{"as_of":"2026-08-10T22:40:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:82b9b85c9b73965f0a74f2b60acaa33417bf43438f4fa57732750fff533a9847","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-27T21:21:32.948717Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T10:18:32.879564Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.07468","snapshot_observed_at":"2026-07-14T10:18:32.879564Z","title":"Minimizing clusters with prescribed asymptotic geometry","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.10636","last_updated":"2026-07-12T08:09:11Z","snapshot_observed_at":"2026-08-03T04:59:16.548222Z","submitted_at":"2026-07-12T08:09:11Z","title":"Anisotropic isoperimetric double tilings of the plane","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-07-14T10:18:32.879564Z"},"links":{"cited_paper":"/paper/2606.07468","citing_paper":"/paper/2607.10636"},"observation_digest":"sha256:204f10ef1ebbc01ae1325fdc4761b81b8cdb7000a22517c056d090a5d339ef05","observation_id":"46d146f6-6bb2-4d54-9369-5410ddeadb01","resolution":{"observed_at":"2026-07-14T10:18:32.879564Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2606.07468/citation-record","integrity":"/paper/2606.07468/integrity","json":"/paper/2606.07468/citation-record.json","paper":"/paper/2606.07468"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T21:21:32.948717Z","title":"Alama, L","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:e30993688748896720049e6652f8d6e671eb90456d5bf195a449397642769703","observation_id":"8f344204-59a8-40f2-9aa0-da8539b64f43","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Alama, L","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:2d8dd1e75bf99b0038eeca0734722d8875e00d4a93c18a308ca124cabe050419","observation_id":"5b8a60b2-7c64-4f5a-a079-2b5713352174","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:3947f8a9e02fd41afb3bd5354c8bb0985333b7f50c03c21e9bf9fd382ca358b4","observation_id":"e2eea60e-b8ab-4458-a712-4d1551097e7b","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":null,"venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:219a9cf060d54c3561456c675a4a1b79bb31ba7cc62b285610f64e167efa5dd5","observation_id":"93ac146f-0761-4d6a-84d4-72d112ec032a","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:e272f97d5667405761b5c9f7fe481789103b05d01ec22a246fbc58900e4aecfa","observation_id":"be4f980b-0df7-4814-ab8d-963e3b28a274","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":null,"venue":null,"work_id":null,"year":1969},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:106be1613e69f0cd76ae2a2237fc1f8f27b2e5a7a0547dafb2ff9aca9a9fca28","observation_id":"8ea02fe4-e761-4c79-8bc1-b53790340f10","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Bonacini, R","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:bfedc340fecd9536903e06dfd9f6783518931b67300d4aa8cced19a5de54245d","observation_id":"16786af1-b66b-4cb5-9110-2a13357d0d9b","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Bronsard, R","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:6a302e225bb06ee117e27f3d257bfd6b32d5100e0132836712856d9455323700","observation_id":"33860505-2be0-48ad-8dc2-0dd2b1576d16","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Bronsard and M","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:7a6d0e239cdf88993f368c03bbd3ed6100f50ef2b09fb3cd84db0afc559c7194","observation_id":"5409684c-a606-49d1-8c33-558ca414c7f8","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Colombo, N","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:d1e98ab9873526baf065695843e4b4d4312483e235244454f593d14e1ba539c6","observation_id":"77ad7ec4-857d-4843-915b-b26e1013f0ea","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Davini,On calibrations for Lawson’s cones, Rend","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:15a34563f962962581c059aa040e76732b207a8873859f11f7cd766f4c559436","observation_id":"1fb359b1-8de7-4411-a430-a53e73c5aa90","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"De Philippis and E","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:42e67e78a6007210832ac2d267eec2f1a17c0d8353cfe457611cb4c1af1c6e74","observation_id":"0a7de689-4dad-4e0d-9ed3-cdb6a1e1029b","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Edelen and L","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:8a279ec5512c6a7b703760e803f9f7ce87df2dcdf24fed336a5e13a4a22cded5","observation_id":"8f61f38a-9df8-4df5-8074-c3791e0a039f","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Edelen and G","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:4a00f3ec8699f60ef7e69fce82b85935a90edbcc2dae6872029a4c5833c09b01","observation_id":"5a5c1b88-484b-4e76-8637-63d35df14a72","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Foisy, M","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:a5a60af75476e6686cf1ffc89b8e7ff4382228df911e64e12f9b0147d4485f7c","observation_id":"7f86f3ea-0528-4e97-ada9-539235764914","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Hardt and L","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:a5cc6bfd317a43068b4a594c64f9bc32af504c4df2de095c31f276dea9398828","observation_id":"be0cc7c4-d297-4032-899a-f2f301ca7e55","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Hutchings, F","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:a7a9da5bc9af2b7f958c265d3baeb91c586e271fa61d0348a29d50c166b75b4f","observation_id":"4ea73803-2d4d-4d66-b93d-dd8f7fc2e79c","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":null,"venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:c1efdbea41d9e47d1442c996acaec9bf974b72eeb9b468ef5b48e06053371abe","observation_id":"603f1e8e-dbcc-4a18-b1b0-95332c9b230b","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Maggi,Sets of finite perimeter and geometric variational problems, Cambridge Studies in Advanced Mathematics, vol","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:aa7ad69ce8f477957304bc533ac2eb0a58fe5a499e4f677ebf5e2f353871c89c","observation_id":"386b9a5e-d1e5-4485-bd7a-ffc00624cdd0","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Milman and J","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:e24bdf2081d6aa0fe8e944d24b8566e290fc4f33e9507231763019f3595dfc75","observation_id":"1ec83051-b3e7-46fb-8471-131fff0f57e7","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"1, 71–188","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:1dde262358522deb170d7a635505418ea34f4d99b86c65acb5baf57f31d292b3","observation_id":"9d3fef74-c5ba-4a12-8c0c-a419089df4e5","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Milman and B","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:caa740b7f7c82e48198c024f9897b5ddb514814ebd6ccc2fb7961b890ad212fb","observation_id":"63a4b35c-9acb-472b-9bbd-fb98f7a069bc","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Novaga, E","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:4aea6633df5c676765f01c80cd6fe8b8fc48556898854941c0325bdce357217c","observation_id":"36e6185e-1655-4f3b-9d21-222fb27f0a63","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:bb7206adcc9949f6a6923a3c848011632ae77431da6e7d91866c4da1baa93f0b","observation_id":"75730a6c-05c4-4071-bfe9-30e9da62d1f7","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Paolini and V","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:3bd1551143c0a6d226a046a78a0c1537132e4f23b7d0cdce8cfefccbb5d357d5","observation_id":"c33615ec-16c7-4de0-8af2-91fc2b1065b9","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:728bfa1a1faaf57a81c67ba9c60acc7650807b329019acf076f8cbdf634de889","observation_id":"e257236a-6fab-41e6-bbe1-68e1f4c58465","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:dc76564396075d2d96c4dd7e906280d0a4516e00d48c235f28aad7519ac39c11","observation_id":"87ed2142-4d95-4679-8ac8-c9938367ada7","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:b70308a7f50a6d27ef652449e67667945d4eaec6918db578e5788d5da6e44af7","observation_id":"7b049722-ba8f-4b74-9bcc-237bea7593de","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Simon,Lectures on geometric measure theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, vol","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:5d774c1e72f883ef77e894fd996e21296a47b69ad608cb4eddceca15c78c0a32","observation_id":"115f9c48-7325-464c-96b3-573537acc594","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"2, 327–335","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:a455dd05d0575c99d5a8aef0c2f30b4725811107136ff082bd3ef1f601aff210","observation_id":"d10a59ce-a197-4b22-bb3d-e27e4ec5d4e2","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Differential Geom.30(1989), no","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:5a81df7cf6842dacf3554fd0872b6e6b7bc2a3a8ab5353aaaeb1d2cf598bc3ba","observation_id":"a118bd81-d9c7-4e8b-8660-13338e84080b","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:f667cc5ca9794627d8b80db5302bbacfce04e362875f3a318539b0cf3e11c103","observation_id":"22737c89-3487-4a35-ae55-fc7a94d095b2","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Simon and B","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:b0d8ff672d8203e4168fb85ed93a1a891f6036baa1636a70f6e24a8f558d0e87","observation_id":"2fe66dff-694d-4d28-9a70-f36d8011c4ac","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Sternberg, G","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:454c7f59534e2e9bf0f027580155c38809511d4e0d4fc74e62c10e5044bbe605","observation_id":"bd2f5cc9-8bf0-45fd-9849-874d86d894c2","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":null,"venue":null,"work_id":null,"year":1973},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:94273af15f40fe0b336e8ee7f2a94b47e7ac50d479639b182b3b715d363f6100","observation_id":"e414c22b-1679-43b0-b0c4-cf2f9b275cef","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Wang,Mean convex smoothing of mean convex cones, Geometric and Functional Analysis34(2024/02/01), no","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:dba7c3d6d1db7462e13ada4fab03a1ccd0e2954c57c2c01215ab71bcbcd195fa","observation_id":"fd037e19-166e-467f-84ae-1a3c85dfec90","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","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":"2026-06-27T21:21:32.948717Z","title":"Wichiramala,Proof of the planar triple bubble conjecture, J","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-06-27T21:21:32.948717Z"},"links":{"citing_paper":"/paper/2606.07468"},"observation_digest":"sha256:8c445034c762c83a266361e00bfc271dd11370fe4301d16a663ac5b438721cff","observation_id":"ab526387-3d08-410a-8fa4-cf7e106d3953","resolution":{"observed_at":"2026-06-27T21:21:32.948717Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.07468","last_updated":"2026-06-05T17:21:08Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-01T08:53:48.097296Z","submitted_at":"2026-06-05T17:21:08Z","title":"Minimizing clusters with prescribed asymptotic geometry"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":37,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":37},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2606.07468."}