{"as_of":"2026-08-12T05:56:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:494d5fde141b07726a6944fcb3318744b31f4760fa5563db853cb08fa81e72f6","coverage":[{"denominator":35,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":35,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T23:17:42.933944Z","state":"measured"},{"denominator":37,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":37,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T00:29:12.996737Z","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":"2026-07-04T11:39:46.803326Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.21194","snapshot_observed_at":"2026-08-07T00:29:12.996737Z","title":"On the clique number of random Cayley graphs and related topics.preprint, arXiv:2412.21194,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.14219","last_updated":"2025-06-17T06:14:30Z","snapshot_observed_at":"2026-08-07T00:15:53.524767Z","submitted_at":"2025-06-17T06:14:30Z","title":"The VC-dimension of random subsets of finite groups","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T00:29:12.996737Z"},"links":{"cited_paper":"/paper/2412.21194","citing_paper":"/paper/2506.14219"},"observation_digest":"sha256:4f0e7e5ead8487fd156945db2a11b33aaa561f33daffe08689ccf5e8cdfc5547","observation_id":"c1bd0312-eedf-41a5-a309-5ab997182fab","resolution":{"observed_at":"2026-08-07T00:29:12.996737Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"cited_work":{"arxiv_id":"2412.21194","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.21194","snapshot_observed_at":"2026-07-04T11:39:46.803326Z","title":"arXiv:2412.21194","venue":null,"work_id":"f5a95316-f0c1-4ed4-a342-8f884652f510","year":2024},"citing_paper":{"arxiv_id":"2606.23762","last_updated":"2026-06-22T13:46:32Z","snapshot_observed_at":"2026-07-31T05:45:32.248340Z","submitted_at":"2026-06-22T13:46:32Z","title":"Coloring sparse random Cayley graphs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-26T07:50:43.153960Z"},"links":{"cited_paper":"/paper/2412.21194","citing_paper":"/paper/2606.23762"},"observation_digest":"sha256:b9d4aa686f6f1c826989e3e25eea786e9f5b3a11b3c97d4438f3f6e042405094","observation_id":"196713fe-ddbc-4de3-93ed-cc3d850896c6","resolution":{"observed_at":"2026-07-04T11:39:46.804885Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2412.21194/citation-record","integrity":"/paper/2412.21194/integrity","json":"/paper/2412.21194/citation-record.json","paper":"/paper/2412.21194"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:17:43.435996Z","title":null,"venue":null,"work_id":"9b198d42-2fa0-4e42-a8cd-d7f6d1dd1a8b","year":1994},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.783829Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:7976675f56e7240569e2e9275d1d19a5fb91282f13b6579f98f98ce67d4831eb","observation_id":"723788c4-85bb-4634-b1c9-ceacdf8f4a9f","resolution":{"observed_at":"2026-08-10T23:17:43.440377Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.424042Z","title":"Alon, Research problems, Discrete Math","venue":null,"work_id":"62b41f15-156a-498c-b925-e12d7d9fced3","year":1995},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.789040Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:1773b585fb1fe6acd9781e60ab33465ece7a7eefab858d5628ac3bd71bc1e44b","observation_id":"d0a8acb8-f3eb-44b4-848c-125870bc01f3","resolution":{"observed_at":"2026-08-10T23:17:43.427967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.411472Z","title":"Alon, Graph powers, in Contemporary combinatorics, 1 1–28, Bolyai Soc","venue":null,"work_id":"66e29a09-2f85-4cbf-9442-d38a424b85ad","year":2002},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.793581Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:a9f6f95ef6a7f5ced3c73f64513b5c7fc01be8fc853aafd9ec3660cded1dd2cc","observation_id":"47f1358c-d827-45e0-81c0-f0636c4d9aef","resolution":{"observed_at":"2026-08-10T23:17:43.415858Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.397674Z","title":"Alon, Ramsey properties of Cayley graphs, Open proble m garden, available at http://www.openproblemgarden.org/op/ramsey_properties_of_cayley_graphs","venue":null,"work_id":"5e226f3c-5ab1-461f-b323-ccb658092303","year":null},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.798175Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:b4f87a67734f2e79b37be2779c4df6bd957446075ae3fa166e189dacc25b9560","observation_id":"f018eae7-87a4-4307-bff0-c47369ac6aff","resolution":{"observed_at":"2026-08-10T23:17:43.402737Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.384794Z","title":"Alon, The chromatic number of random Cayley graphs, European J","venue":null,"work_id":"3d98631d-04ca-41ca-9ac3-4f76064845db","year":2013},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.803382Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:26b54e507aeb83901f3e95d491985eb8e8f9ff75b4cc69edef79a443724c3327","observation_id":"7ecf45fb-876a-49db-9429-b869353f59b4","resolution":{"observed_at":"2026-08-10T23:17:43.389109Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.04460","last_updated":"2025-02-26T14:45:22Z","snapshot_observed_at":"2026-08-05T03:19:08.140633Z","submitted_at":"2023-09-08T17:42:11Z","title":"Essentially tight bounds for rainbow cycles in proper edge-colourings","version":2},"cited_work":{"arxiv_id":"2309.04460","doi":null,"metadata_source":"pith","pith_arxiv_id":"2309.04460","snapshot_observed_at":"2026-08-10T23:17:43.004779Z","title":"Essentially tight bounds for rainbow cycles in proper edge-colourings","venue":"math.CO","work_id":"2178ea52-bc93-41b5-89ea-c91653b0504d","year":2023},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.808289Z"},"links":{"cited_paper":"/paper/2309.04460","citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:f2ca629b6fd27774760bf05be6816c43395bd01eb09112c0e7714f3d5cb24b40","observation_id":"93863461-0e16-4a0a-9c34-09c1d5ee9320","resolution":{"observed_at":"2026-08-10T23:17:43.009428Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.370295Z","title":"Alon and A","venue":null,"work_id":"d87f6fd1-a36f-471c-ae21-af8e9a507e3f","year":1995},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.813143Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:2eac5e537847c9cb44fe14b73383b1a737d5c391e823ddbd919e739dcae0e5e7","observation_id":"60d0312c-aab6-4080-8a31-b23c2ad166bd","resolution":{"observed_at":"2026-08-10T23:17:43.375077Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.356718Z","title":"Bollobás and P","venue":null,"work_id":"f00cd468-8cf3-48c0-83a3-51d4e81153f2","year":1976},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.818094Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:9692ae51576a9781bd35d1e6dab07d6baba55cb6ca74b91ef66e706556265cfc","observation_id":"eced4a34-bc1a-492b-b2c6-1817f2c4e43f","resolution":{"observed_at":"2026-08-10T23:17:43.361653Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.343783Z","title":"Campos, On the number of sets with a given doubling cons tant, Israel J","venue":null,"work_id":"48ac3acc-1153-4282-91dc-c349a83e6ad4","year":2020},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.822923Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:e3c7d1dc294707bbd9bda8e4e4a428f19b9b5e7432de628ea5fa53c98e009f5d","observation_id":"d5b2ff41-9651-41d1-ab8e-0ee222b9677c","resolution":{"observed_at":"2026-08-10T23:17:43.348628Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.330094Z","title":"Campos, M","venue":null,"work_id":"975990a3-b31c-4227-8077-690a496385c8","year":2022},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.827242Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:78dcee5847209e4681eda9d33678d6a25198894656f537e57cf7d002efbefac9","observation_id":"7217e58f-5d76-41a2-b5e8-22bdcd202e9a","resolution":{"observed_at":"2026-08-10T23:17:43.334282Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.316119Z","title":"Campos, M","venue":null,"work_id":"6f385b5f-fc57-43dd-b5e2-1e92233c9720","year":2023},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.831477Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:ebf43ab0452477b95444fa9202e9a0f5fd1059c27c7f7c42739be094acdb65e2","observation_id":"43de7ebf-7355-41cf-8c5b-b8012a7746a6","resolution":{"observed_at":"2026-08-10T23:17:43.321098Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2303.09521","last_updated":"2025-08-04T22:39:40Z","snapshot_observed_at":"2026-07-06T15:04:23.117620Z","submitted_at":"2023-03-16T17:38:08Z","title":"An exponential improvement for diagonal Ramsey","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.09521","snapshot_observed_at":"2026-08-10T23:17:42.836018Z","title":"Campos, S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.836018Z"},"links":{"cited_paper":"/paper/2303.09521","citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:0c44940c6ade203dcd5a5ffd80eb8c6afad420f5c186af6e4e3479450fa23422","observation_id":"9bfb10e3-ea6b-48ca-8ec9-90e06421ecde","resolution":{"observed_at":"2026-08-10T23:17:42.836018Z","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":"2026-08-10T23:17:43.303119Z","title":"Chattopadhyay and J.-J","venue":null,"work_id":"5a33f62f-58c6-47aa-b68b-2357a6be9f50","year":2022},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.841074Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:9245451dbcc3d6314fd82967eb66fb32efc5109d0df70ebba9aec26a375084d4","observation_id":"c59186ac-cfc6-46f5-9de7-ae93e3b8af7f","resolution":{"observed_at":"2026-08-10T23:17:43.307450Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.291280Z","title":"Christofides and K","venue":null,"work_id":"e045a45e-4f6b-4b97-a172-814e46c06700","year":2012},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.844786Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:e5b12fe892bfb1987b83742317e383aa8af93349554fbdaee584bdcdd0454050","observation_id":"a6741441-4b78-4b13-b289-9d0abd86e21e","resolution":{"observed_at":"2026-08-10T23:17:43.294922Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.277965Z","title":"Conlon, J","venue":null,"work_id":"d519100a-d1c5-4ac3-8bec-9f3416b2db36","year":null},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.848886Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:23df2fb80e22d887cafc7a35d4003a1afe7f0ff2ec0911651d39f2d5a1d670fd","observation_id":"b3a44a53-ef7e-43d8-9f27-813b1cc60f36","resolution":{"observed_at":"2026-08-10T23:17:43.282432Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.263034Z","title":"Erdős, Some remarks on the theory of graphs, Bull","venue":null,"work_id":"b260adc5-b56c-4a60-a60c-45dd51611488","year":1947},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.852678Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:4f0a10d02e905b7068c146feb437ecd151b459ad706853705155978c9999c4c9","observation_id":"6e3e04e6-2b02-4395-885a-b12fa391b898","resolution":{"observed_at":"2026-08-10T23:17:43.268322Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.249070Z","title":"Erdős, A","venue":null,"work_id":"21fd71ef-e4c1-4f7b-b690-92668949b860","year":1965},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.856262Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:82eeffa796c606879775231e84b597f96f381302e6957db9843e67a6bb3c3162","observation_id":"4533e259-1cab-4409-8ce2-170791a7b26e","resolution":{"observed_at":"2026-08-10T23:17:43.253822Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.236941Z","title":"Erdős and G","venue":null,"work_id":"6f959c4c-9fd2-40c2-b28f-2610c37aff92","year":1935},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.859853Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:37fef964bf1e8ea363ebe11d5427d066ac36dd060bae1eb18d8e9d84d9b58e99","observation_id":"24e59439-1309-4146-9c36-b86e60f6024b","resolution":{"observed_at":"2026-08-10T23:17:43.240460Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.224381Z","title":"Erdős and A","venue":null,"work_id":"edbcb4d0-9fc6-4b09-9680-ef24f3d2ab80","year":1972},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.864087Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:7b4082edad72ff106635ea87c0cde83db2ecd133c3544595466b5f8581acbe3f","observation_id":"f2b7a8b1-934e-49ca-b78e-f96e939d6ecb","resolution":{"observed_at":"2026-08-10T23:17:43.228583Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.210557Z","title":"Even-Zohar, On sums of generating sets in Zn 2 , Combin","venue":null,"work_id":"0bef1f5c-e58f-475a-91a9-c7661080023d","year":2012},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.868398Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:5528105b817d66f66eb473877c7f8da772f6d3aecfd5becdfd22e694680f3eb6","observation_id":"8b7de6bd-7a1a-458a-aaf9-87145e2d2552","resolution":{"observed_at":"2026-08-10T23:17:43.215203Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.197351Z","title":"Even-Zohar and S","venue":null,"work_id":"534e481e-6675-4b3f-92f8-35c5fa037ccf","year":2014},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.872779Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:c93fcd1c1701f95a422d2c86cefe39bc2cbd4c7d55cfbdb3f3bb3690205e9b70","observation_id":"f539983d-8495-42cf-9fa8-3c33534dcd0a","resolution":{"observed_at":"2026-08-10T23:17:43.201713Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.183934Z","title":"Fox and H","venue":null,"work_id":"10cb442b-6de3-491a-920f-06ea0cec74a1","year":null},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.877868Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:57244b5bc1e920b47bdf26b8d76b74d78e770edcb9ff0aa34d5cd20932157e4c","observation_id":"cdd4c165-1170-42f7-9ba9-ae074ec68d1d","resolution":{"observed_at":"2026-08-10T23:17:43.188396Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.171155Z","title":"Green, Counting sets with small sumset, and the cliqu e number of random Cayley graphs, Combi- natorica 25 (2005), 307–326","venue":null,"work_id":"c7058642-7e6e-41bb-8b4e-2039793645af","year":2005},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.882137Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:cb06a3557bc68a4052b64ef67f6bb1ce3e46fe1ae5123c847522d1fdfd7f2966","observation_id":"0b57d8d3-4687-42ee-b0ef-e43551248b6c","resolution":{"observed_at":"2026-08-10T23:17:43.175676Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.157729Z","title":"Green and R","venue":null,"work_id":"c11fa6db-81a5-48be-8702-2924f50c9e02","year":2016},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.886232Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:780d121b94d9cb6d6016db754d3c619119433290c5da766044c32c89f1603f9c","observation_id":"0d0beae6-afdd-4505-a834-5a6805df2cc0","resolution":{"observed_at":"2026-08-10T23:17:43.162038Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.143610Z","title":null,"venue":null,"work_id":"a8e72061-bb35-4d02-8784-f31cd817a2a5","year":2018},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.890889Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:68329175aa9419f9173e342578efa9e6388e8af3a26f4c79f80f1204750cac66","observation_id":"1d040c2d-eb9f-4425-9c4f-522d644174e1","resolution":{"observed_at":"2026-08-10T23:17:43.148936Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.04492","last_updated":"2025-04-13T12:30:26Z","snapshot_observed_at":"2026-08-03T12:55:25.813297Z","submitted_at":"2024-07-05T13:30:27Z","title":"On the number of sets with small sumset","version":2},"cited_work":{"arxiv_id":"2407.04492","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.04492","snapshot_observed_at":"2026-08-10T23:17:42.968180Z","title":"On the number of sets with small sumset","venue":"math.CO","work_id":"d4f01f77-064d-4efa-baac-ddad7d688d51","year":2024},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.895956Z"},"links":{"cited_paper":"/paper/2407.04492","citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:43ae561ac8f0c1c4ad619b2688612d6a89e3be3f92eb25591a4ac46a06fd8435","observation_id":"d2ee5331-721a-4c9c-8005-120cc598c8e6","resolution":{"observed_at":"2026-08-10T23:17:42.974667Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.130324Z","title":null,"venue":null,"work_id":"ac71ad13-2048-4afe-baa6-c8b6580b0d3e","year":1976},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.901564Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:1f22ccff460ed616ed426ad5bf398e1d73d6c626097d733bf7ea441b9dbdf5a5","observation_id":"c6d28a61-ecf0-4d4c-8974-613207939106","resolution":{"observed_at":"2026-08-10T23:17:43.134588Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.118152Z","title":"McDiarmid and A","venue":null,"work_id":"f273a2c0-c304-4efa-bafd-1181a578b13e","year":1996},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.905875Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:597b464e475398550e7c219157b4f5e7076742d22f255411ec7807b21daf368e","observation_id":"24427e2b-73bc-4503-9614-a49a04af1d92","resolution":{"observed_at":"2026-08-10T23:17:43.121883Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.105500Z","title":"Mrazović, One-point concentration of the clique and chromatic numbers of the random Cayley graph on Fn 2 , SIAM J","venue":null,"work_id":"5ed7f32e-9434-4fa2-a8af-375b956818b7","year":2017},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.910499Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:53bed683c9b5f79990d5060227a2a2309f54737da213a8afb111c079f60551e5","observation_id":"78329ebb-12f1-4f7c-9cbf-9d3dd09c3e0d","resolution":{"observed_at":"2026-08-10T23:17:43.109803Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.091680Z","title":"Otter, The number of trees, Ann","venue":null,"work_id":"7923c7b2-9722-43f7-bb9c-650da9a4ab1b","year":1948},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.914510Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:5c6fb83057bb937283ed99daf299b1d03ebe68372bfaca861e610bbe5eac9ed2","observation_id":"dcc64536-06a1-49fe-9ead-2a8f496f90d5","resolution":{"observed_at":"2026-08-10T23:17:43.096163Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.076820Z","title":null,"venue":null,"work_id":"39164382-a009-4072-ba0f-d63c7a500751","year":1999},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.918139Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:3294ff48b3bf1772df7848ab6ea09b0f88e1057d29c85c390ef253ceb43ffa0c","observation_id":"f8cb9ba4-32e3-4354-93b1-0eab1a399636","resolution":{"observed_at":"2026-08-10T23:17:43.081791Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.062222Z","title":"Sanders, On a theorem of Shkredov, Online J","venue":null,"work_id":"d0de3882-b51b-4a7b-a884-9bb1fa21be9e","year":2010},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.922033Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:be0196488814777f6ee570b9ab3ecac92def9dfeca9561f4ea393bc782e37ac9","observation_id":"1b76fa36-28ef-4bbe-87ea-af0a550affc2","resolution":{"observed_at":"2026-08-10T23:17:43.066757Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.047230Z","title":"Sanders, Bootstrapping partition regularity of lin ear systems, Proc","venue":null,"work_id":"9a54ad95-22aa-4c23-a23d-d2bc7da7ff81","year":2020},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.925903Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:19f879aa0b270322e31c56055dbe6d1ca9d0e80cd26f6c7c0d4e1ad02fe6fade","observation_id":"54a75f67-9c97-49d9-b775-caef3bd93423","resolution":{"observed_at":"2026-08-10T23:17:43.052111Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.033796Z","title":"Schoen and I","venue":null,"work_id":"0706d77e-ce0c-45df-89b4-b6f3d27e45fc","year":2016},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.929942Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:21b4f72b7d535b92258ff2af38e70c44b2e61193d6cbc4aa695baab1c9df767b","observation_id":"aef0ef85-ef37-4a35-83d2-4ff985da3dd5","resolution":{"observed_at":"2026-08-10T23:17:43.038084Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-10T23:17:43.019682Z","title":null,"venue":null,"work_id":"f32a6e25-2555-4a84-9318-8964c19c17bb","year":1964},"citing_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T23:17:42.933944Z"},"links":{"citing_paper":"/paper/2412.21194"},"observation_digest":"sha256:9e9d61208b8e7bb63214abbc9ec72ed9f23cef40ceffaad8b3611f4524a43362","observation_id":"8cdd4e1c-17b0-425d-acb3-277a549527dc","resolution":{"observed_at":"2026-08-10T23:17:43.024245Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-11T06:51:36.682955Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics"},"reference_resolution":{"displayed":35,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":2,"verified_fuzzy":27},"total_outbound_references":35},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 2 inbound Pith citation observations for arXiv:2412.21194."}