{"as_of":"2026-08-21T03:56:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:bbe8bf98d78264bf760352ae73672704f58aff60ab3885bee8ee5f27604fb4f7","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":"2026-08-16T11:58:40.581718Z","state":"measured"},{"denominator":14,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":14,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+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":"2026-05-20T01:46:07.823705Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-20T01:47:57.348946Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","version":1},"cited_work":{"arxiv_id":"2504.14629","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2504.14629","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"2025;26(2):176-185","venue":null,"work_id":"ba9bbce2-a7c6-408d-995c-34fa483f6659","year":2025},"citing_paper":{"arxiv_id":"2605.19680","last_updated":"2026-05-19T11:12:28Z","snapshot_observed_at":"2026-08-17T01:19:27.233640Z","submitted_at":"2026-05-19T11:12:28Z","title":"Contractibility of the space of $\\varepsilon$-nets in $\\mathbb{R}$","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-05-20T01:46:07.823705Z"},"links":{"cited_paper":"/paper/2504.14629","citing_paper":"/paper/2605.19680"},"observation_digest":"sha256:93f79c2058a9ae42937987ad3d20d534b53ed26333d9a19fe85d9a7dfcba4cf6","observation_id":"6f0f41bb-2910-4430-9aab-8bb5bb79b2bf","resolution":{"observed_at":"2026-05-20T01:47:57.352279Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2504.14629/citation-record","integrity":"/paper/2504.14629/integrity","json":"/paper/2504.14629/citation-record.json","paper":"/paper/2504.14629"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2110.06101","last_updated":"2021-10-12T15:49:45Z","snapshot_observed_at":"2026-08-16T17:49:55.793552Z","submitted_at":"2021-10-12T15:49:45Z","title":"Gromov-Hausdorff class: its completeness and cloud geometry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2110.06101","snapshot_observed_at":"2026-08-16T11:58:40.469995Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T11:58:40.469995Z"},"links":{"cited_paper":"/paper/2110.06101","citing_paper":"/paper/2504.14629"},"observation_digest":"sha256:aa940df4ca28e5713977c0506fc139dd7fc84dd4f6969ded6e2cb6bea5178b41","observation_id":"539a6072-7adc-4af3-98a2-62a74734a95a","resolution":{"observed_at":"2026-08-16T11:58:40.469995Z","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":"2026-08-16T11:58:40.475383Z","title":"Burago, Yu","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T11:58:40.475383Z"},"links":{"citing_paper":"/paper/2504.14629"},"observation_digest":"sha256:c66b0336f0b073aabc7b2feac9e82feb47d2c78c5c98f001a47e7dc14ceff51e","observation_id":"1631098a-f147-4a90-9b43-6cba47f30ef0","resolution":{"observed_at":"2026-08-16T11:58:40.475383Z","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":"2026-08-16T11:58:40.906607Z","title":"Edwards, The structure of superspace , Studies in Topology, Academic Press, 1975","venue":null,"work_id":"cd40bfdc-b379-4411-9de2-73487d7d7cc9","year":1975},"citing_paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T11:58:40.479737Z"},"links":{"citing_paper":"/paper/2504.14629"},"observation_digest":"sha256:41ece808cac8eee9a299dc687a64e8105e5a18a8e2385c248158c1e0382a9651","observation_id":"f70d9747-aef3-4529-8ce9-144aaced6abb","resolution":{"observed_at":"2026-08-16T11:58:40.966364Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:58:40.818209Z","title":"Gromov, Groups of polynomial growth and expanding maps , Publications Mathematiques I.H.E.S., 53 1981","venue":null,"work_id":"50a0856e-6493-43aa-b130-3691a7084e97","year":1981},"citing_paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T11:58:40.484024Z"},"links":{"citing_paper":"/paper/2504.14629"},"observation_digest":"sha256:90649dcfd162f13dd6de2067dcead540b22ef1fd79dab2424d73a0d58174550e","observation_id":"7cfcaaaf-7888-42a5-9a4e-a505fde4f19b","resolution":{"observed_at":"2026-08-16T11:58:40.823692Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:58:40.489046Z","title":"Gromov, Structures m´ etriques pour les vari´ et´ es riemanniennes, Textes Math","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T11:58:40.489046Z"},"links":{"citing_paper":"/paper/2504.14629"},"observation_digest":"sha256:05d1de9bda60673d2bfc885c82cd4125257c673fd80bf6308db97d8073c1da14","observation_id":"55e69380-76b2-470d-9318-1d9d2916f30e","resolution":{"observed_at":"2026-08-16T11:58:40.489046Z","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":"2026-08-16T11:58:40.796633Z","title":null,"venue":null,"work_id":"f1f57357-283e-4413-b153-75d92d48d16a","year":null},"citing_paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T11:58:40.493620Z"},"links":{"citing_paper":"/paper/2504.14629"},"observation_digest":"sha256:b58d1440f73a282bc8eacc3ea95cb066c92ea837c217adc71156a2766bf66413","observation_id":"e80a57a1-9aa7-43f7-b860-c3e6e4d90c16","resolution":{"observed_at":"2026-08-16T11:58:40.800973Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:58:40.498501Z","title":"Gromov, Metric structures for Riemannian and non-Riemannian space s, Birkh¨ user (1999)","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T11:58:40.498501Z"},"links":{"citing_paper":"/paper/2504.14629"},"observation_digest":"sha256:cf4997718ac07db712ce80b481aeec043139a924e3586ef79b2972a440e06ef4","observation_id":"59dba4f1-07a9-4cfb-ac42-c744cf7cfdc8","resolution":{"observed_at":"2026-08-16T11:58:40.498501Z","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":"2026-08-16T11:58:40.774943Z","title":"Sobolev, Distribution of integer lattice points in a ball centred at a diophantine point , Mathematika 56(01):118 - 134, 2010","venue":null,"work_id":"a665f403-adec-4a8e-b406-771ba3d0feec","year":2010},"citing_paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T11:58:40.503296Z"},"links":{"citing_paper":"/paper/2504.14629"},"observation_digest":"sha256:59885ade6401bad474e796a42953c3c766e43efe9e4a9d512bed7680d2469d47","observation_id":"f088d163-dbba-42ce-bc56-db16fd4a8354","resolution":{"observed_at":"2026-08-16T11:58:40.779486Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2105.00611","last_updated":"2022-10-18T11:13:15Z","snapshot_observed_at":"2026-08-20T14:30:02.748431Z","submitted_at":"2021-05-03T02:47:29Z","title":"The Gromov-Hausdorff distance between spheres","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.00611","snapshot_observed_at":"2026-08-16T11:58:40.507384Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T11:58:40.507384Z"},"links":{"cited_paper":"/paper/2105.00611","citing_paper":"/paper/2504.14629"},"observation_digest":"sha256:c6617374ded44116bba1118b88b43b3217094554c62147df00f9db2839f56eb0","observation_id":"836df00a-dfbd-44b0-be0c-5a2c44071926","resolution":{"observed_at":"2026-08-16T11:58:40.507384Z","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":"2026-08-16T11:58:40.761287Z","title":null,"venue":null,"work_id":"8a1fa4bb-7ffa-4c50-83e2-10240aa9b4d3","year":2025},"citing_paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T11:58:40.511734Z"},"links":{"citing_paper":"/paper/2504.14629"},"observation_digest":"sha256:a79c0be845e9972ab6fa6f5641ddae9e3ed768d2cb6e097776e0b267840d5cd2","observation_id":"88a59836-520d-4356-b0c5-425f4219036e","resolution":{"observed_at":"2026-08-16T11:58:40.765878Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.00756","last_updated":"2020-12-01T20:13:15Z","snapshot_observed_at":"2026-08-16T19:01:46.146125Z","submitted_at":"2020-12-01T20:13:15Z","title":"Lectures on Hausdorff and Gromov-Hausdorff Distance Geometry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2012.00756","snapshot_observed_at":"2026-08-16T11:58:40.515639Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T11:58:40.515639Z"},"links":{"cited_paper":"/paper/2012.00756","citing_paper":"/paper/2504.14629"},"observation_digest":"sha256:20abd9adf8262804be90c3855df7dc8463229692b4a80edd3f9f162a182c2c5a","observation_id":"0d68218a-06dc-4f3d-ace3-cd99947afa68","resolution":{"observed_at":"2026-08-16T11:58:40.515639Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1612.00728","last_updated":"2016-12-01T20:33:10Z","snapshot_observed_at":"2026-08-14T21:27:32.937685Z","submitted_at":"2016-12-01T20:33:10Z","title":"Who Invented the Gromov-Hausdorff Distance?","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1612.00728","snapshot_observed_at":"2026-08-16T11:58:40.519739Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T11:58:40.519739Z"},"links":{"cited_paper":"/paper/1612.00728","citing_paper":"/paper/2504.14629"},"observation_digest":"sha256:be0e1f96e864eee4e4c2edbbda6b39bd0b44fc37621e458b53c299b98c66a770","observation_id":"6ce9773a-b5c0-4d71-87d6-623559f99418","resolution":{"observed_at":"2026-08-16T11:58:40.519739Z","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":"2026-08-16T11:58:40.716977Z","title":"Vihrov, Denseness of metric spaces in general position in the Gromov –Hausdorff class , Topol","venue":null,"work_id":"37e59df6-23a7-4bd7-8d9d-1125b538159d","year":2024},"citing_paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T11:58:40.581718Z"},"links":{"citing_paper":"/paper/2504.14629"},"observation_digest":"sha256:bf788ed5c384dd5fcb02749c63b8e04f0fb0c5d483bfc9cc22cc46bc5c6b1435","observation_id":"c61479a4-f10a-4a81-9729-3b8b81133854","resolution":{"observed_at":"2026-08-16T11:58:40.751639Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2504.14629","last_updated":"2025-04-20T14:11:57Z","latest_version":1,"primary_category":"math.MG","snapshot_observed_at":"2026-08-16T11:42:05.428071Z","submitted_at":"2025-04-20T14:11:57Z","title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line"},"reference_resolution":{"displayed":13,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":0,"verified_fuzzy":4},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 1 inbound Pith citation observation for arXiv:2504.14629."}