{"as_of":"2026-08-18T12:24:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:57d56e0b0dc8a66ccbbe5d0876a9e11d0b9ef0548d021c95044aec64b8422aef","coverage":[{"denominator":36,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":36,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T19:29:44.118936Z","state":"measured"},{"denominator":36,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":36,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+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/2506.16858/citation-record","integrity":"/paper/2506.16858/integrity","json":"/paper/2506.16858/citation-record.json","paper":"/paper/2506.16858"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T19:29:44.625832Z","title":"Ajtai, J","venue":null,"work_id":"a0ff6046-9a05-42bc-91d5-b1218bbc2444","year":1981},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:43.943733Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:31e185f11dc48bbbcac9dbd07e61b203b2a5c5ac570c9c4836f937381d97bedc","observation_id":"9fbc4c95-3201-4719-b34b-d5ea957bc5f0","resolution":{"observed_at":"2026-08-15T19:29:44.631130Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.613006Z","title":"Ajtai, J","venue":null,"work_id":"71953dcd-e699-458b-a640-416bbcf5f779","year":1982},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:43.948913Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:aeec9e5bf75699263bd505582a5aa26880e39ee9468abf6c49ca71acfc031e94","observation_id":"c8aa5d54-0cb5-4ccc-ae6c-5036a101a93a","resolution":{"observed_at":"2026-08-15T19:29:44.617350Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:43.953645Z","title":"Alon and J","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:43.953645Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:0700f6d554b2cccb17a13a4e679ca5d66d3420768a80347314f6462de51a3a26","observation_id":"88ba7af2-df21-44b0-831a-c9021f2c84c6","resolution":{"observed_at":"2026-08-15T19:29:43.953645Z","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":"2026-08-15T19:29:44.591819Z","title":null,"venue":null,"work_id":"b65585f3-e9cb-4b5f-b523-e993fa69e4d8","year":2022},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:43.958429Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:aee5b860522f8d6bc8553492ee9b3ffc3853aca705f9df8b449ea2ace59d05e1","observation_id":"221c0afd-cbc2-40cc-826e-0c0607af509b","resolution":{"observed_at":"2026-08-15T19:29:44.596315Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.579653Z","title":null,"venue":null,"work_id":"d7ff4be0-5222-4477-b856-d8c0ad8967e2","year":2023},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:43.963300Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:7eae1def715159605ef0688b675ea53ac5de30ffa615f0a9cb4138025e0257b3","observation_id":"cabcc8e8-cb3e-4703-8b7d-a466eaad8e66","resolution":{"observed_at":"2026-08-15T19:29:44.583575Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.567001Z","title":"Anastos, S","venue":null,"work_id":"18f0931c-6bd6-4d0f-9ba6-ad06ad482c5c","year":2024},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:43.967805Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:67ce2380167fb22774e96b97a8769e5752dc6eb1537412f048828c1b672af8bd","observation_id":"72462993-fedc-43ba-bb40-c834b48a7481","resolution":{"observed_at":"2026-08-15T19:29:44.572005Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.04436","last_updated":"2025-05-07T14:03:39Z","snapshot_observed_at":"2026-08-17T16:37:33.347111Z","submitted_at":"2025-05-07T14:03:39Z","title":"Nearly spanning cycle in the percolated hypercube","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.04436","snapshot_observed_at":"2026-08-15T19:29:43.972585Z","title":"Anastos, S","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:43.972585Z"},"links":{"cited_paper":"/paper/2505.04436","citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:6813861adb8a73a698540d6869671a99d26392659ce3f55a2130ac54e375c3c6","observation_id":"fbffa5e2-5a67-4c59-9e85-d83f09f70baa","resolution":{"observed_at":"2026-08-15T19:29:43.972585Z","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":"2026-08-15T19:29:43.977498Z","title":"Beveridge, A","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:43.977498Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:de6e4a3ddccde05361810f24b5f9a6c75ce55ba64cea317ff92b8208a1702202","observation_id":"80ea6e12-3b69-4606-97bb-a1af99d31eb4","resolution":{"observed_at":"2026-08-15T19:29:43.977498Z","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":"2026-08-15T19:29:44.547449Z","title":"Bollob´ as","venue":null,"work_id":"d6aa48c4-7b43-4cf6-a682-bd73c705187f","year":1983},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:43.982777Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:945c755fbab253a82bbe1e7ab85afce7fad2235e89014201d9bbba02328ce637","observation_id":"ddf559ed-37a4-4e01-8151-47a51b4880a3","resolution":{"observed_at":"2026-08-15T19:29:44.551230Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.531472Z","title":"Bollob´ as.Random graphs, volume 73 ofCambridge Studies in Advanced Mathematics","venue":null,"work_id":"996812c5-68c3-4174-a5ce-539cfe681cde","year":2001},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:43.988054Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:48f94d9a5e26b40cec4a7652b05b7c8e20d38ada8a670435aa383ce8bdf1cec4","observation_id":"14cdce34-8b15-4001-b13f-ad2cbf30d52e","resolution":{"observed_at":"2026-08-15T19:29:44.537104Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.517472Z","title":"Bollob´ as, Y","venue":null,"work_id":"22b83a95-cd4b-43e7-a04e-e34c5829684b","year":1992},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:43.992884Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:40ca3bce5bacf995e73b923ef415443049d16936ef6ed559ea3c15dc5dc03871","observation_id":"cfa1ffa9-ca12-449f-bddf-b87dabee1010","resolution":{"observed_at":"2026-08-15T19:29:44.521577Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.504284Z","title":null,"venue":null,"work_id":"51dbc7f0-626b-468e-abc4-e7f47cb8c04a","year":1976},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:43.997737Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:181d09350e3351e2741d72feaa26cf9354ede9cae0f51068faaf66ea68439ab4","observation_id":"93c361ae-a2c9-4626-82a2-10078ac4658e","resolution":{"observed_at":"2026-08-15T19:29:44.508342Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.491223Z","title":"Chv´ atal","venue":null,"work_id":"755007a4-a058-4a6a-8c73-7c87505ca9c2","year":1972},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.003342Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:da6f298553bf8778a2bbbcfb9b10dfc6a218ee1fd8746abcdcf12584219bf7aa","observation_id":"e6c7fce8-2b5e-4321-84c4-c6d9703b7c21","resolution":{"observed_at":"2026-08-15T19:29:44.495705Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.478766Z","title":"Condon, A","venue":null,"work_id":"e726149b-ac8e-4b2b-a5df-493e5c6eb813","year":2024},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.007596Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:5ee423b0f0cd0be829b3c092aed068fd79b846cdb803f87e7c48a45f5184c1f6","observation_id":"f0592935-bdf1-4fa2-ba97-716c5cbbf46f","resolution":{"observed_at":"2026-08-15T19:29:44.482527Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.466887Z","title":"Cooper and A","venue":null,"work_id":"89273134-fcb7-4d49-984f-06387d0e9d9d","year":1987},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.013700Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:c13ecd0144cdfcd1ed11f790e84798edc0e0a4777b6c3f68854a46cbef3f19f9","observation_id":"ddfc1dd3-592a-4d6c-95f4-00a3efa9b62a","resolution":{"observed_at":"2026-08-15T19:29:44.470770Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.018521Z","title":null,"venue":null,"work_id":null,"year":1952},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.018521Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:3563c7515ead8b55dc684e22e2b1469a400ca43dd9b42c0320250e9221f23ce5","observation_id":"c462683d-7122-4026-a801-a403613747de","resolution":{"observed_at":"2026-08-15T19:29:44.018521Z","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":"2026-08-15T19:29:44.446385Z","title":"Diskin, J","venue":null,"work_id":"475d8168-d7fb-4112-9a0f-2156640c12f0","year":2024},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.023719Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:9e7c25672f1127f832a518569d1dce3e767f93e0ce4133abcd2998c2e10a98f8","observation_id":"4c2ad68a-affa-4705-908c-4a90aa9573da","resolution":{"observed_at":"2026-08-15T19:29:44.450714Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.430918Z","title":"Diskin and M","venue":null,"work_id":"8899d0b9-f4e8-4e9c-a840-53eb7b7fc07f","year":2023},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.027583Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:6faaa5e9e91745b3a890432f669d2ff5f135e1c454379316ab0a497fddc6cf81","observation_id":"3e99d135-73ea-490b-97cb-5e0676846f01","resolution":{"observed_at":"2026-08-15T19:29:44.436063Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.417840Z","title":"Diskin and M","venue":null,"work_id":"98b7a411-616b-4162-8e83-29e2d82b041d","year":2024},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.032199Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:293f78a354cc07fd52d3112c386d56bb6c45196e44f24a25feb05b770dc4200a","observation_id":"12be25d1-2288-46cc-9419-7124da2ed366","resolution":{"observed_at":"2026-08-15T19:29:44.421991Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.06603","last_updated":"2024-04-14T09:20:38Z","snapshot_observed_at":"2026-08-16T14:19:47.893781Z","submitted_at":"2024-02-09T18:29:38Z","title":"Hamiltonicity of expanders: optimal bounds and applications","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.06603","snapshot_observed_at":"2026-08-15T19:29:44.036973Z","title":"Dragani´ c, R","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.036973Z"},"links":{"cited_paper":"/paper/2402.06603","citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:e0de8ec06e76f19986b2a56a8eb42fd356bd6f4208ef1ee79c24eb32b529bf82","observation_id":"68237444-ea2a-4cbf-9b90-d1f0d30df051","resolution":{"observed_at":"2026-08-15T19:29:44.036973Z","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":"2026-08-15T19:29:44.042144Z","title":"Erd˝ os and A","venue":null,"work_id":null,"year":1960},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.042144Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:a97edb11d0cd31db71712391e78b37e47930b1f5a7689a4f2f8959eb71e0694a","observation_id":"9e25bdd8-2c07-4125-b045-903bd7d562fa","resolution":{"observed_at":"2026-08-15T19:29:44.042144Z","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":"2026-08-15T19:29:44.396433Z","title":"Fernandez de la Vega","venue":null,"work_id":"9fe9861a-145d-43b3-b11a-23729b3ce264","year":1979},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.046211Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:192f48f89340d0d273bb7eb15fa28c2b360f0e9010e9fd55c97f8f8815020be9","observation_id":"cf8924bf-d89f-4e91-b939-0101e6db081e","resolution":{"observed_at":"2026-08-15T19:29:44.400512Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.382079Z","title":"Friedman and M","venue":null,"work_id":"5272179f-19fd-4500-a4b8-5ec622c5bd37","year":2021},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.051424Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:0f723027863a503f3a1e757d166199b40016cfcb31626ff8bc8580b111189dcf","observation_id":"57b34a8c-256b-48d6-a6f0-33b1dafa231a","resolution":{"observed_at":"2026-08-15T19:29:44.386358Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.367691Z","title":null,"venue":null,"work_id":"3fc13512-1f7a-4a2b-b72b-b9a71ef3e049","year":2003},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.057250Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:3ffaebf1f420bf33e4a50c055946d929157f9cf64b04d0dc4a8d6eff5d61bab2","observation_id":"85b983f6-b155-46fa-8a14-45c1335e87ed","resolution":{"observed_at":"2026-08-15T19:29:44.371837Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.353415Z","title":null,"venue":null,"work_id":"924260e5-fe54-4667-84ca-6c4db9627699","year":1966},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.062808Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:c20515d430797c592c844aebf81ed9be436a0c505c5ce9b8617667a9e53a4bd0","observation_id":"a7f69fdd-4988-4b6c-a589-51df6c4b8078","resolution":{"observed_at":"2026-08-15T19:29:44.357894Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.340402Z","title":"Hefetz, M","venue":null,"work_id":"878879ad-902a-4290-b5c0-49d2c63ecc1d","year":2009},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.067665Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:e547d45060046951ce99326ab50f42d8606dad43b542375948e159b7d8ad15ab","observation_id":"0c0327f7-d501-4784-b5d9-c4beb9059aa6","resolution":{"observed_at":"2026-08-15T19:29:44.344680Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.326611Z","title":"Karo´ nski and A","venue":null,"work_id":"31bb0f85-5d1e-4694-a461-7545a1bb9e59","year":1981},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.072054Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:0b410cd4e490d0aa18adf7d87a13e5a02e84bb9e09ee33db4fac15c63b906cb1","observation_id":"e936b50e-2dc7-41de-b9c1-e762ff435125","resolution":{"observed_at":"2026-08-15T19:29:44.330605Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.311393Z","title":null,"venue":null,"work_id":"103b1a96-7826-44ee-a4b2-67146a8a3836","year":1972},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.077471Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:c66d3aa4ba6ced96c629f1d4ac085f873f7a9aa4d1c43298cba45bb9c9de4259","observation_id":"3493eb26-187f-4e20-9a78-cf6e2bbe5a9f","resolution":{"observed_at":"2026-08-15T19:29:44.315806Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.082647Z","title":"Koml´ os and E","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.082647Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:ca7e46c49fa04ff309a953c6b4575e08e643e7749584efd41b58e28d0446a3b4","observation_id":"b268f4a3-8dcd-44f7-b69d-4d7b6832541d","resolution":{"observed_at":"2026-08-15T19:29:44.082647Z","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":"2026-08-15T19:29:44.286861Z","title":null,"venue":null,"work_id":"2b1efeca-b46c-47fc-b2ad-4fb117fc8922","year":1977},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.086811Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:9770deeb0d7518348333afe66a1aa7b2cd840b4961a68cfacfcbc8e48071e42d","observation_id":"3d57251c-1da5-4eb1-b59f-92effe28bbbe","resolution":{"observed_at":"2026-08-15T19:29:44.292012Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.07210","last_updated":"2023-11-13T10:12:07Z","snapshot_observed_at":"2026-08-16T19:08:55.361400Z","submitted_at":"2023-11-13T10:12:07Z","title":"Component sizes in the supercritical percolation on the binary cube","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.07210","snapshot_observed_at":"2026-08-15T19:29:44.090934Z","title":"Krivelevich","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.090934Z"},"links":{"cited_paper":"/paper/2311.07210","citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:b68abb6b94a3dbd471226c53c69fa8a04a5065adce7c263e3e7506645ca099c8","observation_id":"6dca8077-a9b6-48d9-8fb9-dcfc1cb99e1b","resolution":{"observed_at":"2026-08-15T19:29:44.090934Z","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":"2026-08-15T19:29:44.273390Z","title":"Krivelevich, C","venue":null,"work_id":"5d7e185b-6580-402c-b442-61f54e9fd172","year":2010},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.097810Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:bdd55fa7b5fd193d873a46912ec60432c51b8e356174223a3500fec15c7e5899","observation_id":"69eb2a42-441f-49a8-b4b5-d86f48751e27","resolution":{"observed_at":"2026-08-15T19:29:44.278000Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.102909Z","title":"Krivelevich and B","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.102909Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:b0033e74203c28e4cc975555957424a0ca0a80a0dd56728d062ab5b9053819e9","observation_id":"683b66df-88ef-411f-9607-5edfc17bb569","resolution":{"observed_at":"2026-08-15T19:29:44.102909Z","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":"2026-08-15T19:29:44.242373Z","title":"Lee and W","venue":null,"work_id":"b6e9177c-016b-4860-a781-59f8362b20f6","year":2012},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.108667Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:c2d8370ab78e92c0f21211c65cd8776a60518e3024c641a18f40a658aa8e5698","observation_id":"c28c13a9-3fd9-4aa2-b0f6-5e7bfdcbdbb1","resolution":{"observed_at":"2026-08-15T19:29:44.249809Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T19:29:44.113842Z","title":null,"venue":null,"work_id":null,"year":1960},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.113842Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:0c561e6211ba29c5711cd1938f8c1c4983dcf132d5da6e8d00774ffd49ae7833","observation_id":"959e29be-7871-4e2a-8c38-e5280de2e3f3","resolution":{"observed_at":"2026-08-15T19:29:44.113842Z","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":"2026-08-15T19:29:44.208912Z","title":null,"venue":null,"work_id":"25b690c3-2843-4b92-b656-c7569c10f937","year":1976},"citing_paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-15T19:29:44.118936Z"},"links":{"citing_paper":"/paper/2506.16858"},"observation_digest":"sha256:323de174cd4859e9f39c5513a0645d53f2db44329cbc6ad705ece03afc9d82d5","observation_id":"bf49848d-3497-4c90-9957-533f740d0472","resolution":{"observed_at":"2026-08-15T19:29:44.215846Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.16858","last_updated":"2025-06-20T09:15:22Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-17T23:38:20.978714Z","submitted_at":"2025-06-20T09:15:22Z","title":"Cycle lengths in the percolated hypercube"},"reference_resolution":{"displayed":36,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":18,"verified_exact":0,"verified_fuzzy":18},"total_outbound_references":36},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2506.16858."}