{"as_of":"2026-08-14T08:45:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e441e34d3ec622b602a8da8bbbece6a9ceb57848964f818fd976273f957a5bd7","coverage":[{"denominator":56,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":56,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T08:58:22.240369Z","state":"measured"},{"denominator":56,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":56,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/2607.21031/citation-record","integrity":"/paper/2607.21031/integrity","json":"/paper/2607.21031/citation-record.json","paper":"/paper/2607.21031"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:58:22.037859Z","title":"Alonso Ruíz and F","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.037859Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:d416e3727a98832272f326b122d6801e637a5707949735d7c56e39f2313b8ef0","observation_id":"dbd3cdcd-37e0-4f76-9bf1-195c5df28afc","resolution":{"observed_at":"2026-08-01T08:58:22.037859Z","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":"2026-08-01T08:58:22.042471Z","title":"Ambrosio","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.042471Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:bb2c5303b4a2f047f08b1cbcf59fa15655e44e2581524ed12d398c898db7c227","observation_id":"e3b8d4ad-818b-41de-9977-c0338ea09399","resolution":{"observed_at":"2026-08-01T08:58:22.042471Z","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":"2026-08-01T08:58:22.046298Z","title":"Ambrosio and S","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.046298Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:131ab8b8189f14406bdd938c39fd47e433648d43f6ffb49c547efe2e7baa79b9","observation_id":"61a41e7b-8bd0-402e-ac76-c1493f011e09","resolution":{"observed_at":"2026-08-01T08:58:22.046298Z","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":"2026-08-01T08:58:22.050282Z","title":"Ambrosio, N","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.050282Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:2feb4a042467e0db4fc0a7a77524808628196c77a47f79fbe88fef6c1e639a80","observation_id":"9017b182-f993-4c65-9a94-4a02780c8588","resolution":{"observed_at":"2026-08-01T08:58:22.050282Z","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":"2026-08-01T08:58:22.053956Z","title":"Ambrosio, R","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.053956Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:3d4d38ea2fb5040c7141da659b1de01be8ec597c55ab4b78f6c7cf637868cc69","observation_id":"2396d86e-d8e2-4172-a834-dd6185fffd9a","resolution":{"observed_at":"2026-08-01T08:58:22.053956Z","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":"2026-08-01T08:58:22.057747Z","title":"Ambrosio, M","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.057747Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:716c65969804630f4db2e6b15c083229a7b656d801fe1027253a01feddaa7bfc","observation_id":"4a5ccd02-f520-49d5-a903-94382976cfdb","resolution":{"observed_at":"2026-08-01T08:58:22.057747Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.10360","last_updated":"2026-07-16T07:36:48Z","snapshot_observed_at":"2026-08-14T06:58:43.930391Z","submitted_at":"2024-03-15T14:52:11Z","title":"An inflated dynamic Laplacian to track the emergence and disappearance of semi-material coherent sets","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.10360","snapshot_observed_at":"2026-08-01T08:58:22.061853Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.061853Z"},"links":{"cited_paper":"/paper/2403.10360","citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:6c15c30bac18377441e3b3755c1cf8b081788044b6b41a6f88ed2a13c58a97a8","observation_id":"a7b32d75-76a0-4e2e-9e1f-20acbf2b1a48","resolution":{"observed_at":"2026-08-01T08:58:22.061853Z","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":"2026-08-01T08:58:22.065645Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.065645Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:a8f1b2626b42acd1a7c61fee3e7f2172de58f8b726bde674a8a6aaf218cfa88f","observation_id":"bd99cfe6-6370-4d99-8409-d0548d0c807b","resolution":{"observed_at":"2026-08-01T08:58:22.065645Z","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":"2026-08-01T08:58:22.068996Z","title":"Berline, E","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.068996Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:6ef0e8b0bcdd01e5c3c56f1c6473adff849024ca5f0c3bff1bf37ca40c935ace","observation_id":"8729a236-74b9-40a4-86d9-41052d27a46f","resolution":{"observed_at":"2026-08-01T08:58:22.068996Z","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":"2026-08-01T08:58:22.072316Z","title":"Brokman, M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.072316Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:a1d92e9687d931c99bc6d491f507df42721f9ef69b70fa93d616db7f17f24166","observation_id":"2ca3ce0e-ed1d-46cb-b073-b1309f34bb8c","resolution":{"observed_at":"2026-08-01T08:58:22.072316Z","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":"2026-08-01T08:58:22.075709Z","title":"Buet and G","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.075709Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:7dd637e8b3380e9d1fabef7ff556bef69f52b786efa64ea2cc4676088e061039","observation_id":"68b4d1cc-beb6-4244-af9b-d7c1a1899814","resolution":{"observed_at":"2026-08-01T08:58:22.075709Z","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":"2026-08-01T08:58:22.079486Z","title":"Bögelein, F","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.079486Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:4b94f607786fd1a235ade328a4e26b56fdae7faf2344d58ccae34cf5bf13b57c","observation_id":"50efc0c3-5578-419b-ae80-a706f932d401","resolution":{"observed_at":"2026-08-01T08:58:22.079486Z","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":"2026-08-01T08:58:22.082892Z","title":"Bögelein, F","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.082892Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:674e7c59882d89b85f3f8fd20ba4d959b7780064dd7f7bb3200245bfd9aa4a17","observation_id":"df5db970-38b0-4faa-8493-9cf9887d11c2","resolution":{"observed_at":"2026-08-01T08:58:22.082892Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.15716","last_updated":"2025-03-19T21:57:44Z","snapshot_observed_at":"2026-08-07T16:50:35.338084Z","submitted_at":"2025-03-19T21:57:44Z","title":"Closed BV-extension and $W^{1,1}$-extension sets","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.15716","snapshot_observed_at":"2026-08-01T08:58:22.086220Z","title":"Caputo, J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.086220Z"},"links":{"cited_paper":"/paper/2503.15716","citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:4e5dd53723013d663844ae782e685f81263f395f7c4c85f2a7e4007f7dc9e763","observation_id":"f6e26329-e118-4eb5-a7bf-c207c3989475","resolution":{"observed_at":"2026-08-01T08:58:22.086220Z","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":"2026-08-01T08:58:22.089992Z","title":"Caputo, J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.089992Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:a94f58fa9717502fc29d72d77592a3757d72db2effc2ba1f62b96dec67b2a5b3","observation_id":"8a3df4d5-3aab-4660-8d91-38a758f12437","resolution":{"observed_at":"2026-08-01T08:58:22.089992Z","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":"2026-08-01T08:58:22.093474Z","title":"Carbonaro and G","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.093474Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:66929ff3acb20898b779e522d9fd8da3b1eaf92593645066c99d518e69163715","observation_id":"ab4fbfae-a90a-4e07-84f2-861093ae6698","resolution":{"observed_at":"2026-08-01T08:58:22.093474Z","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":"2026-08-01T08:58:22.096989Z","title":"Chodosh, M","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.096989Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:16f7de66fe350bcd1ba5e24745e90f84d68a9791df2f39e12ed3422a8b1c3492","observation_id":"73379261-46fd-44d1-acf1-c3b9bad20d72","resolution":{"observed_at":"2026-08-01T08:58:22.096989Z","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":"2026-08-01T08:58:22.100667Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.100667Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:67424da1a364c79fb96fd34722fe16a8f1576fa2e3eef96214e4a52e244a5761","observation_id":"257340c3-91d4-4fd4-af28-c4c580efb466","resolution":{"observed_at":"2026-08-01T08:58:22.100667Z","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":"2026-08-01T08:58:22.104176Z","title":"De Philippis, N","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.104176Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:d383a1ea1ac9c348f08dc128ca20eef9f79a24b1a268344d7a21a30673edc476","observation_id":"3a32936e-ce46-4e18-a212-3a7960f8833b","resolution":{"observed_at":"2026-08-01T08:58:22.104176Z","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":"2026-08-01T08:58:22.107712Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.107712Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:d656f1f7afbdf33d2741150bf550434f70843c7658fad1653c2066862180d70a","observation_id":"6cad287b-609c-4f50-b09b-ee8a906e5d6c","resolution":{"observed_at":"2026-08-01T08:58:22.107712Z","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":"2026-08-01T08:58:22.111188Z","title":"Elstrodt.Maß- und Integrationstheorie","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.111188Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:307907220755b7d82e5f4cc93f7160cfa9584c9c8868682db97264a1447bf233","observation_id":"d43d9654-0aa0-43f6-aa43-66635ee892bd","resolution":{"observed_at":"2026-08-01T08:58:22.111188Z","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":"2026-08-01T08:58:22.114759Z","title":"Federer.Geometric Measure Theory","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.114759Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:90a4b2c369f9f0d6c558a4abe7234e10d057f34a27722e02f02e0bda6c9f3de6","observation_id":"c08ea038-55a2-4734-bc5d-3976de277b67","resolution":{"observed_at":"2026-08-01T08:58:22.114759Z","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":"2026-08-01T08:58:22.118410Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.118410Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:1e7081c5faa4dc0778533d0608ee44f6c34a1e88002bba19be8d27096068c7b3","observation_id":"71010040-979d-4e3d-a87d-aed41445fe0d","resolution":{"observed_at":"2026-08-01T08:58:22.118410Z","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":"2026-08-01T08:58:22.121882Z","title":"Froyland and P","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.121882Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:30322b269afdd72f75f606a86e71ad50bbe5c43e81c008b43082bba48e075493","observation_id":"6a5c73ac-1f17-49ce-9410-67e60dfcad40","resolution":{"observed_at":"2026-08-01T08:58:22.121882Z","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":"2026-08-01T08:58:22.125455Z","title":"Fusco, V","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.125455Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:2fa76e7b303da3f1cadc2d8b54ab251bcc9516b946eb695e1dd7944b7cbc57e8","observation_id":"130f3d3e-a6fc-4194-a27e-7fe8775e2a9b","resolution":{"observed_at":"2026-08-01T08:58:22.125455Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2605.01979","last_updated":"2026-05-03T17:29:09Z","snapshot_observed_at":"2026-08-13T17:19:59.251203Z","submitted_at":"2026-05-03T17:29:09Z","title":"Sets of finite perimeter on Riemannian manifolds and stochastic completeness","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2605.01979","snapshot_observed_at":"2026-08-01T08:58:22.129117Z","title":"Gennaioli","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.129117Z"},"links":{"cited_paper":"/paper/2605.01979","citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:ba0f35f33208fb16e9d9868e4c88ea80c57a38a8e7a8c8f8bd92589529bf862f","observation_id":"ed060827-63fa-43c2-8306-7a81727f5d97","resolution":{"observed_at":"2026-08-01T08:58:22.129117Z","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":"2026-08-01T08:58:22.133107Z","title":"Grigor’yan.Heat Kernel and Analysis on Manifolds, volume 47 ofAMS/IP Studies in Advanced Mathe- matics","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.133107Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:e727b6c6eab3c43ed5b2faefc158cf233ae23777f2caa6870a4996bd2ef3d689","observation_id":"0b5128ae-9de4-4b29-ac74-3ec79df956e8","resolution":{"observed_at":"2026-08-01T08:58:22.133107Z","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":"2026-08-01T08:58:22.136848Z","title":null,"venue":null,"work_id":null,"year":1949},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.136848Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:32e43b5a7a9fd8794cb79e17159ff380a0457a7bfdd0d2a9a71d1c575eb4ac88","observation_id":"a261fe16-f6e9-4c03-bf85-f541b8fe3049","resolution":{"observed_at":"2026-08-01T08:58:22.136848Z","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":"2026-08-01T08:58:22.140646Z","title":"Guidetti, B","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.140646Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:785b2c1bf720e18191688bffd71aac179df06c7ed6d8f097cbc774f8fad71d71","observation_id":"7d8069b6-51da-423b-835b-ee372894dbf2","resolution":{"observed_at":"2026-08-01T08:58:22.140646Z","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":"2026-08-01T08:58:22.144376Z","title":"Güneysu and D","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.144376Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:1b5b1db0513a7aa3527e01bf43b3fcf5d2d14eaeea7f15b2f963673c89829d60","observation_id":"eabb08da-6643-4f09-b0a7-588dcdf199c8","resolution":{"observed_at":"2026-08-01T08:58:22.144376Z","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":"2026-08-01T08:58:22.147818Z","title":"Hakkarainen, J","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.147818Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:d10c8d0eaa50398497e7b6a6660b1240e1c9be3e3ee527d9abc2e83012bd136a","observation_id":"432d200b-b68a-4ca9-afc1-0e1b7907d21d","resolution":{"observed_at":"2026-08-01T08:58:22.147818Z","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":"2026-08-01T08:58:22.151226Z","title":"Hebey.Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities, volume 5 ofCourant Lecture Notes in Mathematics","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.151226Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:321bd705778f17664ebb79eb67748f68a59523044b522b593a437bbf351ae3ff","observation_id":"0dc13508-8285-4660-ac8a-468d7c06c3c2","resolution":{"observed_at":"2026-08-01T08:58:22.151226Z","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":"2026-08-01T08:58:22.154777Z","title":"Hong and A","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.154777Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:fb815abc4cb8dd96adc9957ff1c1bf597fe070942b42ae76edd163430ef9a3b4","observation_id":"e3ecc280-0a15-4cd6-b174-63561df45627","resolution":{"observed_at":"2026-08-01T08:58:22.154777Z","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":"2026-08-01T08:58:22.158407Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.158407Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:90a6df65e866cdb7730e508868bef842fbad4863faa24d4cb1d45d1205f36b1d","observation_id":"bed745fc-c814-425b-8c45-78f0120efebd","resolution":{"observed_at":"2026-08-01T08:58:22.158407Z","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":"2026-08-01T08:58:22.161820Z","title":"Korte, P","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.161820Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:c7d8ec383adaf039d6b743a0166241ac6144baf12560b3b1e1239243ec0a5c79","observation_id":"24c817ba-d657-4722-8d1b-3e049f33cde8","resolution":{"observed_at":"2026-08-01T08:58:22.161820Z","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":"2026-08-01T08:58:22.165668Z","title":"Kreuml and O","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.165668Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:25c66bab15dae5da8da43c77105ec082aa02234b51a175db713c0e212077b0d3","observation_id":"2a971b71-a1b5-4f2b-971d-67aedd88ee57","resolution":{"observed_at":"2026-08-01T08:58:22.165668Z","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":"2026-08-01T08:58:22.169072Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.169072Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:d9567154d528977311c7c0a8884d3615fb79778d531c00e5d9e22dc9b0ee0b79","observation_id":"81590f11-528c-43d0-a939-f427b55edc30","resolution":{"observed_at":"2026-08-01T08:58:22.169072Z","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":"2026-08-01T08:58:22.172542Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.172542Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:f47160ee77bd8b6009643f3a3555cc966e18c504b3f97c7ceac3243b106751f9","observation_id":"ea08edca-acf3-405c-9d51-fa2aac0b0b64","resolution":{"observed_at":"2026-08-01T08:58:22.172542Z","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":"2026-08-01T08:58:22.176021Z","title":"Lahti and N","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.176021Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:f00b51a56267291ea1c1f3d31a6b404b57cfb516658a13492b5bd659e4ec5ae6","observation_id":"9c079f88-2dc2-4f57-bd4d-62ced28607c8","resolution":{"observed_at":"2026-08-01T08:58:22.176021Z","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":"2026-08-01T08:58:22.179769Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.179769Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:f4582bde8d5b68e09bb02327c8dd5c5bff517f04f72ed25a121f4990b2662838","observation_id":"506dad9b-fd69-482d-9feb-e63085064835","resolution":{"observed_at":"2026-08-01T08:58:22.179769Z","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":"2026-08-01T08:58:22.183394Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.183394Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:d4e78a97e9b2b0e989285a4f8ba0f46ab346b80f590b38f5f195e7c649e49c33","observation_id":"7cd7ab76-6f55-4de1-bf97-e704adce3e7e","resolution":{"observed_at":"2026-08-01T08:58:22.183394Z","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":"2026-08-01T08:58:22.186927Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.186927Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:91d643b70a35f71d4b6bf75f0308fd6f3ff70d76608553aaba4c301e5ef695c0","observation_id":"fb00d267-e931-4d78-bac5-0ba549d7231c","resolution":{"observed_at":"2026-08-01T08:58:22.186927Z","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":"2026-08-01T08:58:22.190636Z","title":"Maggi.Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.190636Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:46a7d19309daddea59aea16dbe60706964bdaec56d7cb19acf8b2c1030a6e752","observation_id":"ed66ad3d-ad3a-4098-b6c3-448278fc9b79","resolution":{"observed_at":"2026-08-01T08:58:22.190636Z","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":"2026-08-01T08:58:22.195026Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.195026Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:475ed8631fab72feb2d9334ae6b5a6153cfc23668da4f45e82b45d386b399e0e","observation_id":"53c920bc-d06b-427c-a344-cd36f62be3d0","resolution":{"observed_at":"2026-08-01T08:58:22.195026Z","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":"2026-08-01T08:58:22.199148Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.199148Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:583c834ce3e83af79d0e02bfc37c82d18b70d7129c85ab1863f868902504145e","observation_id":"654bd502-f5da-433a-a543-28779075f291","resolution":{"observed_at":"2026-08-01T08:58:22.199148Z","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":"2026-08-01T08:58:22.202827Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.202827Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:772b3a1de8778af5cb1870bae97273651b4601013404d9afebc63a7d07d64815","observation_id":"a9d42291-e4c5-404e-944d-c38b30bd1d85","resolution":{"observed_at":"2026-08-01T08:58:22.202827Z","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":"2026-08-01T08:58:22.206418Z","title":"Miranda, D","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.206418Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:0e7c09439eba45330e5cb54164c3e9645ee08b355faa543c31bdd8d8045bdfb4","observation_id":"f0920685-a80e-4a56-bb6e-66c96b909bfa","resolution":{"observed_at":"2026-08-01T08:58:22.206418Z","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":"2026-08-01T08:58:22.210210Z","title":"Müller and G","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.210210Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:ab6fc463a52a9fc37910802f930687a9d04c4d9845380af6e0da2783dc80e7ff","observation_id":"7e557f08-27ae-4b90-a031-3141d1483d32","resolution":{"observed_at":"2026-08-01T08:58:22.210210Z","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":"2026-08-01T08:58:22.213664Z","title":"Nardi, B","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.213664Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:6e549731c6970801e24ec76e5f83c8fe6e3a8d46860d5d63ee158cc7fb17cf83","observation_id":"f1c99c35-6e3a-43fd-ae1c-5a21d19a101f","resolution":{"observed_at":"2026-08-01T08:58:22.213664Z","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":"2026-08-01T08:58:22.217350Z","title":"Pascale and M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.217350Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:88590ef7d073286da0f5d08a440ca9611154177bb86aac7125e6dc3c294947d6","observation_id":"45e725d6-419f-4e54-80fd-e457afd32c8f","resolution":{"observed_at":"2026-08-01T08:58:22.217350Z","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":"2026-08-01T08:58:22.221787Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.221787Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:254708c426093823e43642f8d6288f2fcad93c8ac4bc5a7b5065498d32e74044","observation_id":"824db6bf-5085-4817-9647-736eec7ddfa7","resolution":{"observed_at":"2026-08-01T08:58:22.221787Z","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":"2026-08-01T08:58:22.225816Z","title":"Ritoré.Isoperimetric Inequalities in Riemannian Manifolds, volume 348 ofProgress in Mathematics","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.225816Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:70265ed1c8aad71ac16bed41fabf954b75b3a518696510711016a928d715f8ae","observation_id":"be961051-8254-434e-be5c-2e954e430f22","resolution":{"observed_at":"2026-08-01T08:58:22.225816Z","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":"2026-08-01T08:58:22.229406Z","title":"Saloff-Coste","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.229406Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:31b70d93308f2d62266430e44bc8368ae63b970dd9390fa16f0f8f48ce4bf040","observation_id":"860a8eef-c4f4-47b6-ba30-1d84288fd24a","resolution":{"observed_at":"2026-08-01T08:58:22.229406Z","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":"2026-08-01T08:58:22.233140Z","title":"Saloff-Coste.Aspects of Sobolev-type Inequalities","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.233140Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:b01c928f19855acadec97c0e948a5bf64dd7b89ac6c1507e3d455b645f67b6ae","observation_id":"b9a95d5f-ab3e-4fd1-a0e0-27410dfcbeef","resolution":{"observed_at":"2026-08-01T08:58:22.233140Z","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":"2026-08-01T08:58:22.236901Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.236901Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:d48a91f62eb0b4a9fa54d3814ff4809c70efbb440fbf66c2f82a9947dbf481bd","observation_id":"2e392dbb-f6ba-4e77-a0fd-2d030a5c6b3a","resolution":{"observed_at":"2026-08-01T08:58:22.236901Z","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":"2026-08-01T08:58:22.240369Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-01T08:58:22.240369Z"},"links":{"citing_paper":"/paper/2607.21031"},"observation_digest":"sha256:c7ad79861da85c878b8c4dfb2b70cacbda4e023ee5856940aedb9ffdcb3a1367","observation_id":"d2a648f8-bd96-43ba-adc1-8e89b932e9a1","resolution":{"observed_at":"2026-08-01T08:58:22.240369Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.21031","last_updated":"2026-07-23T08:13:27Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-08-13T17:21:36.461461Z","submitted_at":"2026-07-23T08:13:27Z","title":"Structure theory of $BV$ functions and finite perimeter sets on Riemannian manifolds"},"reference_resolution":{"displayed":56,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":56,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":56},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 56 of 56 outbound references and 0 inbound Pith citation observations for arXiv:2607.21031."}