{"as_of":"2026-08-23T10:14:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ca56595b61cf6ccc2e8ce7af9c3497a9ef2a77c2907b0bd840745748bd6d929d","coverage":[{"denominator":48,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":48,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T06:05:22.762984Z","state":"measured"},{"denominator":51,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":51,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-30T14:11:19.315088Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-06-30T12:54:39.742803Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"cited_work":{"arxiv_id":"1909.00381","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1909.00381","snapshot_observed_at":"2026-06-30T12:54:39.742803Z","title":"Bru\\`e, E","venue":null,"work_id":"e336fd8b-7ae2-4830-a258-409975aa1349","year":1909},"citing_paper":{"arxiv_id":"2112.06962","last_updated":"2026-04-21T06:17:55Z","snapshot_observed_at":"2026-07-06T12:18:18.529747Z","submitted_at":"2021-12-13T19:01:39Z","title":"One-phase Free Boundary Problems on RCD Metric Measure Spaces","version":4},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-05-24T12:46:33.904843Z"},"links":{"cited_paper":"/paper/1909.00381","citing_paper":"/paper/2112.06962"},"observation_digest":"sha256:2d3f3e13abab15114b239bf7bb31706b30f7a63d9406356cbb0c43663f834623","observation_id":"0f8ba49a-3c95-4a2a-9d2b-58432e57d37f","resolution":{"observed_at":"2026-05-24T12:49:29.589126Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"cited_work":{"arxiv_id":"1909.00381","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1909.00381","snapshot_observed_at":"2026-06-30T12:54:39.742803Z","title":"Bru\\`e, E","venue":null,"work_id":"e336fd8b-7ae2-4830-a258-409975aa1349","year":1909},"citing_paper":{"arxiv_id":"2605.24380","last_updated":"2026-05-23T03:38:38Z","snapshot_observed_at":"2026-08-15T09:04:37.023281Z","submitted_at":"2026-05-23T03:38:38Z","title":"Fibrations, the First Betti Number, and Almost Nonnegative Ricci Curvature","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-06-30T12:54:16.211059Z"},"links":{"cited_paper":"/paper/1909.00381","citing_paper":"/paper/2605.24380"},"observation_digest":"sha256:71f5f9e9c954faca8b871ec606382ed77b4a5df3cadbd2236895877862933f54","observation_id":"9ba675b5-39af-4cd0-9b7c-36a046c6e2f2","resolution":{"observed_at":"2026-06-30T12:54:39.744438Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1909.00381","snapshot_observed_at":"2026-07-30T14:11:19.315088Z","title":"arXiv , author =:1909.00381 , howpublished =","venue":null,"work_id":null,"year":1909},"citing_paper":{"arxiv_id":"2607.27010","last_updated":"2026-07-29T15:06:11Z","snapshot_observed_at":"2026-08-22T04:57:27.596218Z","submitted_at":"2026-07-29T15:06:11Z","title":"Lipschitz continuity of harmonic maps between ${\\rm RCD}(K,N)$ spaces and ${\\rm CAT}(\\kappa)$ spaces","version":1},"reference_index":128,"source":"arxiv_source","source_observed_at":"2026-07-30T14:11:19.315088Z"},"links":{"cited_paper":"/paper/1909.00381","citing_paper":"/paper/2607.27010"},"observation_digest":"sha256:456d14feabc950498f4a9c00b5ffbc618f79188fb191ac51897ac7fb361e6fa6","observation_id":"5f9c3646-1890-4fda-a759-3afe0e355839","resolution":{"observed_at":"2026-07-30T14:11:19.315088Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/1909.00381/citation-record","integrity":"/paper/1909.00381/integrity","json":"/paper/1909.00381/citation-record.json","paper":"/paper/1909.00381"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T06:05:23.314095Z","title":"Ambrosio , Fine properties of sets of finite perimeter in doubling metri c measure spaces, Set-Valued Anal., 10 (2002), pp","venue":null,"work_id":"840375b3-3f7b-4fa6-a1f4-99e57beb3180","year":2002},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.587007Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:f6974475c623fcfbd794316188a17a9e41640dc9a34185455e81d7a0c5175308","observation_id":"256a6d96-41be-4c2d-b299-27624f3cd9e8","resolution":{"observed_at":"2026-08-14T06:05:23.318893Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1812.07890","last_updated":"2019-09-11T14:41:20Z","snapshot_observed_at":"2026-08-16T19:48:29.232521Z","submitted_at":"2018-12-19T11:41:25Z","title":"Rigidity of the 1-Bakry-\\'Emery inequality and sets of finite perimeter in RCD spaces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1812.07890","snapshot_observed_at":"2026-08-14T06:05:22.591976Z","title":"Ambrosio, E","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.591976Z"},"links":{"cited_paper":"/paper/1812.07890","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:1e6c891b693fe2ef122c6726f1f402af4a442ed0e5c28a382b793f95f5e88e38","observation_id":"e6b34468-4dc7-4e43-be17-d17a409d9812","resolution":{"observed_at":"2026-08-14T06:05:22.591976Z","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":"2026-08-14T06:05:23.302936Z","title":"Ambrosio and S","venue":null,"work_id":"78a39dad-8cf9-4a35-8676-b41bd4daf0e6","year":2014},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.597072Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:88ace031a9af5f3edd2d91cfe9ee00345f1a3c6c93fc13e8ba0c188e98cee802","observation_id":"4dfd8147-5efd-4041-b604-22d90644cc4d","resolution":{"observed_at":"2026-08-14T06:05:23.306496Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:22.601616Z","title":"Ambrosio, N","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.601616Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:80ae41f4da97eb7827d504d70d9990f3eaa11e0f4d6b2a2965fb8718f5fb51ee","observation_id":"836850f6-5b02-49ec-b4d5-b48daf8a4584","resolution":{"observed_at":"2026-08-14T06:05:22.601616Z","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":"2026-08-14T06:05:23.286206Z","title":"Ambrosio, N","venue":null,"work_id":"10e14468-d145-4f44-a132-4182525de005","year":2014},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.605523Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:b1d7dde5cd5227848c78240bd31f7162ebbcc2bdc101c1c76bdc11780d953a0e","observation_id":"27628e68-5e90-4438-a383-684959e43125","resolution":{"observed_at":"2026-08-14T06:05:23.289981Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.276581Z","title":"Ambrosio and S","venue":null,"work_id":"f9a0a6b7-3894-4460-8c13-260485b1dcd9","year":2017},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.609788Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:ff03d8f676dc11c4650b273eb011921dca08da5c6e748b9e53383e74a8a1e163","observation_id":"d264f415-a992-4873-a084-8838add9262e","resolution":{"observed_at":"2026-08-14T06:05:23.279841Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.265127Z","title":null,"venue":null,"work_id":"6c72d939-0f90-4fd4-bd77-50b09ea3926e","year":2018},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.613987Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:fb7835f681ad13a9fcc0e4146147b6088ed722b2754cbd4455ebde3c905f66fe","observation_id":"0a794ce4-131b-44da-a2a6-835e7c64c6c7","resolution":{"observed_at":"2026-08-14T06:05:23.269458Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1812.03712","last_updated":"2021-02-18T10:05:15Z","snapshot_observed_at":"2026-08-18T21:23:19.356632Z","submitted_at":"2018-12-10T10:11:42Z","title":"Embedding of $RCD^*(K,N)$ spaces in $L^2$ via eigenfunctions","version":2},"cited_work":{"arxiv_id":"1812.03712","doi":null,"metadata_source":"pith","pith_arxiv_id":"1812.03712","snapshot_observed_at":"2026-08-14T06:05:22.970929Z","title":"Embedding of $RCD^*(K,N)$ spaces in $L^2$ via eigenfunctions","venue":"math.MG","work_id":"86f1bfb3-1aa6-46c9-b082-28cfefa75fe2","year":2018},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.617733Z"},"links":{"cited_paper":"/paper/1812.03712","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:a0d281f78cbdd060726b01559ef5f7ed0824cca932f6a8dffcb7ceac1574f691","observation_id":"c6b695a3-5eef-4148-81d2-96f3fb05c2dc","resolution":{"observed_at":"2026-08-14T06:05:22.975202Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1509.07273","last_updated":"2017-02-10T18:05:32Z","snapshot_observed_at":"2026-08-21T18:00:32.248733Z","submitted_at":"2015-09-24T08:34:03Z","title":"Nonlinear diffusion equations and curvature conditions in metric measure spaces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1509.07273","snapshot_observed_at":"2026-08-14T06:05:22.621759Z","title":"Ambrosio, A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.621759Z"},"links":{"cited_paper":"/paper/1509.07273","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:6f6750a096948e29c6ac465b32d89309ba006d9f44178bf3820b8568ccc5d315","observation_id":"8d87d6d9-0144-4c42-a324-561cae0c3256","resolution":{"observed_at":"2026-08-14T06:05:22.621759Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1907.02735","last_updated":"2019-07-05T09:25:21Z","snapshot_observed_at":"2026-08-19T01:51:17.800475Z","submitted_at":"2019-07-05T09:25:21Z","title":"Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces","version":1},"cited_work":{"arxiv_id":"1907.02735","doi":null,"metadata_source":"pith","pith_arxiv_id":"1907.02735","snapshot_observed_at":"2026-08-14T06:05:22.945760Z","title":"Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces","venue":"math.MG","work_id":"b7d6b32b-cfdb-48f3-aa92-28319b82a0cc","year":2019},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.625841Z"},"links":{"cited_paper":"/paper/1907.02735","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:a6b6f581a8b9a84f0af91c0c70f91d6c4b50491c30594616ef867b6d8b460a31","observation_id":"ab372d85-d613-4b16-bbec-0e0953d01ee0","resolution":{"observed_at":"2026-08-14T06:05:22.950540Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1804.07128","last_updated":"2019-09-11T14:31:49Z","snapshot_observed_at":"2026-08-16T05:25:16.956998Z","submitted_at":"2018-04-19T12:58:03Z","title":"Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows","version":2},"cited_work":{"arxiv_id":"1804.07128","doi":null,"metadata_source":"pith","pith_arxiv_id":"1804.07128","snapshot_observed_at":"2026-08-14T06:05:22.930958Z","title":"Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows","venue":"math.MG","work_id":"5b245238-b9d5-467f-b61f-09c28b7d257a","year":2018},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.629875Z"},"links":{"cited_paper":"/paper/1804.07128","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:e9f2f098466a9960b369872e96cf5c18010609ba53f00970da19a7b5ddfd1a60","observation_id":"f244088f-174a-4d07-9d87-08f62825f074","resolution":{"observed_at":"2026-08-14T06:05:22.935317Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1906.07432","last_updated":"2021-09-22T13:26:46Z","snapshot_observed_at":"2026-08-18T23:14:46.791546Z","submitted_at":"2019-06-18T08:11:58Z","title":"On $BV$ functions and essentially bounded divergence-measure fields in metric spaces","version":5},"cited_work":{"arxiv_id":"1906.07432","doi":null,"metadata_source":"pith","pith_arxiv_id":"1906.07432","snapshot_observed_at":"2026-08-14T06:05:22.914896Z","title":"On $BV$ functions and essentially bounded divergence-measure fields in metric spaces","venue":"math.DG","work_id":"3f816894-a3fd-4065-9486-0ba7f0f7b370","year":2019},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.634213Z"},"links":{"cited_paper":"/paper/1906.07432","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:a43db38a53d065a08d43a7e8d883f20e096c10e4bb49f950b0e4414d1cb844a3","observation_id":"7be6f825-9f6b-4494-8ddb-64fdfe0b9ca5","resolution":{"observed_at":"2026-08-14T06:05:22.920720Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1612.07623","last_updated":"2021-02-24T20:46:30Z","snapshot_observed_at":"2026-08-14T21:24:04.734182Z","submitted_at":"2016-12-22T14:44:40Z","title":"The Globalization Theorem for the Curvature Dimension Condition","version":2},"cited_work":{"arxiv_id":"1612.07623","doi":null,"metadata_source":"pith","pith_arxiv_id":"1612.07623","snapshot_observed_at":"2026-08-14T06:05:22.900337Z","title":"The Globalization Theorem for the Curvature Dimension Condition","venue":"math.MG","work_id":"fd1b3296-800d-4ae6-903d-8c236f316da1","year":2016},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.638452Z"},"links":{"cited_paper":"/paper/1612.07623","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:e4cb8c47bdd4deeefa53e87555d552adc4de852120b2fc8536f5bc95f04cf79d","observation_id":"a978f556-721b-43c1-82d3-1e908e4b1d2e","resolution":{"observed_at":"2026-08-14T06:05:22.904656Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.253884Z","title":"Cheeger and T","venue":null,"work_id":"56866978-34d8-4a2d-8e89-c2afca280f54","year":1996},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.642291Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:53cefe7256f311df4a33c57ea367705be37de14674cdf0ce929b01229a0339ed","observation_id":"4a7e7ef2-1e29-412e-83b5-447a3967fe69","resolution":{"observed_at":"2026-08-14T06:05:23.257605Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:22.645642Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.645642Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:8b5724abb27e12f0c1bebebbeeb8775ea04098dd1c85c6bcd0f9a335d85ee422","observation_id":"cac45403-948b-4b31-be84-1ec1fa6d58fa","resolution":{"observed_at":"2026-08-14T06:05:22.645642Z","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":"2026-08-14T06:05:23.236827Z","title":null,"venue":null,"work_id":"df49ba9a-5ca6-44bd-b0a6-ea71b67e4b54","year":2000},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.649084Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:804a61e6e4f8a4e7dbfb5f52f7524a97164a106e9a6b3d8e5bd3d90065d4062c","observation_id":"d46d93fc-987d-4e4b-bdd7-a9c0d33771be","resolution":{"observed_at":"2026-08-14T06:05:23.240668Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1805.07988","last_updated":"2018-05-21T11:09:55Z","snapshot_observed_at":"2026-08-14T19:13:02.928754Z","submitted_at":"2018-05-21T11:09:55Z","title":"Rectifiability of Singular Sets in Noncollapsed Spaces with Ricci Curvature bounded below","version":1},"cited_work":{"arxiv_id":"1805.07988","doi":null,"metadata_source":"pith","pith_arxiv_id":"1805.07988","snapshot_observed_at":"2026-08-14T06:05:22.885777Z","title":"Rectifiability of Singular Sets in Noncollapsed Spaces with Ricci Curvature bounded below","venue":"math.DG","work_id":"3fc4e4b3-9b26-46b2-8203-4797af047030","year":2018},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.652643Z"},"links":{"cited_paper":"/paper/1805.07988","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:d69cd9aa4c644f4de6682a31995ee69c445afb93b83d8eec07d038cc62d3e60b","observation_id":"49ca960a-69bb-4a1d-96a0-b9c7a113f0a7","resolution":{"observed_at":"2026-08-14T06:05:22.889821Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.225438Z","title":"Cheeger and A","venue":null,"work_id":"d7914040-85dd-4579-b07d-f66cfac6e32e","year":2015},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.656252Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:ac7e4a20edb78ece49f616b147b96ee9328179fc565c4ce659e3b2cceb5477e8","observation_id":"5f596135-f77d-4126-8ad4-c43565297305","resolution":{"observed_at":"2026-08-14T06:05:23.229256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.214186Z","title":"De Philippis, A","venue":null,"work_id":"9cc9435d-cb92-46b2-b676-f6ada3e2a582","year":2017},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.659653Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:e110e4d491674a58b885f03fe296f19b61b82b1149cb28c10b2191252067ed71","observation_id":"14a9600c-ad01-46c6-b9d9-62ae8a0f8088","resolution":{"observed_at":"2026-08-14T06:05:23.218086Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1903.04302","last_updated":"2019-03-13T12:35:30Z","snapshot_observed_at":"2026-08-22T04:57:27.024187Z","submitted_at":"2019-03-11T13:54:05Z","title":"Quasi-continuous vector fields on RCD spaces","version":2},"cited_work":{"arxiv_id":"1903.04302","doi":null,"metadata_source":"pith","pith_arxiv_id":"1903.04302","snapshot_observed_at":"2026-08-14T06:05:22.870469Z","title":"Quasi-continuous vector fields on RCD spaces","venue":"math.FA","work_id":"29b7d264-0908-4b04-a9c9-b4693b24dd03","year":2019},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.663341Z"},"links":{"cited_paper":"/paper/1903.04302","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:7ea383df32060113e83279b7f0be5cd4553f723ca8b1ccdea8647fb3de3cc285","observation_id":"3351b6e0-a342-4760-aa9f-e1cfe8abe61f","resolution":{"observed_at":"2026-08-14T06:05:22.874667Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1409.5620","last_updated":"2014-09-19T12:14:50Z","snapshot_observed_at":"2026-08-15T17:15:04.329086Z","submitted_at":"2014-09-19T12:14:50Z","title":"Sobolev and BV spaces on metric measure spaces via derivations and integration by parts","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1409.5620","snapshot_observed_at":"2026-08-14T06:05:22.667127Z","title":"Di Marino , Sobolev and BV spaces on metric measure spaces via derivatio ns and integration by parts","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.667127Z"},"links":{"cited_paper":"/paper/1409.5620","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:2d55ed5dd77680659a930a2427a50c705be9ab8f88d6b6fc741c3543aa6147e0","observation_id":"9139296d-420d-4346-8f7b-4ce55f7ff615","resolution":{"observed_at":"2026-08-14T06:05:22.667127Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1812.02086","last_updated":"2018-12-05T16:21:26Z","snapshot_observed_at":"2026-08-14T17:48:01.150129Z","submitted_at":"2018-12-05T16:21:26Z","title":"Infinitesimal Hilbertianity of locally CAT($\\kappa$)-spaces","version":1},"cited_work":{"arxiv_id":"1812.02086","doi":null,"metadata_source":"pith","pith_arxiv_id":"1812.02086","snapshot_observed_at":"2026-08-14T06:05:22.845977Z","title":"Infinitesimal Hilbertianity of locally CAT($\\kappa$)-spaces","venue":"math.MG","work_id":"7427daea-5e66-43bf-ac29-9c5308af360c","year":2018},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.670702Z"},"links":{"cited_paper":"/paper/1812.02086","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:3bcd923b0b8e4c7ecdd1d00b76d5bec745eb141c9db9f4b5ae731d8559f62bc9","observation_id":"d61260b5-c686-4620-a057-bdda92bc8124","resolution":{"observed_at":"2026-08-14T06:05:22.849760Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.203952Z","title":"Erbar, K","venue":null,"work_id":"359a1ac1-2166-449b-a206-c206d19ed965","year":2014},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.674657Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:2699dd27e80423a2d436ba68c9121f21c702455ffcc759db26b4bd821a49a08c","observation_id":"0895011b-dbda-403c-913f-fd1a80e26c33","resolution":{"observed_at":"2026-08-14T06:05:23.207464Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.194099Z","title":"Evans and R","venue":null,"work_id":"b560637d-dfe1-4af8-ad8f-1b3434c6b954","year":1991},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.677963Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:aeac41c0f17cc6114f354a869362252e63ada3002efc4f633658156dd9a99039","observation_id":"b75fb15d-3609-4de3-8916-5811a75d6809","resolution":{"observed_at":"2026-08-14T06:05:23.197554Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.183187Z","title":"Gigli , Nonsmooth differential geometry - an approach tailored for s paces with Ricci curvature bounded from below","venue":null,"work_id":"1dbb2d1d-f7fa-466e-8758-ccc88b906597","year":2015},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.681323Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:65050f42ef18a840907869b6eea5ddc30dd29768337b03dc72c7464c879b266a","observation_id":"1fe9c6d8-96f3-447f-87d5-8fdeb293b507","resolution":{"observed_at":"2026-08-14T06:05:23.186840Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:22.684699Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.684699Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:d40051624321df22199e83e4b965620848896f3bb5992cdf1980036e5d5a7f3f","observation_id":"68dae988-2e0d-416b-9854-947f848bbc45","resolution":{"observed_at":"2026-08-14T06:05:22.684699Z","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":"2026-08-14T06:05:23.163848Z","title":null,"venue":null,"work_id":"400297ea-d424-489f-b72d-7c8e7329ab63","year":2018},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.688096Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:2821efee512e3ec2b73b11166f2e8dcc7f5d97ac7ab64253d80e718991f7716a","observation_id":"3042f043-3d22-40b4-9348-92a17bd62ee3","resolution":{"observed_at":"2026-08-14T06:05:23.167714Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:22.691533Z","title":"Gigli and B","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.691533Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:b85369f4cd9f9883682b499196c1008f6e6e0fed53273c79f9af80406d5b5682","observation_id":"74b7d330-47c0-46b4-b66d-5afc12bf9c47","resolution":{"observed_at":"2026-08-14T06:05:22.691533Z","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":"2026-08-14T06:05:23.147224Z","title":"Gigli, A","venue":null,"work_id":"8d59f8bb-5ede-4934-9f2f-d15110ecce73","year":2015},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.694833Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:8b4a32aeb4a264a815ca74bb8ab3453524ad32827bf8be0b58c43a06f6aa9eaf","observation_id":"e6b38de6-e757-4b1f-8380-f37840f273df","resolution":{"observed_at":"2026-08-14T06:05:23.150563Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.137116Z","title":"Gigli and E","venue":null,"work_id":"d9ae6f59-4d50-42e2-a68f-47dfb8d5130e","year":null},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.698471Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:b17b15d62f66251039354dd583d373a23f6880a5abb01841bb62a9438ee63b17","observation_id":"8eff57df-1d74-45bc-8c12-c054d02e2890","resolution":{"observed_at":"2026-08-14T06:05:23.140880Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.126360Z","title":"Accepted at Communications in Analysis and Geometry, arXiv:1611.09 645","venue":null,"work_id":"f411c580-fa34-49d8-b57c-5c657f8e843d","year":null},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.702014Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:58bbfdc458ea1815c5cf418610818c537f59777a4aea4bfc978e2d72e355ecf3","observation_id":"042a3669-a4f1-4e55-9313-65049142d38b","resolution":{"observed_at":"2026-08-14T06:05:23.129699Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1412.0441","last_updated":"2018-07-16T20:09:59Z","snapshot_observed_at":"2026-08-18T09:45:38.977101Z","submitted_at":"2014-12-01T11:49:07Z","title":"Ricci tensor on ${\\rm RCD}^*(K,N)$ spaces","version":4},"cited_work":{"arxiv_id":"1412.0441","doi":null,"metadata_source":"pith","pith_arxiv_id":"1412.0441","snapshot_observed_at":"2026-08-14T06:05:22.831011Z","title":"Ricci tensor on ${\\rm RCD}^*(K,N)$ spaces","venue":"math.MG","work_id":"c16180de-4427-446f-8c86-272f540c2ec7","year":2014},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.705373Z"},"links":{"cited_paper":"/paper/1412.0441","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:50a7a6c3831733a0dd5cc0051511d8486301f1571a049f305986217dffe2a683","observation_id":"3820ca49-b841-4fe8-8486-70034f46b009","resolution":{"observed_at":"2026-08-14T06:05:22.834834Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.116925Z","title":"Jiang , Cheeger-harmonic functions in metric measure spaces revis ited, J","venue":null,"work_id":"8013244b-359d-44f2-a462-eaf83fa1b82a","year":2014},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.709047Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:83d4b78b4ac63ffc8e369012c726d430be0a85893c11e75704c3567551143087","observation_id":"b44a34fd-e487-4a94-886a-f8e632285530","resolution":{"observed_at":"2026-08-14T06:05:23.120119Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1705.04767","last_updated":"2020-07-31T06:47:26Z","snapshot_observed_at":"2026-08-17T00:22:04.120591Z","submitted_at":"2017-05-12T23:16:37Z","title":"Metric-measure boundary and geodesic flow on Alexandrov spaces","version":3},"cited_work":{"arxiv_id":"1705.04767","doi":null,"metadata_source":"pith","pith_arxiv_id":"1705.04767","snapshot_observed_at":"2026-08-14T06:05:22.813061Z","title":"Metric-measure boundary and geodesic flow on Alexandrov spaces","venue":"math.DG","work_id":"bf8153af-95b3-46f2-a6ae-46794129f44d","year":2017},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.712463Z"},"links":{"cited_paper":"/paper/1705.04767","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:ccff38af8174a7bb045ac5b24544545dd1b7e87558f0140b02085eabc9a9d5d5","observation_id":"abcc6684-172e-4066-a6de-bae6ad687b83","resolution":{"observed_at":"2026-08-14T06:05:22.819999Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.02614","last_updated":"2020-03-31T15:30:30Z","snapshot_observed_at":"2026-08-16T12:13:40.626397Z","submitted_at":"2019-07-04T22:16:54Z","title":"On the topology and the boundary of N-dimensional RCD(K,N) spaces","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1907.02614","snapshot_observed_at":"2026-08-14T06:05:22.716733Z","title":"Kapovitch and A","venue":null,"work_id":null,"year":1907},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.716733Z"},"links":{"cited_paper":"/paper/1907.02614","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:7a21e754efdb54d23cffee893da7510eea35bee93b8cc6e250ba77236dfeece7","observation_id":"947ae89d-0f39-4713-a2ee-4765cc741ba3","resolution":{"observed_at":"2026-08-14T06:05:22.716733Z","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":"2026-08-14T06:05:23.106520Z","title":"Kell and A","venue":null,"work_id":"ce703a80-fdd8-4413-8548-5a84ff8c88ad","year":2018},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.720627Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:0e2eaa5b97f7e351390eef56336e24f9d38d97084105eb0ebdaa24fa228f2ad5","observation_id":"07a8dc8b-1b38-45fb-bfde-b84c87c9c647","resolution":{"observed_at":"2026-08-14T06:05:23.110419Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:22.723996Z","title":"Lott and C","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.723996Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:429d297275c015c983e1fda86c60b7cee11c4d08587b03789694f82c868844c6","observation_id":"f0b40cb7-4e76-414c-85df-a0b8d0c8ec0d","resolution":{"observed_at":"2026-08-14T06:05:22.723996Z","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":"2026-08-14T06:05:23.088452Z","title":"Magnani, On a measure theoretic area formula , Proc","venue":null,"work_id":"13cce5c3-29a5-43ca-bd85-5e39819157b9","year":2015},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.727583Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:1e29acfa0d07cc97df9d4372fa19f9701bc2dbbf45976419ecb3e4de4f7df5e7","observation_id":"f798d33d-8131-4bab-9f40-b316380c7a60","resolution":{"observed_at":"2026-08-14T06:05:23.092757Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.076325Z","title":"Miranda, Jr","venue":null,"work_id":"d4a454a3-f403-46e6-98b2-8dbeb994d751","year":2003},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.731188Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:f4f88c0e16271705f19fb8a6bec71e01f6bf80c1f8ff6ba280ed2aa9f491d54e","observation_id":"4eba4d64-2648-452c-b4ce-7e974df8c203","resolution":{"observed_at":"2026-08-14T06:05:23.081152Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1405.2222","last_updated":"2017-05-04T10:41:44Z","snapshot_observed_at":"2026-08-14T23:34:39.044816Z","submitted_at":"2014-05-09T13:13:40Z","title":"Structure Theory of Metric-Measure Spaces with Lower Ricci Curvature Bounds","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1405.2222","snapshot_observed_at":"2026-08-14T06:05:22.734578Z","title":"Mondino and A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.734578Z"},"links":{"cited_paper":"/paper/1405.2222","citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:bdfe976a1152bb488dce967b09243550a8c94d73dcb793e43c2c0b4f5687c94b","observation_id":"45d79f7a-2e04-4db0-9e77-af236f0ca76a","resolution":{"observed_at":"2026-08-14T06:05:22.734578Z","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":"2026-08-14T06:05:23.064883Z","title":"Petrunin , Alexandrov meets Lott-Villani-Sturm , M¨ unster J","venue":null,"work_id":"9fcba277-457c-45d6-85a5-cb94771f3caf","year":2011},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.738657Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:68674308dac1dd8410cfc6d3d90016f1ae759e52da47e8f6beadaee595697656","observation_id":"a0b9478a-59f1-47de-a88e-e3dcba6e9ec4","resolution":{"observed_at":"2026-08-14T06:05:23.068629Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.053727Z","title":null,"venue":null,"work_id":"1a584792-0cfe-4407-9665-18b60a205761","year":2018},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.742117Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:ce7530bd8487b63927049cd0f9d10ec79d2404fcfc2c45f8e05b7bb981a64427","observation_id":"07f0bc9d-cbbd-49cc-a109-a271429ab4b9","resolution":{"observed_at":"2026-08-14T06:05:23.056843Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.043372Z","title":"Rajala , Local Poincar´ e inequalities from stable curvature conditions on metric spaces , Calc","venue":null,"work_id":"c72e367d-2abb-4d67-81c7-feb0853b1512","year":2012},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.745625Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:29fc2df86193c0599eb32129c46395f5402f9633709057c4ba172488e82db4cf","observation_id":"b7a53c5e-278f-4b64-9d76-80a9b5c987b4","resolution":{"observed_at":"2026-08-14T06:05:23.047108Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:23.031001Z","title":"Savar´e, Self-improvement of the Bakry- ´Emery condition and Wasserstein contraction of the heat flow in RCD(K, ∞ ) metric measure spaces , Discrete Contin","venue":null,"work_id":"1b888120-da42-4831-abe5-e954cb8e7f86","year":2014},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.749154Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:bccd27ed48bac6e8afdf081a9cb9a870e5b61ea941f844b8e00833b7d952e3b4","observation_id":"dbf0218b-4f67-4cf4-a22f-8e136543a7e3","resolution":{"observed_at":"2026-08-14T06:05:23.035489Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:22.752624Z","title":"Sturm , On the geometry of metric measure spaces","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.752624Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:3e5076d4a279e867a609c6cd96984943a3b162093dd6e7d5b70f62541252c783","observation_id":"5f462f59-f224-4fd1-b6e0-f860f8339146","resolution":{"observed_at":"2026-08-14T06:05:22.752624Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T06:05:22.756096Z","title":"II , Acta Math., 196 (2006), pp","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.756096Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:7770f36f1fd2a43c2898884f21dfbc369c72ee9ce47193784ca2842b40d4ff27","observation_id":"e3fc3a5a-f746-4b88-a7d8-66ff452b7ca3","resolution":{"observed_at":"2026-08-14T06:05:22.756096Z","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":"2026-08-14T06:05:23.005312Z","title":"Villani , Optimal transport","venue":null,"work_id":"1f75e5d9-c1c8-4576-a94c-6c8c96e0d614","year":2009},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.759383Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:644cefdce2c9ad0158a55e2dc8cb55c6693dc3268dbb77662adb912fdad9197b","observation_id":"14a70177-2035-4acb-a4ad-334a1c2eec6d","resolution":{"observed_at":"2026-08-14T06:05:23.009438Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-14T06:05:22.993745Z","title":"Weaver , Lipschitz algebras and derivations","venue":null,"work_id":"15fbf5ee-0980-4579-be77-43da1b5ccaaf","year":2000},"citing_paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-14T06:05:22.762984Z"},"links":{"citing_paper":"/paper/1909.00381"},"observation_digest":"sha256:ba09c006c0f6828ddb06da73201cdf0209690637bb108647946e48dd215d361f","observation_id":"cb74d7e1-daaa-440e-bb5f-7125bea603b3","resolution":{"observed_at":"2026-08-14T06:05:22.998076Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1909.00381","last_updated":"2019-09-01T11:23:05Z","latest_version":1,"primary_category":"math.MG","snapshot_observed_at":"2026-08-21T18:00:43.895339Z","submitted_at":"2019-09-01T11:23:05Z","title":"Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces"},"reference_resolution":{"displayed":48,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":10,"verified_fuzzy":22},"total_outbound_references":48},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 3 inbound Pith citation observations for arXiv:1909.00381."}