{"as_of":"2026-08-19T08:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:07b010c21a213012c99a4747002f0c6ed05e0200bf19e053c37de414d3c96532","coverage":[{"denominator":13,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":13,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-26T18:59:58.177328Z","state":"measured"},{"denominator":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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/2606.18569/citation-record","integrity":"/paper/2606.18569/integrity","json":"/paper/2606.18569/citation-record.json","paper":"/paper/2606.18569"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1109/7.104271","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Abel and James W","venue":"IEEE Transactions on Aerospace and Electronic Systems","work_id":"91e1e395-8b40-4e33-8ade-0ddb8ac748cc","year":1991},"citing_paper":{"arxiv_id":"2606.18569","last_updated":"2026-06-17T00:41:19Z","snapshot_observed_at":"2026-08-07T01:47:38.031705Z","submitted_at":"2026-06-17T00:41:19Z","title":"Tangent Spheres and Integer Distances","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-26T18:59:58.177328Z"},"links":{"citing_paper":"/paper/2606.18569"},"observation_digest":"sha256:5a75255df6351278184bb2a0c5eca90b9c56083403522c31fe62277453065204","observation_id":"caebdddd-d8ab-43f5-aa20-78539b98573d","resolution":{"observed_at":"2026-06-26T19:19:48.564817Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T18:59:58.177328Z","title":"Anning and Paul Erdős","venue":null,"work_id":null,"year":1945},"citing_paper":{"arxiv_id":"2606.18569","last_updated":"2026-06-17T00:41:19Z","snapshot_observed_at":"2026-08-07T01:47:38.031705Z","submitted_at":"2026-06-17T00:41:19Z","title":"Tangent Spheres and Integer Distances","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-26T18:59:58.177328Z"},"links":{"citing_paper":"/paper/2606.18569"},"observation_digest":"sha256:6a237e12c739996dc552d5077332fd94765c98d8ec11413ed170324c74691634","observation_id":"f13bbaaf-ddfd-4daa-8938-7725268f489d","resolution":{"observed_at":"2026-06-26T18:59:58.177328Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0020-0190(79)90074-7","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Information Processing Letters","work_id":"ed96e952-c817-4720-ba79-278b8f5df944","year":1979},"citing_paper":{"arxiv_id":"2606.18569","last_updated":"2026-06-17T00:41:19Z","snapshot_observed_at":"2026-08-07T01:47:38.031705Z","submitted_at":"2026-06-17T00:41:19Z","title":"Tangent Spheres and Integer Distances","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-26T18:59:58.177328Z"},"links":{"citing_paper":"/paper/2606.18569"},"observation_digest":"sha256:2e6240bd5b2d7ea3a17866745e45be0c6f0784d3bb43dedec53c3e50af800f2f","observation_id":"7bf645e1-6402-4484-a6c6-dfdb456beb7e","resolution":{"observed_at":"2026-06-26T19:19:48.569660Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01914786","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Chandru, D","venue":"The Visual Computer","work_id":"0eade683-e2f1-440c-8b4d-bccd6b4b083b","year":1989},"citing_paper":{"arxiv_id":"2606.18569","last_updated":"2026-06-17T00:41:19Z","snapshot_observed_at":"2026-08-07T01:47:38.031705Z","submitted_at":"2026-06-17T00:41:19Z","title":"Tangent Spheres and Integer Distances","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-26T18:59:58.177328Z"},"links":{"citing_paper":"/paper/2606.18569"},"observation_digest":"sha256:f52ea9c7d9a9c013957bcf55d4c9c147c9851fdf6a59fbde584811ee1327ba9b","observation_id":"c24dd096-6ebb-47a2-8ace-ca727048efb2","resolution":{"observed_at":"2026-06-26T19:19:48.570352Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T18:59:58.177328Z","title":null,"venue":null,"work_id":null,"year":1960},"citing_paper":{"arxiv_id":"2606.18569","last_updated":"2026-06-17T00:41:19Z","snapshot_observed_at":"2026-08-07T01:47:38.031705Z","submitted_at":"2026-06-17T00:41:19Z","title":"Tangent Spheres and Integer Distances","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-26T18:59:58.177328Z"},"links":{"citing_paper":"/paper/2606.18569"},"observation_digest":"sha256:70d1cffc2209ac674ea292bcac27c811c1aefe3fbfc8bb3c205c471827d305a6","observation_id":"05645671-6723-4b53-8415-30ce1fff367a","resolution":{"observed_at":"2026-06-26T18:59:58.177328Z","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":"2026-06-26T18:59:58.177328Z","title":"A Möbius-invariant power dia- gram and its applications to soap bubbles and planar Lombardi drawing.Discrete & Compu- tational Geometry, 52(3):515–550, 2014.doi:10","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2606.18569","last_updated":"2026-06-17T00:41:19Z","snapshot_observed_at":"2026-08-07T01:47:38.031705Z","submitted_at":"2026-06-17T00:41:19Z","title":"Tangent Spheres and Integer Distances","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-26T18:59:58.177328Z"},"links":{"citing_paper":"/paper/2606.18569"},"observation_digest":"sha256:8ad22feb45a75b1cfb01a6fc019a77c7e579354eefdbcdfc0525f2664141fadf","observation_id":"1851bed2-8cd8-4b4a-97fc-170ea6fabbbd","resolution":{"observed_at":"2026-06-26T18:59:58.177328Z","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":"10.7155/jgaa.00571","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Bipartite and series-parallel graphs without planar Lombardi drawings.J","venue":"Journal of Graph Algorithms and Applications","work_id":"ac9c6e66-7ee9-4e9c-8654-f2454b155605","year":2021},"citing_paper":{"arxiv_id":"2606.18569","last_updated":"2026-06-17T00:41:19Z","snapshot_observed_at":"2026-08-07T01:47:38.031705Z","submitted_at":"2026-06-17T00:41:19Z","title":"Tangent Spheres and Integer Distances","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-26T18:59:58.177328Z"},"links":{"citing_paper":"/paper/2606.18569"},"observation_digest":"sha256:cd1285f9b5b45e43bce014b328bef31dedf5fa422d4ac7d3fd45b804e756d82e","observation_id":"7b9a378b-0ac5-4df3-9876-82e840c53c04","resolution":{"observed_at":"2026-06-26T19:19:48.565756Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-07-11T16:19:39.808658+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-11T16:19:39.808658+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.20382/jocg.v17i2a2","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Non-Euclidean Erdős–Anning the- orems.J","venue":"arXiv (Cornell University)","work_id":"33aac7ca-24e0-4f16-b945-75bda2578c18","year":2026},"citing_paper":{"arxiv_id":"2606.18569","last_updated":"2026-06-17T00:41:19Z","snapshot_observed_at":"2026-08-07T01:47:38.031705Z","submitted_at":"2026-06-17T00:41:19Z","title":"Tangent Spheres and Integer Distances","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-26T18:59:58.177328Z"},"links":{"citing_paper":"/paper/2606.18569"},"observation_digest":"sha256:1b19ee5db2e45eed9d8a054b7e56086d92eb382377950c5c4ef17baaafc0b4ad","observation_id":"68f6f431-e0b7-45bd-b314-e31ba42ea8d8","resolution":{"observed_at":"2026-06-26T19:19:48.571899Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/s0002-9904-1945-08490-0","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Integral distances.Bulletin of the American Mathematical Society, 51:996","venue":"Bulletin of the American Mathematical Society","work_id":"0bfae365-cf9e-47b6-a0ac-38a0d421faf6","year":1945},"citing_paper":{"arxiv_id":"2606.18569","last_updated":"2026-06-17T00:41:19Z","snapshot_observed_at":"2026-08-07T01:47:38.031705Z","submitted_at":"2026-06-17T00:41:19Z","title":"Tangent Spheres and Integer Distances","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-26T18:59:58.177328Z"},"links":{"citing_paper":"/paper/2606.18569"},"observation_digest":"sha256:63a4947ffc8a8115acb4e2f7dcc87e1190401858dd5de302d2de3f5c20731756","observation_id":"49bf991d-d635-495a-a93f-384e5bb9f23c","resolution":{"observed_at":"2026-06-26T19:19:48.571415Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.10821","last_updated":"2025-08-25T13:51:01Z","snapshot_observed_at":"2026-08-16T14:26:06.135969Z","submitted_at":"2024-01-19T17:13:56Z","title":"On integer distance sets","version":3},"cited_work":{"arxiv_id":"2401.10821","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2401.10821","snapshot_observed_at":"2026-07-04T15:49:57.278357Z","title":"On integer distance sets","venue":null,"work_id":"3c8d6ec2-0ed2-4af7-9873-226472521c64","year":2024},"citing_paper":{"arxiv_id":"2606.18569","last_updated":"2026-06-17T00:41:19Z","snapshot_observed_at":"2026-08-07T01:47:38.031705Z","submitted_at":"2026-06-17T00:41:19Z","title":"Tangent Spheres and Integer Distances","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-26T18:59:58.177328Z"},"links":{"cited_paper":"/paper/2401.10821","citing_paper":"/paper/2606.18569"},"observation_digest":"sha256:773ccd0571516768e303ad212fbb5063ae01fa7f9d7af85785521f05f7dfdbd0","observation_id":"bd76d3d0-e118-4ede-86cc-1ffe3406f49d","resolution":{"observed_at":"2026-07-04T02:49:25.112435Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T18:59:58.177328Z","title":"Chelsea Publishing, 1952","venue":null,"work_id":null,"year":1952},"citing_paper":{"arxiv_id":"2606.18569","last_updated":"2026-06-17T00:41:19Z","snapshot_observed_at":"2026-08-07T01:47:38.031705Z","submitted_at":"2026-06-17T00:41:19Z","title":"Tangent Spheres and Integer Distances","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-26T18:59:58.177328Z"},"links":{"citing_paper":"/paper/2606.18569"},"observation_digest":"sha256:3472ba2ac76075915ebd86ffbd574bb9e3c70cd3d5cf5a5a79a8e29611c3645a","observation_id":"c7108fc8-0310-479b-8099-aec7eef6fa1b","resolution":{"observed_at":"2026-06-26T18:59:58.177328Z","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":"10.3233/fi-1995-2242","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Convex distance functions in 3-space are different.Fundamenta Informaticae, 22(4):331–352, 1995.doi:10.3233/FI-1995-2242","venue":"Fundamenta Informaticae","work_id":"92c7a92a-2143-4efa-9e98-3894966f9fc5","year":1995},"citing_paper":{"arxiv_id":"2606.18569","last_updated":"2026-06-17T00:41:19Z","snapshot_observed_at":"2026-08-07T01:47:38.031705Z","submitted_at":"2026-06-17T00:41:19Z","title":"Tangent Spheres and Integer Distances","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-26T18:59:58.177328Z"},"links":{"citing_paper":"/paper/2606.18569"},"observation_digest":"sha256:4054ba1b1dff55eebd83cdfd8eb18438938f94e40d69b3cdc8b000b420bcc469","observation_id":"34240f5d-2a01-439e-b7b9-5b26bcbf31ed","resolution":{"observed_at":"2026-06-26T19:19:48.566841Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00454-003-0014-7","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Noteonintegraldistances.Discrete & Computational Geometry, 30(2):337–342, 2003","venue":"Discrete & Computational Geometry","work_id":"1d1f06b7-6cf5-450d-af29-4e856d418d61","year":2003},"citing_paper":{"arxiv_id":"2606.18569","last_updated":"2026-06-17T00:41:19Z","snapshot_observed_at":"2026-08-07T01:47:38.031705Z","submitted_at":"2026-06-17T00:41:19Z","title":"Tangent Spheres and Integer Distances","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-26T18:59:58.177328Z"},"links":{"citing_paper":"/paper/2606.18569"},"observation_digest":"sha256:c87baec72a0edde7f098e67ab5f188239b1e60c92b54ae58d504ceea695d1b4c","observation_id":"783ba9a7-5c34-4e20-85cf-04348f55b367","resolution":{"observed_at":"2026-06-26T19:19:48.568750Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2606.18569","last_updated":"2026-06-17T00:41:19Z","latest_version":1,"primary_category":"cs.CG","snapshot_observed_at":"2026-08-07T01:47:38.031705Z","submitted_at":"2026-06-17T00:41:19Z","title":"Tangent Spheres and Integer Distances"},"reference_resolution":{"displayed":13,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":9,"verified_fuzzy":0},"total_outbound_references":13},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2606.18569."}