{"as_of":"2026-08-21T21:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0f3f794b62222b76108a55af4dc4ca0b83cdf6a0ec893cdb5418ec38e4910bb5","coverage":[{"denominator":11,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":11,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T14:27:53.034139Z","state":"measured"},{"denominator":11,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":11,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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/2505.19172/citation-record","integrity":"/paper/2505.19172/integrity","json":"/paper/2505.19172/citation-record.json","paper":"/paper/2505.19172"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2503.02613","last_updated":"2025-03-04T13:33:35Z","snapshot_observed_at":"2026-08-21T20:21:25.489294Z","submitted_at":"2025-03-04T13:33:35Z","title":"A full classification of the isometries of the class of ball-bodies","version":1},"cited_work":{"arxiv_id":"2503.02613","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.02613","snapshot_observed_at":"2026-08-07T14:27:53.244030Z","title":"A full classification of the isometries of the class of ball-bodies","venue":"math.MG","work_id":"04282f1e-c9b5-4e7a-bdad-86fbcf87772b","year":2025},"citing_paper":{"arxiv_id":"2505.19172","last_updated":"2025-08-20T14:28:29Z","snapshot_observed_at":"2026-08-21T16:35:26.271869Z","submitted_at":"2025-05-25T14:44:39Z","title":"Some inequalities of isoperimetric type for the c-affine surface area","version":4},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T14:27:52.976680Z"},"links":{"cited_paper":"/paper/2503.02613","citing_paper":"/paper/2505.19172"},"observation_digest":"sha256:cfe274d7db80c7a37d86ffdc6c57877c71fe55ca58e2defde0631bd397c04954","observation_id":"2b0bfcf7-1db9-439b-9d6f-0d5d73241fbb","resolution":{"observed_at":"2026-08-07T14:27:53.248942Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:27:53.357088Z","title":"Florentin","venue":null,"work_id":"b2e9a69e-a938-4fd0-af4d-588b36282411","year":2025},"citing_paper":{"arxiv_id":"2505.19172","last_updated":"2025-08-20T14:28:29Z","snapshot_observed_at":"2026-08-21T16:35:26.271869Z","submitted_at":"2025-05-25T14:44:39Z","title":"Some inequalities of isoperimetric type for the c-affine surface area","version":4},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T14:27:52.982700Z"},"links":{"citing_paper":"/paper/2505.19172"},"observation_digest":"sha256:3ced7030ebfc24bccb7ea25c00011dd9b4613da2d9cc6d37e35f2048c02de4a9","observation_id":"91912e4f-baa0-41d1-a825-9ffd3abdd7eb","resolution":{"observed_at":"2026-08-07T14:27:53.361853Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.09200","last_updated":"2025-05-18T13:26:51Z","snapshot_observed_at":"2026-08-20T18:33:56.403657Z","submitted_at":"2025-05-14T07:24:42Z","title":"An in-depth study of ball-bodies","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.09200","snapshot_observed_at":"2026-08-07T14:27:52.987756Z","title":"Florentin","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.19172","last_updated":"2025-08-20T14:28:29Z","snapshot_observed_at":"2026-08-21T16:35:26.271869Z","submitted_at":"2025-05-25T14:44:39Z","title":"Some inequalities of isoperimetric type for the c-affine surface area","version":4},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T14:27:52.987756Z"},"links":{"cited_paper":"/paper/2505.09200","citing_paper":"/paper/2505.19172"},"observation_digest":"sha256:518993ac0166b1d93d4cf1affb442876cb76067fbfcfbc20e0910aaab15be88d","observation_id":"5e3fd2bf-33c5-48a0-8660-a56c57c9c0dd","resolution":{"observed_at":"2026-08-07T14:27:52.987756Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:27:53.340661Z","title":null,"venue":null,"work_id":"0dcbe49a-e6bc-4908-91d2-85dc04e81a04","year":2015},"citing_paper":{"arxiv_id":"2505.19172","last_updated":"2025-08-20T14:28:29Z","snapshot_observed_at":"2026-08-21T16:35:26.271869Z","submitted_at":"2025-05-25T14:44:39Z","title":"Some inequalities of isoperimetric type for the c-affine surface area","version":4},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T14:27:52.994490Z"},"links":{"citing_paper":"/paper/2505.19172"},"observation_digest":"sha256:3e290fc31cd2cbcbfe3d1512d0fc195621be3fabb30fc634ee622615cde4b7b2","observation_id":"fb93976d-bb4c-48ec-86e9-9d6626e55e25","resolution":{"observed_at":"2026-08-07T14:27:53.345064Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2411.10302","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:27:53.203855Z","title":"Selected topics from the theory of intersections of balls","venue":null,"work_id":"f22646e7-864b-4de9-9168-5424528e6a86","year":2024},"citing_paper":{"arxiv_id":"2505.19172","last_updated":"2025-08-20T14:28:29Z","snapshot_observed_at":"2026-08-21T16:35:26.271869Z","submitted_at":"2025-05-25T14:44:39Z","title":"Some inequalities of isoperimetric type for the c-affine surface area","version":4},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T14:27:52.999935Z"},"links":{"citing_paper":"/paper/2505.19172"},"observation_digest":"sha256:22629ac1d8e6036729f80560521b42a3e6c6d74bb52006052ac28078d1a7e3e0","observation_id":"fc8db2f8-500c-496d-b1f2-3f3e1085a989","resolution":{"observed_at":"2026-08-07T14:27:53.211261Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:27:53.322820Z","title":"Bonnesen and W","venue":null,"work_id":"597fb961-a329-4a65-9dde-0035aff70de5","year":1974},"citing_paper":{"arxiv_id":"2505.19172","last_updated":"2025-08-20T14:28:29Z","snapshot_observed_at":"2026-08-21T16:35:26.271869Z","submitted_at":"2025-05-25T14:44:39Z","title":"Some inequalities of isoperimetric type for the c-affine surface area","version":4},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T14:27:53.005503Z"},"links":{"citing_paper":"/paper/2505.19172"},"observation_digest":"sha256:9ef37aa3f6585a78411faa46eb038ddc8f8d06c63ab5b91076507c33cb0de28d","observation_id":"a8b2a281-33ab-4ade-831f-b64d13e37104","resolution":{"observed_at":"2026-08-07T14:27:53.329006Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:27:53.307311Z","title":"Geometric inequalities , volume 285","venue":null,"work_id":"d144793e-0618-47a4-a7cd-f0ab045c42de","year":2013},"citing_paper":{"arxiv_id":"2505.19172","last_updated":"2025-08-20T14:28:29Z","snapshot_observed_at":"2026-08-21T16:35:26.271869Z","submitted_at":"2025-05-25T14:44:39Z","title":"Some inequalities of isoperimetric type for the c-affine surface area","version":4},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T14:27:53.011521Z"},"links":{"citing_paper":"/paper/2505.19172"},"observation_digest":"sha256:71ab0f8838f770fda840fe6884862d0cb5259c42d4ad6e5bc8b2edba64509063","observation_id":"7de322cd-d1f7-4a9f-a0b2-3bdebc807701","resolution":{"observed_at":"2026-08-07T14:27:53.312419Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:27:53.292615Z","title":"Chakerian","venue":null,"work_id":"add7c6c3-504e-4d60-8eb2-4846f16a5c1d","year":1967},"citing_paper":{"arxiv_id":"2505.19172","last_updated":"2025-08-20T14:28:29Z","snapshot_observed_at":"2026-08-21T16:35:26.271869Z","submitted_at":"2025-05-25T14:44:39Z","title":"Some inequalities of isoperimetric type for the c-affine surface area","version":4},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T14:27:53.016341Z"},"links":{"citing_paper":"/paper/2505.19172"},"observation_digest":"sha256:ce95103860292a010287b340c82d0192b3fdfa5dffc1e54197cc6364a38e61c6","observation_id":"63b96fa6-a288-433b-bd68-f7975408dc33","resolution":{"observed_at":"2026-08-07T14:27:53.297189Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:27:53.275929Z","title":"Absolute continuity for curvature measures of convex sets, iii","venue":null,"work_id":"788fbf15-ebab-472c-831e-52ffca6f2e22","year":2002},"citing_paper":{"arxiv_id":"2505.19172","last_updated":"2025-08-20T14:28:29Z","snapshot_observed_at":"2026-08-21T16:35:26.271869Z","submitted_at":"2025-05-25T14:44:39Z","title":"Some inequalities of isoperimetric type for the c-affine surface area","version":4},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T14:27:53.022747Z"},"links":{"citing_paper":"/paper/2505.19172"},"observation_digest":"sha256:63945989d6ee6029a1ef0a30239d50bfb6794ec9654f48c1c710163705740e89","observation_id":"69e18de9-d210-44c2-8215-d8167d889a39","resolution":{"observed_at":"2026-08-07T14:27:53.281974Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:27:53.260321Z","title":"Convex Bodies: The Brunn-Minkowski Theory , volume 151 of Encyclopedia of Mathematics and its Applications","venue":null,"work_id":"7545526f-1e00-45da-b5d9-637757a3e047","year":2013},"citing_paper":{"arxiv_id":"2505.19172","last_updated":"2025-08-20T14:28:29Z","snapshot_observed_at":"2026-08-21T16:35:26.271869Z","submitted_at":"2025-05-25T14:44:39Z","title":"Some inequalities of isoperimetric type for the c-affine surface area","version":4},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T14:27:53.028030Z"},"links":{"citing_paper":"/paper/2505.19172"},"observation_digest":"sha256:425c3ec7d4c2d4868714a136a6d99eb424176d3232981890a290113e0aace039","observation_id":"21f75b28-e26e-440c-9bb8-a13631e44a98","resolution":{"observed_at":"2026-08-07T14:27:53.265615Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.15488","last_updated":"2025-04-21T23:43:09Z","snapshot_observed_at":"2026-08-21T15:58:13.093649Z","submitted_at":"2025-04-21T23:43:09Z","title":"Floating bodies for ball-convex bodies","version":1},"cited_work":{"arxiv_id":"2504.15488","doi":null,"metadata_source":"pith","pith_arxiv_id":"2504.15488","snapshot_observed_at":"2026-08-07T14:27:53.070958Z","title":"Floating bodies for ball-convex bodies","venue":"math.MG","work_id":"3e9a28b8-db1a-4315-887a-a3acc67d3bcc","year":2025},"citing_paper":{"arxiv_id":"2505.19172","last_updated":"2025-08-20T14:28:29Z","snapshot_observed_at":"2026-08-21T16:35:26.271869Z","submitted_at":"2025-05-25T14:44:39Z","title":"Some inequalities of isoperimetric type for the c-affine surface area","version":4},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T14:27:53.034139Z"},"links":{"cited_paper":"/paper/2504.15488","citing_paper":"/paper/2505.19172"},"observation_digest":"sha256:84bb4a3afbd3f118f5028a270f76c2eaf1e14465de9e4674d65e7b3daf8259e9","observation_id":"eac57a42-c9e9-4ca5-9355-d9134ce876b0","resolution":{"observed_at":"2026-08-07T14:27:53.078330Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.19172","last_updated":"2025-08-20T14:28:29Z","latest_version":4,"primary_category":"math.MG","snapshot_observed_at":"2026-08-21T16:35:26.271869Z","submitted_at":"2025-05-25T14:44:39Z","title":"Some inequalities of isoperimetric type for the c-affine surface area"},"reference_resolution":{"displayed":11,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":2,"verified_exact":2,"verified_fuzzy":6},"total_outbound_references":11},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 0 inbound Pith citation observations for arXiv:2505.19172."}