{"as_of":"2026-08-19T03:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e4f2e0b520b587145c085886b81d926dee13483ff76db77b0f8dcb86c4543792","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T15:04:39.421281Z","state":"measured"},{"denominator":37,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":37,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2507.17344/citation-record","integrity":"/paper/2507.17344/integrity","json":"/paper/2507.17344/citation-record.json","paper":"/paper/2507.17344"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.684892Z","title":"Al ´ ıas, D","venue":null,"work_id":"c2fda1f2-3c80-4d4a-858c-419c632e69e9","year":2013},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.340348Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:5b31a6db75f55983455d0f5cf2afd5e394b63c37af33e1551efec0d6561057f1","observation_id":"98fa197d-49a4-43a6-a81d-3baf0b126685","resolution":{"observed_at":"2026-08-06T15:04:39.687275Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.677917Z","title":"Alexsandorov, Uniqueness theorem for surfaces in the large I , Vestnik Leningrad Univ., 1956, 11: 5-17","venue":null,"work_id":"af7c31e9-0af0-4c2d-9bd2-ed04f16f16c7","year":1956},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.343184Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:8d7e52cd37e8f5caa605e21a56b6b1ae702668485e867d2b969c5654f9c88edd","observation_id":"94416a75-d088-4f8e-9449-54c82146a318","resolution":{"observed_at":"2026-08-06T15:04:39.680432Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.671407Z","title":"Andrews, Contraction of convex hypersurfaces in Riemannian spaces , Journal of Differential Geometry, 1994, 39(2): 407-431","venue":null,"work_id":"344bc4d1-b3b0-4cdc-b183-408c1711ecc4","year":1994},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.345670Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:8789ee716f28a4b1d07b4f3b23da259624e51c67252960c425a7f9cc06dd6060","observation_id":"33ab1544-08df-4f5f-a469-80f5ec4dcc40","resolution":{"observed_at":"2026-08-06T15:04:39.673923Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.665314Z","title":"Andrews, X","venue":null,"work_id":"7fcf6956-4440-43a3-8200-0dc3016eceda","year":2021},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.348425Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:bf5ce34b6ef0de7fc6cd2f30b5ecbdf706c119a0a7555e655834c57f40b46f59","observation_id":"35add6db-b757-4780-9ad0-a2fd92b84fda","resolution":{"observed_at":"2026-08-06T15:04:39.667480Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.657696Z","title":"Aquino and H.F","venue":null,"work_id":"74ea1ae6-2623-4de2-a0df-7b34543da94d","year":2014},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.350955Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:aa02a583eff51f71bac38b036b67fa84017df0f6630c257db080c88fafb7d3e8","observation_id":"5ba33766-fde8-4fec-ae47-ace83c159fb3","resolution":{"observed_at":"2026-08-06T15:04:39.659840Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.650692Z","title":"Barbosa and A.G","venue":null,"work_id":"85bebcc7-f77b-478e-a9af-54802e3caa87","year":1997},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.353195Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:0b6fe510095bb553f66e4872cb1e7b6a93bbe2abefe132c2693ab73e48860540","observation_id":"2e57a565-5469-4f90-9c7f-bdbd9d0e58d7","resolution":{"observed_at":"2026-08-06T15:04:39.652825Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.644331Z","title":"Brendle, Constant mean curvature surfaces in warped product manifolds , Publications math´ ematiques de l’IH´ES, 2013, 117(1): 247-269","venue":null,"work_id":"a1916181-984c-43e9-8c6e-5319ad3b72d5","year":2013},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.355506Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:07269a224ab2e49608753f534add211a9ee40fff5e8f342d2ec81a4c633104bc","observation_id":"0be4797e-952b-4d92-8aa1-38f3b56a10a8","resolution":{"observed_at":"2026-08-06T15:04:39.646782Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.637679Z","title":"Brendle and M","venue":null,"work_id":"40605eaf-0561-4a1f-bef6-ee2e6fe61726","year":2013},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.357827Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:815c6a07c1420d75e2385c52ddd28362e8ddf3fa008bb44775d913c8f15a1a16","observation_id":"991199ad-45b1-4236-a275-e36b671c802d","resolution":{"observed_at":"2026-08-06T15:04:39.640399Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.631486Z","title":"Brendle and G","venue":null,"work_id":"a88e5fce-d2f1-4a0a-a5cf-925aed6a0bb6","year":2017},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.359962Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:c9cd6dd8556853ced429f36b1ceb6dbfb71deb120946858f3b08dec3243d97fd","observation_id":"488420c8-cae1-4f8e-b9cf-5bbe07ffec35","resolution":{"observed_at":"2026-08-06T15:04:39.633566Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.625256Z","title":"Brendle, P.K","venue":null,"work_id":"621aa3ee-fafa-4469-b693-8197c072ac09","year":2016},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.362234Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:dc04335fab64d60c7531eeda7d55196a07d3af105c67b37c7b6672fab077a116","observation_id":"2bde2192-aaf3-4bf0-956c-ee7d90f033c0","resolution":{"observed_at":"2026-08-06T15:04:39.627525Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.617659Z","title":"Gao, Closed self-similar solutions to flows by negative powers of curvature , The Journal of Geometric Analysis, 2023, 33(12): 370","venue":null,"work_id":"b15a897f-f5f5-4981-9e0d-a5ea34486a5e","year":2023},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.364273Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:dc3482384e70ffd561b3377f182079d0e56b7967ea1fe10abacd0921114db177","observation_id":"77ce31b7-41ee-44b2-a0e0-b2bc1829d10f","resolution":{"observed_at":"2026-08-06T15:04:39.620990Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.611749Z","title":"Gao and H","venue":null,"work_id":"4a3af5ed-5a84-4f50-bde7-d69e06b62160","year":2021},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.366431Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:b99c28f01d1570bd0bdb92e439834df538996a316126f65304006541aef1d794","observation_id":"7c7f3093-3079-4a0a-9846-d1c7140ac603","resolution":{"observed_at":"2026-08-06T15:04:39.613848Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.605492Z","title":"Guan, Topics in geometric fully nonlinear equations , Lecture Notes, http://www","venue":null,"work_id":"99739edb-42db-40c4-babb-bfa445db72b3","year":2002},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.368862Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:1c6260a1eba7cc0a3b6b4758fb49128ccc25374de93436c6eb26b573dc0ebd09","observation_id":"1fbe74af-073d-4c7e-b12b-7337c4a72d04","resolution":{"observed_at":"2026-08-06T15:04:39.607939Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.599323Z","title":null,"venue":null,"work_id":"40c37a39-b7cc-47ba-b9bd-bf5ecbcd16d5","year":2019},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.370856Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:380f2a6fb7298d19bba6dd3e2adf2461ac8e5b6723eb1be6a7318cca2031b0a9","observation_id":"f3ba8d24-1c58-462b-b48c-c61e3047cfe1","resolution":{"observed_at":"2026-08-06T15:04:39.601390Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.593423Z","title":"Heintze and H","venue":null,"work_id":"cda9d0be-b67b-4428-82fa-4a4131b4b488","year":1978},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.372848Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:03531abe05bf4fceb19854775bd348c7e3a033f15c5286ad307be6a7d63ac8dd","observation_id":"12350f49-7a53-4b66-b05b-6d5f150c33ca","resolution":{"observed_at":"2026-08-06T15:04:39.595503Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.587348Z","title":null,"venue":null,"work_id":"ed56cec0-cfe9-4b59-b503-f974836b5854","year":2009},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.375009Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:0c64e03f78c3ff33168407f8c7e4e5590e18a29b26ee2173588773217a62241b","observation_id":"d7ebea3b-42d7-4ad4-9650-d84b9cac2aa5","resolution":{"observed_at":"2026-08-06T15:04:39.589429Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.581310Z","title":"Hijazi, S","venue":null,"work_id":"aa2bd4f1-2471-4f5a-ba25-06aecd462d2f","year":2001},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.376981Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:5ae52a82bc6874ee97dadb84a6b8a0df6ccfee817ef503160547f253aa115f1e","observation_id":"37505dfa-e7cf-436e-a076-320e20bbb0b1","resolution":{"observed_at":"2026-08-06T15:04:39.583480Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.575296Z","title":null,"venue":null,"work_id":"4a74004c-6082-47a5-bc20-d69d357b92c1","year":2022},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.379158Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:0bbdd4ab1cb3b10791cd231029e40330f6e1c1196c9447e126afbcef8edab1b8","observation_id":"480b9de6-744d-44a3-a6b3-dd808e318887","resolution":{"observed_at":"2026-08-06T15:04:39.577451Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.569271Z","title":null,"venue":null,"work_id":"06a47780-0dde-4627-b09e-3f0ddaaf2e5b","year":2024},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.381281Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:37637d8ce10f9fb955445686c56e03681b877e06eac7d2e36ea27a7130930eb8","observation_id":"9c61177b-1e40-435e-8f83-88200e14d2b8","resolution":{"observed_at":"2026-08-06T15:04:39.571350Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.562480Z","title":"Koh, A characterization of round spheres, Proceedings of the American Mathematical Society, 1998, 126(12): 3657-3660","venue":null,"work_id":"3d089121-7112-486d-abf1-731e3993d6da","year":1998},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.383452Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:806b8296e3a7f6f56d5c5c0f2fd7462458305a3180e25f185308f6d79358cda8","observation_id":"728dac98-6599-4718-b7fd-d8cda8e50ed0","resolution":{"observed_at":"2026-08-06T15:04:39.565262Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.556061Z","title":"Koh, Sphere theorem by means of the ratio of mean curvature functions, Glasgow Mathematical Journal, 2000, 42(1): 91-95","venue":null,"work_id":"f5981db3-c971-45fe-bd50-2e60dc82e870","year":2000},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.385480Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:9994a947ee243b8adae620de3c7eb5f25e1694779b34ed6c8d21cc6b237acbba","observation_id":"ada14f7b-2e28-42f4-b8b4-4442cc49eb49","resolution":{"observed_at":"2026-08-06T15:04:39.558423Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.549620Z","title":"Kwong, H","venue":null,"work_id":"d0d4ea69-94eb-40d6-a22b-3c54f198f898","year":2018},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.387500Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:cb8b49be70c066361e01ed991665718209eac43f4d1b5092a386892dff86c2e4","observation_id":"a035555a-bed5-4fac-9699-0af4ad95944a","resolution":{"observed_at":"2026-08-06T15:04:39.551755Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.543603Z","title":null,"venue":null,"work_id":"0791653b-96a3-41cc-8c4b-0e3d0d5779f6","year":2014},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.389441Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:54716ce1cb3eb69fb76c28442d76f9f8d9d5a7a6e8969c614a7c9438a1bb96ca","observation_id":"7504fe69-fbcc-4d0d-84e3-323d424d4053","resolution":{"observed_at":"2026-08-06T15:04:39.545651Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.15109","last_updated":"2025-04-21T14:02:09Z","snapshot_observed_at":"2026-08-16T11:30:56.431922Z","submitted_at":"2025-04-21T14:02:09Z","title":"New Heintze-Karcher type inequalities in sub-static warped product manifolds","version":1},"cited_work":{"arxiv_id":"2504.15109","doi":null,"metadata_source":"pith","pith_arxiv_id":"2504.15109","snapshot_observed_at":"2026-08-06T15:04:39.462493Z","title":"New Heintze-Karcher type inequalities in sub-static warped product manifolds","venue":"math.DG","work_id":"308361a3-552b-46ed-94a6-053272d0ff6f","year":2025},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.391610Z"},"links":{"cited_paper":"/paper/2504.15109","citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:70524da585ad5276023eac26b98b3c28371589e3216a32a41d9c5840d5bf3f24","observation_id":"002742d1-8c2e-459d-92dc-c34635953d87","resolution":{"observed_at":"2026-08-06T15:04:39.465223Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2211.06875","last_updated":"2022-11-13T11:06:04Z","snapshot_observed_at":"2026-08-16T16:16:37.055286Z","submitted_at":"2022-11-13T11:06:04Z","title":"Hyperbolic $p$-sum and Horospherical $p$-Brunn-Minkowski theory in hyperbolic space","version":1},"cited_work":{"arxiv_id":"2211.06875","doi":null,"metadata_source":"pith","pith_arxiv_id":"2211.06875","snapshot_observed_at":"2026-08-06T15:04:39.452888Z","title":"Hyperbolic $p$-sum and Horospherical $p$-Brunn-Minkowski theory in hyperbolic space","venue":"math.MG","work_id":"910c7947-84c6-43ec-8f1b-1dc8c7149010","year":2022},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.394520Z"},"links":{"cited_paper":"/paper/2211.06875","citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:d7b5c3439e0394884cebe6c73637c6734217a8649f08da0d68ec9c8c3c3cd993","observation_id":"41bcea31-8d40-493f-a0b9-2cbe46caf15e","resolution":{"observed_at":"2026-08-06T15:04:39.455789Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.537317Z","title":"Li and C","venue":null,"work_id":"94abe48b-4ba1-48a7-becf-67db2f9d40dc","year":2019},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.397083Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:1bc061385c3964078a1b69d3e744bef240558d2691573c691ba43e67dbedfde2","observation_id":"2ed68154-415c-493f-abd5-c62ac756148c","resolution":{"observed_at":"2026-08-06T15:04:39.539514Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.531078Z","title":"Montiel, Uniqueness of spacelike hypersurfaces of constant mean curvature in foliated spacetimes, Mathematische Annalen, 1999, 314(3): 529-553","venue":null,"work_id":"73e31c6e-acab-4a4f-a6c3-a439b8f37235","year":1999},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.399549Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:07abaec2ffcfaad5934c2102b18e9d18ec80f36a83af018b70d9b92fc0d0d08e","observation_id":"4d675910-a071-4499-98cf-1ec007682a79","resolution":{"observed_at":"2026-08-06T15:04:39.533315Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.524995Z","title":"Montiel and A","venue":null,"work_id":"9163065f-1d27-4eb9-ac95-0af7da508121","year":1991},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.401386Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:bdba9b5151f6d0ccb2fd9e3ce94b23290f8b43fae91a12c16615d509cd5fa1a4","observation_id":"1375625c-52a2-4189-a8d9-e28e807a5504","resolution":{"observed_at":"2026-08-06T15:04:39.527104Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.518539Z","title":"Reilly, On the Hessian of a function and the curvatures of its graph , Michigan Mathematical Journal, 1974, 20(4): 373-383","venue":null,"work_id":"ac915813-cbc1-476e-b10e-603c75860a99","year":1974},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.403698Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:03260a6a5dad2417eb8330ed6b1cc62e82be89926bf0f9fbe9e2bc72f79a4dae","observation_id":"d4da99d7-adcd-458e-a82a-f1efeb4cfd87","resolution":{"observed_at":"2026-08-06T15:04:39.520816Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.511951Z","title":"Reilly, Applications of the Hessian operator in a Riemannian manifold , Indiana University Mathematics Journal, 1977, 26(3): 459-472","venue":null,"work_id":"3a3a6a67-9ae1-433b-99d2-5ac5c5871fd7","year":1977},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.405683Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:073d727cb5a81bb1c0ca14111042e4f218e73992fbf8af796279eded86c8629e","observation_id":"af4c5be6-9c2d-4eb7-8a42-008cd1162f35","resolution":{"observed_at":"2026-08-06T15:04:39.514377Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.505153Z","title":"Ros, Compact hypersurfaces with constant scalar curvature and a congruence theorem , Journal of Differential Geometry, 1988, 27(2): 215-220","venue":null,"work_id":"e13ad8f9-8ad7-470a-a94c-865231b9e68c","year":1988},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.407989Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:3d3502054e2a5e3a1674e74429b74e8119425574c1395756e480506f39c66add","observation_id":"1fb25bca-c55c-47c0-8c3b-f942c73127e8","resolution":{"observed_at":"2026-08-06T15:04:39.507854Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.498480Z","title":"Ros, Compact hypersurfaces with constant higher order mean curvatures , Revista Matem´ atica Iberoamericana, 1987, 3(3): 447-453","venue":null,"work_id":"f9b11ec3-341d-46b7-aa86-da2dc15f827a","year":1987},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.409948Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:953dc5abbaebef82fba0d6d38b7c7703ffbe41726eaec65b225f7f913da6166c","observation_id":"352050de-7e5e-4eaa-8097-3a6138140a13","resolution":{"observed_at":"2026-08-06T15:04:39.500843Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.491641Z","title":"Stong, Some characterizations of Riemann n-spheres, Proceedings of the American Mathemat- ical Society, 1960, 11(6): 945-951","venue":null,"work_id":"c3fb7c78-25c7-41bb-a2a4-3b01e88c6e7d","year":1960},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.411942Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:e3c482a6430916bf8d7e37c68aa37b7f187e151fd971d8f04d8de6bd1fea3049","observation_id":"5eab8498-cad8-45b1-b039-933011f2c333","resolution":{"observed_at":"2026-08-06T15:04:39.494113Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.04622","last_updated":"2024-02-22T15:51:25Z","snapshot_observed_at":"2026-08-19T01:44:41.725157Z","submitted_at":"2024-02-07T07:10:18Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in hyperbolic space","version":2},"cited_work":{"arxiv_id":"2402.04622","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.04622","snapshot_observed_at":"2026-08-06T15:04:39.440929Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in hyperbolic space","venue":"math.DG","work_id":"af15924c-e272-40b8-a2c2-1b37142da33b","year":2024},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.414121Z"},"links":{"cited_paper":"/paper/2402.04622","citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:392ad4ca346881b15938aef88df6af952801dc913b13a19de9c066a42db75ed8","observation_id":"7187e0dc-6762-4291-b95b-f585b943133e","resolution":{"observed_at":"2026-08-06T15:04:39.445590Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.484541Z","title":null,"venue":null,"work_id":"d7ac01c0-17a0-40df-812d-4fd63c998afa","year":2023},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.416739Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:cbf8afdc7bcc0c18485a95f63a9c9b6bce8c7b6c51fdc5ba52d1db1e5f42cdad","observation_id":"1b76ac3f-4086-4c79-9a1e-1d28a1a43ce5","resolution":{"observed_at":"2026-08-06T15:04:39.487076Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.477550Z","title":"Wu, A new characterization of geodesic spheres in the hyperbolic space , Proceedings of the American Mathematical Society, 2016, 144(7): 3077-3084","venue":null,"work_id":"363763b7-57b8-4dc8-a504-fc3e968855ff","year":2016},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.419073Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:dd79db6ca451056b509eb518286ff71419e70d2815781bb854d5de599ce3db81","observation_id":"d36917f6-8509-40ba-8678-23b808e32547","resolution":{"observed_at":"2026-08-06T15:04:39.480076Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:04:39.470176Z","title":"Wu and C","venue":null,"work_id":"e00b670a-affe-4911-a7df-8c0e36970a78","year":2014},"citing_paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T15:04:39.421281Z"},"links":{"citing_paper":"/paper/2507.17344"},"observation_digest":"sha256:be1f04cd5028d654eda7bb250ef2e79e19c3313749bd264ceea17be0cca129aa","observation_id":"ad1ba250-6fde-4e21-bde1-922a8e5ebe78","resolution":{"observed_at":"2026-08-06T15:04:39.473001Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.17344","last_updated":"2025-07-23T09:16:29Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-08-06T14:47:46.271987Z","submitted_at":"2025-07-23T09:16:29Z","title":"On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":3,"verified_fuzzy":28},"total_outbound_references":37},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2507.17344."}