind":"pith_short_12","alias_value":"ON2VULP2T4CA","created_at":"2026-07-05T10:51:56Z"},{"alias_kind":"pith_short_16","alias_value":"ON2VULP2T4CA4W5Z","created_at":"2026-07-05T10:51:56Z"},{"alias_kind":"pith_short_8","alias_value":"ON2VULP2","created_at":"2026-07-05T10:51:56Z"}],"graph_snapshots":[{"event_id":"sha256:580bd705b35c6d9e618bd55f7052f826eac29d857ebe144a4cd63ed0c6ba4f17","target":"graph","created_at":"2026-07-05T10:51:56Z","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/2504.15109/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove Heintze-Karcher type inequalities involving the shifted mean curvature for smooth bounded domains in certain sub-static warped product manifolds. In particular, we prove a Heintze-Karcher-type inequality for non mean-convex domains in the hyperbolic space. As applications, we obtain uniqueness results for hypersurfaces satisfying a class of curvature equations.","authors_text":"Botong Xu, Haizhong Li, Yong Wei","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-04-21T14:02:09Z","title":"New Heintze-Karcher type inequalities in sub-static warped product manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.15109","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":"sha256:0901e7cb4b7c650367f87f9a5ef4e85820835b826c5b19fa702450a5f5fb2b27","target":"record","created_at":"2026-07-05T10:51:56Z","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":"e930ec80b2e7ef3463197a0f714b31862de60947719088548843387f4138b6c6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-04-21T14:02:09Z","title_canon_sha256":"14ad7da3dc708b862f3d2adf40dc3118b796f8a353bbeafdb2b7bcb63fc8ec6c"},"schema_version":"1.0","source":{"id":"2504.15109","kind":"arxiv","version":1}},"canonical_sha256":"73755a2dfa9f040e5bb9b53c1d619ca4d33357a7b95da104cba7452607110807","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73755a2dfa9f040e5bb9b53c1d619ca4d33357a7b95da104cba7452607110807","first_computed_at":"2026-07-05T10:51:56.419273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:51:56.419273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9O5Rhkz0LWduFPmnGecki2WwZwN6JjTG1Mcs0sSDcJIwffX/sN3UXvp5xGA7aeg4fbgIuJv9E0OO8eMSW7GQDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:51:56.419733Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.15109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0901e7cb4b7c650367f87f9a5ef4e85820835b826c5b19fa702450a5f5fb2b27","sha256:580bd705b35c6d9e618bd55f7052f826eac29d857ebe144a4cd63ed0c6ba4f17"],"state_sha256":"6b41628847e2f50a24b6eca131be8591f26c6bc71228f5d4f3a97b4b78b0530a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1lFPlGQQWKMg6yhVdjobLo4SSTTDzyvR8A8ayNHV7lApj74CArpUYZEcm7Va7fyLs2v+NN3Kfs7K96xhr3XyAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T08:54:27.593134Z","bundle_sha256":"e9880fd5b61af0db5c2ca51ee2009c31c70ee1739fb8e7db49f2f0318e8d54ce"}}