{"as_of":"2026-08-08T13:38:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8d2316d57e85516dbb5ccba11cb397eee4abb665ef5bc33ef4534d3d6c40e339","coverage":[{"denominator":53,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":53,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T04:26:48.649152Z","state":"measured"},{"denominator":53,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":53,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2506.10809/citation-record","integrity":"/paper/2506.10809/integrity","json":"/paper/2506.10809/citation-record.json","paper":"/paper/2506.10809"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:26:54.093310Z","title":"Alexander and Richard L","venue":null,"work_id":"1bada656-b139-4487-92d7-194e8921bb60","year":1998},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:45.624436Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:ed3b28f442ea42e36328d55eef36d77387524ef534ea42626fbd5378c30116b7","observation_id":"dabcd6bc-48a8-4a81-bcb1-36c9b31f9b4f","resolution":{"observed_at":"2026-08-07T04:26:54.096002Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:54.085274Z","title":"Alexander and Richard L","venue":null,"work_id":"309ad1c1-946d-43ea-be38-7674271efb08","year":2004},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:45.662953Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:bfd506c96a5c5b34f49fcdcf3bda95aab47e3dbbd592d2c76823a4daed87c44d","observation_id":"fe127d9d-1ac8-4893-8df5-7ae998edf769","resolution":{"observed_at":"2026-08-07T04:26:54.088027Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:54.077439Z","title":"Alexander and Richard L","venue":null,"work_id":"3e7af215-95a7-47ee-88ad-8f8a30a91af8","year":2005},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:45.754406Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:4285eabbb71d063822e29e64b719c9171f23d160c406521395527f43eb11da65","observation_id":"16f1e600-e383-4899-a582-de31bdc5c699","resolution":{"observed_at":"2026-08-07T04:26:54.080439Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:54.068438Z","title":"Alexander and Richard L","venue":null,"work_id":"71e3c484-7802-4f45-8dd6-a364d30c38b9","year":2016},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:45.807064Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:fe5f560edf104d90054fdf6027afa1efca138b18bbfc5ee2f6354ecc55d5706c","observation_id":"23de0c3e-0517-4ea9-a42d-2c7d9e81219d","resolution":{"observed_at":"2026-08-07T04:26:54.071751Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:54.060927Z","title":"Gradient flows in metric spaces and in the space of probability measures","venue":null,"work_id":"56978556-2a1d-4997-9070-6a92fbcae224","year":2008},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:45.885018Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:502f69db79ad3529123c1075527248aece68be623b42cb615ac5514b351cc3f3","observation_id":"33c9d99c-db0a-49af-9c97-05e48feb1e5a","resolution":{"observed_at":"2026-08-07T04:26:54.063594Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:54.053597Z","title":"Metric measure spaces with Rie- mannian Ricci curvature bounded from below","venue":null,"work_id":"268a44d4-047f-4cbf-91bc-7af06b9ad083","year":2014},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:45.947126Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:1f76a046224695e2f6a79360193fc7516017c513e8fd7d21df9c8ccb77779c88","observation_id":"ffe08a24-e8b5-4dab-b8fc-d674e091136e","resolution":{"observed_at":"2026-08-07T04:26:54.056130Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:54.046123Z","title":"Bakry- ´Emery curvature- dimension condition and Riemannian Ricci curvature bounds","venue":null,"work_id":"899c935c-e980-42e3-b67d-d16c286621c1","year":2015},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.023713Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:ebe0cec435a77613cbe11e6c5c0ec5d76f38041c411fc541fb4c5f2b58ceede2","observation_id":"a68b03b3-3772-471f-91c6-21352dbb49f7","resolution":{"observed_at":"2026-08-07T04:26:54.048657Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:54.038888Z","title":"Nonlinear Diffusion Equa- tions and Curvature Conditions in Metric Measure Spaces","venue":null,"work_id":"c97470db-ec6f-44f2-ae4a-5cb1fc4d1f1f","year":2019},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.100084Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:f03b87906dfd1a49bad5463b98521f76947b8f587f93b7a326ab05b55413e91c","observation_id":"733f28be-49d9-4c74-be90-0d7a4829dad5","resolution":{"observed_at":"2026-08-07T04:26:54.041378Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:54.031552Z","title":"Anderson","venue":null,"work_id":"c9063347-3005-47de-8ce8-c8583580e5d4","year":1990},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.151816Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:9c5c54594ea9b4ffc0fa961277f0a7d9b1427cf9d4cb976c010604966bea2732","observation_id":"344fa5fa-8434-43b6-a19b-2ff8dbed53f5","resolution":{"observed_at":"2026-08-07T04:26:54.033855Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:54.024148Z","title":"Localization and tensorization properties of the curvature-dimension condition for metric measure spaces","venue":null,"work_id":"4b87b107-072a-40ab-8b18-109a353da02b","year":2010},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.242501Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:81040a82979a1408d53431cb3a95efea617acf00360c2f2456470df77d64eb59","observation_id":"f69f4e01-d947-4f38-b3e5-73b794abc684","resolution":{"observed_at":"2026-08-07T04:26:54.026768Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:54.016050Z","title":"A course in metric geometry , vol- ume 33 of Graduate Studies in Mathematics","venue":null,"work_id":"1f1a128a-29c6-4ae6-b82c-d022866485fb","year":2001},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.282624Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:53468b6a46ed523f4b5cd6d5b0eb17b4665a31a267f43c423078d100d9e7c6c2","observation_id":"d959be70-ccd4-4961-9a2a-665f5ee2a725","resolution":{"observed_at":"2026-08-07T04:26:54.018911Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:26:46.359008Z","title":"Generalized cones admit- ting a curvature-dimension condition, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.359008Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:17f960ae0c9267089d3df8db33d558161b84cff46ff72c21fc1d814d5d6f331a","observation_id":"964d553c-33a5-4b41-aaf3-45ce83b7cfa7","resolution":{"observed_at":"2026-08-07T04:26:46.359008Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:26:54.004003Z","title":"The globalization theorem for the curvature- dimension condition","venue":null,"work_id":"f0f75f41-8544-47e5-8810-038ff4c0fd46","year":2021},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.424101Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:4ffbe449e34fc0baf06fdf1577edbf0514de0a6ce6240d28a5b6b911c21ada14","observation_id":"6f0bb31f-2fd1-4ab4-a9cb-ed4ee895e9c5","resolution":{"observed_at":"2026-08-07T04:26:54.006545Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:26:46.470224Z","title":"Scalar and mean curvature comparison via the Dirac operator","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.470224Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:cd1ab880b0e0afd9e2eb85ae551a0fe44ccee3453d692730beeaa378a66bc253","observation_id":"92c6e80d-d4ca-4cb1-91e2-1af702590357","resolution":{"observed_at":"2026-08-07T04:26:46.470224Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:26:53.991644Z","title":"Differentiability of Lipschitz functions on metric measure spaces","venue":null,"work_id":"fb81d22e-6733-4f8d-a406-2da1d2247251","year":1999},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.540091Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:c5510092da24d7687c9150ae7510ff47f9e8d98fe8100ba429663181585ec252","observation_id":"cdbb297c-575b-462a-b5ff-e52ae07b37d2","resolution":{"observed_at":"2026-08-07T04:26:53.994118Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:26:46.603233Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.603233Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:c63fc6093f7def8ca51cc31aaeded6f093987f78d69ea779466d8cfadcb04bd0","observation_id":"d32c1c74-2b6c-4b33-b8df-c5eb03ec9351","resolution":{"observed_at":"2026-08-07T04:26:46.603233Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:26:53.979847Z","title":null,"venue":null,"work_id":"99c9b1ee-67fa-43f3-b849-efb755781184","year":1997},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.691333Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:3ff736bf4d3466ddcbfa9d80e4917c08ecaf6ace88a07db24999f866ee01b53a","observation_id":"bc7a3d01-c18e-41ba-8919-5f678c75f969","resolution":{"observed_at":"2026-08-07T04:26:53.982134Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2112.09353","last_updated":"2022-01-20T08:44:34Z","snapshot_observed_at":"2026-08-07T21:57:13.158535Z","submitted_at":"2021-12-17T07:10:50Z","title":"Almost volume cone implies almost metric cone for annuluses centered at a compact set in $RCD(K, N)$-spaces","version":3},"cited_work":{"arxiv_id":"2112.09353","doi":null,"metadata_source":"pith","pith_arxiv_id":"2112.09353","snapshot_observed_at":"2026-08-07T04:26:48.995233Z","title":"Almost volume cone implies almost metric cone for annuluses centered at a compact set in $RCD(K, N)$-spaces","venue":"math.DG","work_id":"76743c26-d717-4897-831c-2fe933c289fe","year":2021},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.760871Z"},"links":{"cited_paper":"/paper/2112.09353","citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:62975454eb36f38b023df8f3e7dab0694988ad6706ccc5c4218b30658cf058a1","observation_id":"4c42c6a0-8e93-40fb-bad5-c7ed2cbb438d","resolution":{"observed_at":"2026-08-07T04:26:49.066346Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:53.972609Z","title":"Characterization of tangent cones of non- collapsed limits with lower Ricci bounds and applications","venue":null,"work_id":"780eed70-600e-40c7-a19a-16d344a7421c","year":2013},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.815110Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:a0d3a49159691231d90938e88c8e02d5c75dea0798b8a7a17f5453386cdf76b4","observation_id":"449b1836-8c0f-44e8-a3b0-736510029a33","resolution":{"observed_at":"2026-08-07T04:26:53.975361Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:53.965586Z","title":"Maximal volume entropy rigidity for RCD∗(−(N − 1), N) spaces","venue":null,"work_id":"56033905-dc73-4200-87c2-516092d133c5","year":2021},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.915767Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:d31152d381be1a731451e3753eb79766496b00a53b7e4950b8531dfc650867ea","observation_id":"3742a366-afb6-428e-b569-bb8721b3cf30","resolution":{"observed_at":"2026-08-07T04:26:53.968285Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:53.957831Z","title":"From volume cone to metric cone in the non- smooth setting","venue":null,"work_id":"b17f8f56-3fe2-48c5-8dfe-0053157c3345","year":2016},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:46.969575Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:32f9958758a8fcdd599b33260f1401ce28be6a632a021e85ec3843f9fae25107","observation_id":"d092f540-4309-44d7-b50f-d8bb4983c859","resolution":{"observed_at":"2026-08-07T04:26:53.960869Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:53.950528Z","title":"H¨ older continuity of tangent cones in RCD(K, N) spaces and applications to nonbranching","venue":null,"work_id":"567ac8c3-a53b-461c-b890-1ed8dcbabebc","year":2025},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.037204Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:3c8bf6eb81732ffc7472a3ba2a21ac9b2d6a3dbb8e83912a3307294357022916","observation_id":"7cb06e50-17a2-4bf2-a5c8-f59b8d462123","resolution":{"observed_at":"2026-08-07T04:26:53.952995Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:53.861347Z","title":"On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces","venue":null,"work_id":"e872e5f7-e555-4a2b-ab3f-c96b85658e59","year":2015},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.091861Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:0625f98d7add634ae84b13ef17b192c58c9499eb3418db77708408d556a72c9c","observation_id":"aadcb108-3885-449e-b4f8-d4cc9db93fc2","resolution":{"observed_at":"2026-08-07T04:26:53.866905Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1302.5555","last_updated":"2026-04-29T10:28:05Z","snapshot_observed_at":"2026-08-07T21:18:03.665699Z","submitted_at":"2013-02-22T11:28:54Z","title":"The splitting theorem in non-smooth context","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1302.5555","snapshot_observed_at":"2026-08-07T04:26:47.127428Z","title":"The splitting theorem in non-smooth context","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.127428Z"},"links":{"cited_paper":"/paper/1302.5555","citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:72ab9373909bd3a49447416ffded2ddc070dead69dd6491330700b37c00aeb3e","observation_id":"5ea40292-159e-41d4-a85a-01e23d8c6546","resolution":{"observed_at":"2026-08-07T04:26:47.127428Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:26:53.687166Z","title":"An overview of the proof of the splitting theorem in spaces with non- negative Ricci curvature","venue":null,"work_id":"d9c39407-1051-4d02-96d3-b4f68b929436","year":2014},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.195069Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:6dd30f213750dd646ccbadd2bf9e0f5c70ccf279642aa579251a911201ea5dd6","observation_id":"44910695-dabc-47ef-9d6e-0ae36da65044","resolution":{"observed_at":"2026-08-07T04:26:53.794136Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:53.506165Z","title":"On the differential structure of metric measure spaces and applications","venue":null,"work_id":"c9826ebe-246a-4619-8440-c1ead8f8f50a","year":2015},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.243079Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:17a0bccaa6b028463909a79bb39e5ccbe4f45f9c794b2acf1fbf6ee188469a95","observation_id":"a8fc2a66-4cc7-46e6-990a-a201ce78bce5","resolution":{"observed_at":"2026-08-07T04:26:53.619449Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:53.469878Z","title":"Nonsmooth differential geometry—an approach tailored for spaces with Ricci curvature bounded from below","venue":null,"work_id":"8869969e-9d53-4d8f-b47a-aecac8d82ac1","year":2018},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.279521Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:5b3c00d7599e54a6fa40ca41e7fcb5f3692427e0c87d341dadd88ee789e24f97","observation_id":"a0f119b3-2df3-49e9-b9ab-0822c1033ce3","resolution":{"observed_at":"2026-08-07T04:26:53.482786Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2306.14604","last_updated":"2023-06-26T11:27:55Z","snapshot_observed_at":"2026-08-08T05:45:22.080002Z","submitted_at":"2023-06-26T11:27:55Z","title":"De Giorgi and Gromov working together","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.14604","snapshot_observed_at":"2026-08-07T04:26:47.345826Z","title":"De Giorgi and Gromov working together","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.345826Z"},"links":{"cited_paper":"/paper/2306.14604","citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:e9c5c2a80af61a1f71480f1e4de89602af62e19f462270705c68092231e24be4","observation_id":"3af4633b-bba9-4547-b6ba-aba2e7adbc50","resolution":{"observed_at":"2026-08-07T04:26:47.345826Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:26:53.266871Z","title":"Sobolev spaces on warped products","venue":null,"work_id":"80030279-1e7e-4d37-b8b3-099cc7884812","year":2018},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.388170Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:cc494852baad07d49f4866a2e176f56dc9dc54193173c1fd914d4fa36ee4a021","observation_id":"38001d86-8993-4623-9087-7982ad32d7af","resolution":{"observed_at":"2026-08-07T04:26:53.381833Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:53.083953Z","title":"Heat flow on Alexandrov spaces","venue":null,"work_id":"bbf393a2-8b1f-48c6-9c52-936e08475c45","year":2013},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.420341Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:449ff77c1a3d93573bf8bc660954a94cab72487514f4955561d1be8d4dd9ddbb","observation_id":"db3c206d-19c2-4d95-ade5-6ebaa4cb2678","resolution":{"observed_at":"2026-08-07T04:26:53.207820Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.06252","last_updated":"2023-12-11T09:49:17Z","snapshot_observed_at":"2026-07-06T16:59:44.172587Z","submitted_at":"2023-12-11T09:49:17Z","title":"A general splitting principle on RCD spaces and applications to spaces with positive spectrum","version":1},"cited_work":{"arxiv_id":"2312.06252","doi":null,"metadata_source":"pith","pith_arxiv_id":"2312.06252","snapshot_observed_at":"2026-08-07T04:26:48.850856Z","title":"A general splitting principle on RCD spaces and applications to spaces with positive spectrum","venue":"math.MG","work_id":"e41dcd8d-96e2-49a0-b119-2e9231ab68f3","year":2023},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.478150Z"},"links":{"cited_paper":"/paper/2312.06252","citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:65be1800a181b5a9134f580c19e35d3cffed42522d1275bc137e16f6a90259a0","observation_id":"c90bc458-18e0-4c08-8510-17fdb7ef5648","resolution":{"observed_at":"2026-08-07T04:26:48.933559Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:52.959032Z","title":"Convergence of pointed non- compact metric measure spaces and stability of Ricci curvature bounds and heat flows","venue":null,"work_id":"2c52a4f0-582c-4769-8448-6d08280d8f0e","year":2015},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.525508Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:cbc8d50e9d95af398ede0de68cc90bee0872e8900126f1ecc448c8f3c777b8ef","observation_id":"6a83b0e1-c017-4bdd-9a3b-2e4146e3bc1e","resolution":{"observed_at":"2026-08-07T04:26:53.034128Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:52.812796Z","title":"Sobolev met Poincar´ e","venue":null,"work_id":"5405e209-3f4a-4da9-88a9-8be3916c5a14","year":2000},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.559685Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:e67753f13ffeb81d19833b5090d5da7a36de92db9ac49343b65e87571e717b89","observation_id":"b825b1f5-7c03-4957-bb1d-e0fe31070266","resolution":{"observed_at":"2026-08-07T04:26:52.850543Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:52.641869Z","title":"Lower Ricci curvature and nonex- istence of manifold structure","venue":null,"work_id":"a0cb6c81-fe11-4077-875c-b08e3bb70ff7","year":2025},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.602917Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:6f382e5604439dedcc379552d5fc71030031c2b38bda1e38f24d2eb292470286","observation_id":"11f9f1d4-a609-4874-b2e4-a7235b35049b","resolution":{"observed_at":"2026-08-07T04:26:52.709676Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:52.475534Z","title":"CD meets CAT","venue":null,"work_id":"d4975fbf-5914-4cd0-a12f-716bc292392d","year":2020},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.668494Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:18e174fae281d51f426bc53be45eda665d0037576c72aa2caa96d9c38dedb952","observation_id":"a543fb9a-f5bd-4705-b617-5c7b97ef58bc","resolution":{"observed_at":"2026-08-07T04:26:52.587947Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:52.310259Z","title":"Ricci curvature bounds for warped products","venue":null,"work_id":"fbfc45c3-94d0-4211-bef5-5a41eec00d2e","year":2013},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.727642Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:66b3145baa6bb24d401e21c3b8bd7d90082ac50cf05c0b9b74c75fada35fbaf3","observation_id":"7db17550-822e-4cf0-b610-7ccc872105b4","resolution":{"observed_at":"2026-08-07T04:26:52.434886Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:52.145953Z","title":"Cones over metric measure spaces and the maximal diameter theorem","venue":null,"work_id":"be478088-9060-4aa3-9cb9-36226a6bb11d","year":2015},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.776670Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:4e1a931462f40eea3324acbddf451c61a8b465100d28668fe35af93c7f69baa8","observation_id":"265244c6-a38e-4903-877a-0ed9ccd7bcdd","resolution":{"observed_at":"2026-08-07T04:26:52.235178Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:52.029625Z","title":"Obata’s rigidity theorem for metric measure spaces","venue":null,"work_id":"0902851c-8e64-44af-bdf8-41dc3a36f7ce","year":2015},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.838965Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:5100795ae98f03d3646f99a9c8679e69ba1cccecebc829c564ddcfb433e757cc","observation_id":"fb835f60-bf8c-484e-8053-89c6940bfb4a","resolution":{"observed_at":"2026-08-07T04:26:52.101886Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.05521","last_updated":"2025-03-14T10:42:01Z","snapshot_observed_at":"2026-08-07T17:21:50.509732Z","submitted_at":"2025-03-07T15:44:08Z","title":"Warped products and synthetic lower curvature bounds: an overview","version":2},"cited_work":{"arxiv_id":"2503.05521","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.05521","snapshot_observed_at":"2026-08-07T04:26:48.736391Z","title":"Warped products and synthetic lower curvature bounds: an overview","venue":"math.DG","work_id":"99d04705-7241-4c50-89c2-1927fa189220","year":2025},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.895027Z"},"links":{"cited_paper":"/paper/2503.05521","citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:ee3f4df6be7e58bbe4fceb1386170025939220eded2537c2d4e021b550f54b8d","observation_id":"da7045cf-4b5d-4ac4-9692-d1e0de041c54","resolution":{"observed_at":"2026-08-07T04:26:48.783102Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:51.776378Z","title":"Geometry and analysis of Dirichlet forms.Adv","venue":null,"work_id":"f8ffb103-ca4c-4032-a42d-8e1ddf39693d","year":2012},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.937579Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:22fea63be7195ebdc2b500483583a5e774dc88f12bb627cee15be7277c86363e","observation_id":"2210477a-e624-4235-a7cb-c3bb338fd11d","resolution":{"observed_at":"2026-08-07T04:26:51.914974Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:51.526227Z","title":"Infinitesimal Bishop-Gromov condition for Alexandrov spaces","venue":null,"work_id":"8ba02be1-3d3e-46c6-942f-e95f7aaf6144","year":2010},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:47.995496Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:92602a87349fc311e54834a0743549b0880074820cd50a73dbe571e4b0a04932","observation_id":"a84ef434-fce6-43a1-9f1a-b5471f38e8b7","resolution":{"observed_at":"2026-08-07T04:26:51.655894Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:51.317766Z","title":"Some geometric properties of the Bakry- ´Emery-Ricci tensor","venue":null,"work_id":"a3be4163-03f3-4607-b375-b4b39857e06a","year":2003},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:48.041803Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:8e77b5f88b7b1efc94efe4d27e17630aefaf0f1469b145863842f52581aaffdc","observation_id":"108ca575-1026-4230-a2f8-fa56832aa470","resolution":{"observed_at":"2026-08-07T04:26:51.423605Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:51.101803Z","title":"Ricci curvature for metric-measure spaces via optimal transport","venue":null,"work_id":"fd5cbb10-8256-4e0f-a5ba-23cb38cb8fad","year":2009},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:48.085317Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:acf8e3ccc8bf1181a15260ed2fd4abd6913004fac0f63861f8eb7eaef6a97f97","observation_id":"04fc1076-ff1f-48ca-884c-6e3ac7149c34","resolution":{"observed_at":"2026-08-07T04:26:51.223179Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:50.811886Z","title":"Ricci curvature in dimension 2","venue":null,"work_id":"97dd2eed-363e-4f4b-92d1-5d26f42d6c14","year":2023},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:48.150730Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:cd37ea20675c2a9bd9b03f49e7b84ddad8b8c80fa12e8648e521db141d1e9e85","observation_id":"c3b7e504-81d9-441a-be6e-d1a400e5bfa0","resolution":{"observed_at":"2026-08-07T04:26:50.887469Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:50.617737Z","title":"On the measure contraction property of metric measure spaces","venue":null,"work_id":"b9e1698f-32db-45b5-a765-fdec735013f1","year":2007},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:48.188965Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:f426a840c8584f26fd0968bc7ac58302bfef03ec3c74d85c0243a2a6de2f8081","observation_id":"2d906eb3-b650-42f2-89b1-18e790650013","resolution":{"observed_at":"2026-08-07T04:26:50.708803Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:50.435701Z","title":"Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm","venue":null,"work_id":"637b53ae-f206-484f-9d64-21ff8d14d77d","year":2012},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:48.219233Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:f357a623c0385075748e71653750712c3129f46e827acda527814dc6c16a4fc5","observation_id":"22287281-3fba-44d8-8f1f-1c401ff6497a","resolution":{"observed_at":"2026-08-07T04:26:50.537556Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:50.265829Z","title":"Methods of modern mathematical physics","venue":null,"work_id":"c41c57c3-f7ed-4c0a-ba75-a52a85ea637d","year":1975},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:48.307541Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:8973376950fd9a03223ee523d6f337342982f80dfaf82c532d0e163005bf7a37","observation_id":"fb4911c4-f0cb-4414-8e94-16ccef3bbf43","resolution":{"observed_at":"2026-08-07T04:26:50.342918Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:50.048809Z","title":"Self-improvement of the Bakry-´Emery condition and Wasserstein contraction of the heat flow in RCD( K, ∞) metric measure spaces","venue":null,"work_id":"f79c6a5d-5098-4f18-bceb-2c0473aa9d7d","year":2014},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:48.348867Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:c3e6e9986038bb4711be2bb20e4af9e54b644705eacf7b3cd36c96a28198c39d","observation_id":"6143b481-92ac-4321-a40f-18af631d63af","resolution":{"observed_at":"2026-08-07T04:26:50.201293Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:49.923170Z","title":"Analysis on local Dirichlet spaces","venue":null,"work_id":"7cab70ad-e099-4fd5-9d61-1de552c118c2","year":1995},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:48.374605Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:517deef526f4be3eb3af948c5294bdaa3544a2079d70dd593b21a2dfaffd241b","observation_id":"84018b35-3d79-420c-983f-e88d3e89e6b0","resolution":{"observed_at":"2026-08-07T04:26:49.979078Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:49.704514Z","title":"Analysis on local Dirichlet spaces","venue":null,"work_id":"2e61c918-9632-4b82-86c9-c4854aae4c7d","year":1996},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:48.433735Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:f6c9fc413961d500519a74383912550160642976eb1fbea5ccd71010690f556a","observation_id":"36685870-d58d-4d1f-9f1c-7c4a23feb5a7","resolution":{"observed_at":"2026-08-07T04:26:49.810840Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:49.501682Z","title":"On the geometry of metric measure spaces","venue":null,"work_id":"2fd77783-e2b3-413f-8519-2fa461af97a6","year":2006},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:48.520080Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:2ee37486f68cb5f64003288873884ae70ab2115d144188f3104673e17a264394","observation_id":"7aa9bc29-6f1b-43ae-a2d6-7f1dfa7c18d5","resolution":{"observed_at":"2026-08-07T04:26:49.634872Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:49.362267Z","title":"On the geometry of metric measure spaces","venue":null,"work_id":"c0491e69-8413-407b-800e-1ed3abf6a262","year":2006},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:48.613163Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:80756984a348241d929fa5b941c6b1ed42de0e9716b944847f1df55e8aa05483","observation_id":"8aebf0f2-1fe8-4f34-8fc7-86cccc923f6a","resolution":{"observed_at":"2026-08-07T04:26:49.406901Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T04:26:49.120404Z","title":"Bakry-´ emery, Hardy, and spectral gap estimates on manifolds with conical singularities","venue":null,"work_id":"815b7fdf-5f33-492d-8420-50a1fd3a8b12","year":2025},"citing_paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition","version":3},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-07T04:26:48.649152Z"},"links":{"citing_paper":"/paper/2506.10809"},"observation_digest":"sha256:72601446857acffcf87ca38d02903ddea643b9d4a06e35e5e96a81c2616711d8","observation_id":"5a56a064-2c29-4982-84d9-942824898194","resolution":{"observed_at":"2026-08-07T04:26:49.237135Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.10809","last_updated":"2026-07-22T09:06:36Z","latest_version":3,"primary_category":"math.DG","snapshot_observed_at":"2026-08-08T05:45:41.993349Z","submitted_at":"2025-06-12T15:24:18Z","title":"Warped products over one-dimensional base spaces and the RCD condition"},"reference_resolution":{"displayed":53,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":3,"verified_fuzzy":44},"total_outbound_references":53},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 0 inbound Pith citation observations for arXiv:2506.10809."}