{"as_of":"2026-08-07T16:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f77fcb4e5f048e69afe2ef5027c481ef5c607ab7735a8a9965df4462079a8ef3","coverage":[{"denominator":67,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":67,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T19:41:01.539676Z","state":"measured"},{"denominator":68,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":68,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T16:02:29.579908Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-05T16:02:29.669103Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"cited_work":{"arxiv_id":"2507.05697","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.05697","snapshot_observed_at":"2026-08-05T16:02:29.669103Z","title":"When does a tree activate the random graph?","venue":"math.CO","work_id":"3e46fcbe-78c7-4393-920e-ae09d307f13e","year":2025},"citing_paper":{"arxiv_id":"2508.19435","last_updated":"2025-08-26T21:09:45Z","snapshot_observed_at":"2026-08-05T16:02:28.498530Z","submitted_at":"2025-08-26T21:09:45Z","title":"Weak saturation numbers of large complete bipartite graphs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T16:02:29.579908Z"},"links":{"cited_paper":"/paper/2507.05697","citing_paper":"/paper/2508.19435"},"observation_digest":"sha256:f925ced30885e7c8da5afe4a9209a8a90eede438d40748d0076537b9bfb90b8a","observation_id":"4ed526f0-d3c2-4496-ba56-b60cca3e0f66","resolution":{"observed_at":"2026-08-05T16:02:29.675761Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.05697/citation-record","integrity":"/paper/2507.05697/integrity","json":"/paper/2507.05697/citation-record.json","paper":"/paper/2507.05697"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:41:02.410093Z","title":"Adler, U","venue":null,"work_id":"8a230e4a-d1b9-437e-a4c7-21e186fe73fa","year":2003},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:59.994330Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:0f0fe60894ad13bcbd6d4dc8e072341dba4d1cf5d888d73ba1c066db934c9cd2","observation_id":"21279f3a-5e0e-479d-8644-5964bfe6b54d","resolution":{"observed_at":"2026-08-06T19:41:02.413758Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.398749Z","title":"Aizenman, J.L","venue":null,"work_id":"18ca3075-1123-429e-bc0b-a6da84075cc4","year":1988},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.075914Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:0e165ec4265bcb0c5f94bcb40a5d1ade4f6c12e64aac3ecef628979bc82b4d96","observation_id":"82d87b89-0622-4fca-876b-0d95d87cd954","resolution":{"observed_at":"2026-08-06T19:41:02.402466Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.386289Z","title":"Ajtai, J","venue":null,"work_id":"3dea36b4-140e-4329-88dd-7da727e11d89","year":1985},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.200446Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:3dd72b58fb326306374d5733879791f238d3b2f4893e48e2ec187db64618b660","observation_id":"9da0a727-0a7d-460b-9ba8-a130faf295d1","resolution":{"observed_at":"2026-08-06T19:41:02.390060Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.374916Z","title":"Alon, An extremal problem for sets with applications to graph theory , Journal of Combina- torial Theory, Series A, 40 (1985) 82–89","venue":null,"work_id":"8c1407c2-f718-406a-b3f1-522464faa4de","year":1985},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.323231Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:99117e8fbaed8406cfd654a8224c70b9708c0fae78c5c28221af28a839a745da","observation_id":"63120782-63e1-4431-8801-bc82dad8f4d6","resolution":{"observed_at":"2026-08-06T19:41:02.378775Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:00.424606Z","title":"Ascoli, X","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.424606Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:18a5b565a26e4f8f8015ffaadad65658fb31274ffdbdfcb3924977fc10e2d796","observation_id":"026d7923-9de5-497f-ae1d-b264a1e85442","resolution":{"observed_at":"2026-08-06T19:41:00.424606Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1207.5028","last_updated":"2013-02-18T19:29:35Z","snapshot_observed_at":"2026-07-06T02:52:16.614843Z","submitted_at":"2012-07-20T19:10:41Z","title":"Fundamental Groups of Random Clique Complexes","version":2},"cited_work":{"arxiv_id":"1207.5028","doi":null,"metadata_source":"pith","pith_arxiv_id":"1207.5028","snapshot_observed_at":"2026-08-06T19:41:01.674876Z","title":"Fundamental Groups of Random Clique Complexes","venue":"math.CO","work_id":"38d46768-b8d7-4176-91f2-be05ef29d1d3","year":2012},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.512609Z"},"links":{"cited_paper":"/paper/1207.5028","citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:08bfeb0e0ffa5ee256ddcd944a6973216177762d46ef57da0d253ac959df5c9e","observation_id":"b8f9a28c-14de-49df-af2f-de1aa5f6dffc","resolution":{"observed_at":"2026-08-06T19:41:01.678801Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.362186Z","title":"Babson, C","venue":null,"work_id":"63cb5907-268a-4f8a-b6c3-4f13b06f4650","year":2011},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.600504Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:1957d09d10af1c328da3b3f60e418aae2beb7a9db21c946cdcd52111b160631c","observation_id":"a90d1fc3-e8c8-4e58-9545-90d9a1f698e2","resolution":{"observed_at":"2026-08-06T19:41:02.366922Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.350986Z","title":"Balogh, B","venue":null,"work_id":"b202feeb-1c03-41e9-b6d9-d2b4dfacc70f","year":2012},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.704123Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:472cda7038c8075223ea3bf14207c0e872f79325917a872dbca66dc27f685214","observation_id":"0bd75418-eecc-4fb1-9944-94beef60f5e7","resolution":{"observed_at":"2026-08-06T19:41:02.354721Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.339107Z","title":"Balogh, B","venue":null,"work_id":"2bc24684-1381-4e44-8b3f-07d00167ef20","year":2012},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.815519Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:70f7d0d80a6beb448903414336636b722c8d5c793b78fc6be654c25389c7b0f7","observation_id":"c3ac6f7f-704c-4703-a6a8-e9074a7b2dc0","resolution":{"observed_at":"2026-08-06T19:41:02.343156Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.327591Z","title":"Baron, J","venue":null,"work_id":"996dd9cc-d16e-4cf3-a7ac-dd23fac2be37","year":2019},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.926370Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:81d28d4fb4fcdc1159b302320de5738dbc99eb426ab62306b9609dc3cc4930eb","observation_id":"51d0acde-349d-42a8-812f-b3c565cd87ff","resolution":{"observed_at":"2026-08-06T19:41:02.331232Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.316223Z","title":"Bartha, B","venue":null,"work_id":"cfed19e5-cf00-4fd2-90fc-48a4a9770ffb","year":2024},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.005645Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:aa258fcb59fd3a2285427cda6079df071ba9f1af29dde8fa504e5e7df2ca4b88","observation_id":"98265ba1-5521-4e0c-9ee4-521a31bed6f9","resolution":{"observed_at":"2026-08-06T19:41:02.319993Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.305054Z","title":"Bernardi, ´E","venue":null,"work_id":"f124a30b-e044-4345-9be4-16672fa7323b","year":2012},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.105146Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:decb6fda4a7895f4c5ee99dae69a19eaa17b2d926cbebf045ffd9736d988c413","observation_id":"e5f50236-7644-4044-b9b1-7982e6f50fa4","resolution":{"observed_at":"2026-08-06T19:41:02.308721Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.293393Z","title":"Bidgoli, A","venue":null,"work_id":"bbb4a4cb-2925-42b0-94e0-6eecf9ffd3e0","year":2024},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.183362Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:4f4696677bc07be161fff41ded711f86fc923471e95fa7d25f674c3a904a1792","observation_id":"77d70494-a588-4a76-b6b1-ebb32316feda","resolution":{"observed_at":"2026-08-06T19:41:02.297196Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.281926Z","title":"Bollob´ as,Random graphs, second edition, Cambridge University Press, 2001","venue":null,"work_id":"7bf7a3da-58de-475f-9920-2883c01323f1","year":2001},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.278599Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:48fdd2c1ac3f0a746ba726cc2aafd132d2751477de7ecbc46cbd20a09bbf104c","observation_id":"7b709cc1-aae0-469b-929a-a0aee900dc1a","resolution":{"observed_at":"2026-08-06T19:41:02.285696Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.269778Z","title":"Bollob´ as, The evolution of sparse graphs , Graph theory and combinatorics (Cambridge, 1983), Academic Press, London, (1984) 35–57","venue":null,"work_id":"f84e1fdb-bfb3-47d5-b269-07462d3dba90","year":1984},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.370272Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:4ac4898f2ae5ac31f72d451afd1562a013c4489b70a28f92d0c13e0c95680f90","observation_id":"6bf01154-8400-4304-9938-39fde5fe6954","resolution":{"observed_at":"2026-08-06T19:41:02.274243Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.257556Z","title":"Bollob´ as,Weakly k-saturated graphs, Beitr¨ age zur Graphentheorie (Kolloquium, Manebach, 1967), Teubner, Leipzig (1968) 25–31","venue":null,"work_id":"d6de2dad-bfdf-4d6e-8cd4-4dbecedcb307","year":1968},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.375496Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:fe2d1e85c17fb52fe3357542e09ca6271a108951d8a6985b5e6dba395ca297e3","observation_id":"56308bf7-c0e9-4f52-a40a-4920d0b67171","resolution":{"observed_at":"2026-08-06T19:41:02.261590Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.245767Z","title":"Brightwell, K","venue":null,"work_id":"a37abc53-6f1a-41d6-8f95-f4ba3c164154","year":2012},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.379032Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:c59ca202e208d0e6fc54b055589be2f6d19ddd5baa828ef88b75c3b78ed0cf53","observation_id":"33e778dc-a3d3-42af-b2f1-77f92fb0c5f9","resolution":{"observed_at":"2026-08-06T19:41:02.249257Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.232591Z","title":"Bulavka, M","venue":null,"work_id":"893cc52e-378e-4d8a-8e4e-d6ea5d736954","year":2023},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.382166Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:c51bee0b8e5d93435e7bcd6aad4a6a292812217ecec026ced5a212ae2a5f13d9","observation_id":"483fda9a-6cec-4e15-9b79-b3f75282beb8","resolution":{"observed_at":"2026-08-06T19:41:02.237128Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.220898Z","title":null,"venue":null,"work_id":"8939c9b8-ff23-4ee5-9d2c-100c8819f701","year":null},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.385396Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:a5586e71cad94d02ac9eaf1af83f4fcded91e3a4d046a63ef410d415f64c5d9d","observation_id":"c803c86e-3fde-48ea-a79b-0f6dd435fc34","resolution":{"observed_at":"2026-08-06T19:41:02.225133Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.209945Z","title":"Conlon, W","venue":null,"work_id":"15d1ae91-07f9-4b28-92b9-b8feba842db6","year":2016},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.389032Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:82fb722512d5de58540fc2a37dbc4d3c2f07c9af9b86daf4918fa934ce2ca5c7","observation_id":"69a51417-0c0b-4dbc-b0cb-eb842377be5d","resolution":{"observed_at":"2026-08-06T19:41:02.213471Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.198613Z","title":"Costa, M","venue":null,"work_id":"ebeb3615-e2cd-43f4-b8b6-c61e768a26fc","year":2015},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.392211Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:585b24cd6356f0bca4970014645d2c0b27c77637cde5e23b9c9a832703183d45","observation_id":"aec5f165-ed07-487a-9ff4-e36607f63183","resolution":{"observed_at":"2026-08-06T19:41:02.202122Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.187895Z","title":null,"venue":null,"work_id":"312cf6de-bd67-425d-a2f7-677caf6b65e7","year":2021},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.395578Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:923f210c37b1e637403dbbcb118b8ef8660009961a8061ddc32942c7f4ce0f23","observation_id":"3c039409-181f-4299-aa94-e82e4af46c17","resolution":{"observed_at":"2026-08-06T19:41:02.191302Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1207.6717","last_updated":"2012-07-28T18:09:19Z","snapshot_observed_at":"2026-07-06T02:52:44.867382Z","submitted_at":"2012-07-28T18:09:19Z","title":"On the triangle space of a random graph","version":1},"cited_work":{"arxiv_id":"1207.6717","doi":null,"metadata_source":"pith","pith_arxiv_id":"1207.6717","snapshot_observed_at":"2026-08-06T19:41:01.659103Z","title":"On the triangle space of a random graph","venue":"math.PR","work_id":"3bc10133-e9b5-485b-a35b-d4b3787f179e","year":2012},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.398790Z"},"links":{"cited_paper":"/paper/1207.6717","citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:608433715f767ede5a7bc78a353908e7b36ea4ba8ab1f238d4cbe8c56494b26f","observation_id":"91030598-4baf-4ee9-a520-3c1b94a737ed","resolution":{"observed_at":"2026-08-06T19:41:01.662785Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.176912Z","title":"DeMarco, J","venue":null,"work_id":"5dfc1b83-5c99-4f09-8018-64c1828b1151","year":2015},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.402040Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:e50f6631e45a77910af4f9f3e69cbce90595844f65b406c15a5c5cbcd9206034","observation_id":"be09fe7f-0a0a-4a7c-8f2c-54c299ae281c","resolution":{"observed_at":"2026-08-06T19:41:02.180471Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.06421","last_updated":"2024-10-08T23:20:40Z","snapshot_observed_at":"2026-07-06T19:30:04.518857Z","submitted_at":"2024-10-08T23:20:40Z","title":"On the $H$-space of a random graph","version":1},"cited_work":{"arxiv_id":"2410.06421","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.06421","snapshot_observed_at":"2026-08-06T19:41:01.643970Z","title":"On the $H$-space of a random graph","venue":"math.CO","work_id":"0e9b9f50-79b3-4f0e-abbe-9be23553fb79","year":2024},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.405099Z"},"links":{"cited_paper":"/paper/2410.06421","citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:bfad114172277ec7ad9a672f5cb8f7eda82c1ae15763a5c2c87830d7256d6a76","observation_id":"656d535a-b670-4f06-be30-526b82b560bb","resolution":{"observed_at":"2026-08-06T19:41:01.647477Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.165989Z","title":"Erd˝ os, Z","venue":null,"work_id":"a80dddb8-b69c-411c-94fd-aebf1b0f7c38","year":1991},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.408512Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:be4b716ce8be6a98f5f42c1f5da98c1928ab7bb47f298a399d997355db52ee21","observation_id":"5ea4ab46-1728-451a-a7b2-80d14bbb2d90","resolution":{"observed_at":"2026-08-06T19:41:02.169255Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.155779Z","title":"Faudree, R.J","venue":null,"work_id":"b3c26594-a62d-418c-9999-2c0ffd8f0272","year":2013},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.411583Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:f5b0462c653d018122c5d9b8b5069404660476427a3d7c20a528b9d012a7c86b","observation_id":"0d130292-377a-4990-a00e-4765f4f7b78d","resolution":{"observed_at":"2026-08-06T19:41:02.158945Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.144614Z","title":"Fontes, R.H","venue":null,"work_id":"17f543e0-1cf8-4663-8ef2-b161a9d56e34","year":2002},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.415050Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:664a553000c32ba6c3b90e5738d5921d51a44af69f5d3280f847b9fbd6a9e6cc","observation_id":"535a7d2b-0884-4337-af75-537dfba101a9","resolution":{"observed_at":"2026-08-06T19:41:02.148293Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.133702Z","title":"Frankl, An extremal problem for two families of sets, European J","venue":null,"work_id":"b59d617e-6a87-4c0f-bc2e-0c1363b280e6","year":1982},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.418328Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:92ecad11f5bc63a189899580cf930fc95b776b9891734b6a2a69c8ded98f9743","observation_id":"542d4d21-7ccd-46d9-be44-86d066b97ed1","resolution":{"observed_at":"2026-08-06T19:41:02.137025Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.123195Z","title":"Frieze, M","venue":null,"work_id":"071ab541-1580-4f74-b3e5-c05bfb092ce9","year":2015},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.421406Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:7ed3a85bdefcd5bfc6d84774b608cd753a8086ec1247e2cbf83261693f3da461","observation_id":"b7ad477c-7153-471c-bc72-4e9b897af29d","resolution":{"observed_at":"2026-08-06T19:41:02.126324Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.112608Z","title":"Gravner, A.E","venue":null,"work_id":"0cea45f1-a658-4f8b-8024-27fd2f8ee75e","year":2019},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.424927Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:2ef1a82cb6b1078a4a57e154a244c07ed62307bb6459009f6d939cc7e1f99c85","observation_id":"52ff7ce6-b945-469d-bbcb-db5808e22b6b","resolution":{"observed_at":"2026-08-06T19:41:02.115666Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.101584Z","title":"Gravner, A.E","venue":null,"work_id":"eb036987-c8be-4ee4-90f6-b63e8bec4ef3","year":2021},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.427993Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:c9606018e141e5b2086411f6107865e28d8eb7cc6f2e09adb55fcec5535993c8","observation_id":"973638aa-fb42-47d6-9ec2-c98f6dfff0cb","resolution":{"observed_at":"2026-08-06T19:41:02.105178Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.091115Z","title":"Gravner, B","venue":null,"work_id":"9a6d0b45-a4cf-49fa-ae47-bf7c177a5fce","year":2023},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.430964Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:2867a1de7e345d810b828029cd461fbf1862ef9af2eac5733371da16109ef97a","observation_id":"933412b4-c333-449f-9bcf-4d0b9320321f","resolution":{"observed_at":"2026-08-06T19:41:02.094398Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.080396Z","title":"Gravner, E","venue":null,"work_id":"fa2cceac-8db7-4482-98c3-ce02b0a7582f","year":1997},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.433938Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:18ed55f39e0587eb50b849830df6d6dffd3bb80dac2366ffa23a10bec09b7143","observation_id":"f7f80b03-9a7c-4c29-bb0a-d34f6c8fd811","resolution":{"observed_at":"2026-08-06T19:41:02.083605Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.069670Z","title":"Gromov, Hyperbolic groups, in Essays in group theory, ed","venue":null,"work_id":"fd18c7a4-1d05-4c91-9750-dc898a2735e4","year":1987},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.437281Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:7619f3a5a3621fc5fd4a65b1ed6e61fdd8ccbe19ed7fd0862bd8a38fddfb8ef9","observation_id":"ec02a631-1051-4a9a-bdc6-5bb693834bbb","resolution":{"observed_at":"2026-08-06T19:41:02.073026Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2308.13455","last_updated":"2023-08-25T16:02:56Z","snapshot_observed_at":"2026-08-06T07:29:17.043686Z","submitted_at":"2023-08-25T16:02:56Z","title":"Simonovits's theorem in random graphs","version":1},"cited_work":{"arxiv_id":"2308.13455","doi":null,"metadata_source":"pith","pith_arxiv_id":"2308.13455","snapshot_observed_at":"2026-08-06T19:41:01.628925Z","title":"Simonovits's theorem in random graphs","venue":"math.CO","work_id":"0af1fd3c-2fe9-4221-a591-455dcddc60e9","year":2023},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.440508Z"},"links":{"cited_paper":"/paper/2308.13455","citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:3ffa84bfd644cb9f8d5d4d0aad9b6350b3925344a228de889f4e3ccdf893bb7b","observation_id":"272624b4-b353-48cf-bd1f-145415b95bec","resolution":{"observed_at":"2026-08-06T19:41:01.632474Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.14620","last_updated":"2024-02-22T15:07:48Z","snapshot_observed_at":"2026-08-07T01:39:37.884234Z","submitted_at":"2024-02-22T15:07:48Z","title":"Stability of large cuts in random graphs","version":1},"cited_work":{"arxiv_id":"2402.14620","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.14620","snapshot_observed_at":"2026-08-06T19:41:01.613552Z","title":"Stability of large cuts in random graphs","venue":"math.CO","work_id":"8e379467-f7b4-47af-972c-9f03489143f7","year":2024},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.443833Z"},"links":{"cited_paper":"/paper/2402.14620","citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:1e223aa958754543122e6d21581080b9a5351bb93d429b10785136b58aa99b87","observation_id":"ed3fd181-f5b2-43cd-a6eb-28a9299d9b16","resolution":{"observed_at":"2026-08-06T19:41:01.617191Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.059209Z","title":"Janson, T","venue":null,"work_id":"4e76242f-c1ca-4251-9c2e-25fc2c1adaaa","year":2000},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.447543Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:aa567541e71a54595d1f5fc008a128c7a175508befad1831bb03db8615ff874b","observation_id":"8558b6eb-4674-45ba-af24-90ec2c44970d","resolution":{"observed_at":"2026-08-06T19:41:02.062408Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.048635Z","title":"Kahle, Topology of random clique complexes , Discrete Math., 309:6 (2009) 1658–1671","venue":null,"work_id":"a4b116ae-eb77-44fa-9bea-4a8eb4abc008","year":2009},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.450696Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:9ba8727ac47a09dfdb5ee286d1aa71136d6dd6bb65a2e1f05f8ae95b8fda4d93","observation_id":"70cd6e39-11ee-4503-bb02-2e7df0dffd45","resolution":{"observed_at":"2026-08-06T19:41:02.051972Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.038113Z","title":"Kalai, Hyperconnectivity of graphs, Graphs Combin., 1 (1985) 65–79","venue":null,"work_id":"09ed17c1-47dd-44c9-a2c3-4f5ac8773227","year":1985},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.453865Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:eff6f27fff3d019ed600078599d06fc1ed2ed69bba5924909b447b648b4e2727","observation_id":"58a106c0-1e41-494c-a443-ffd78bcf7bcc","resolution":{"observed_at":"2026-08-06T19:41:02.041398Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.027609Z","title":"Kalai, Weakly saturated graphs are rigid, in: Convexity and graph theory (Jerusalem, 1981), North-Holland Math","venue":null,"work_id":"cd0d8000-53d1-480d-b98b-e2eb622c865b","year":1984},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.457039Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:03de61738f20d74be86f2512a4c04604e05626a81416a59e114d78df4aa207aa","observation_id":"cab788ce-b904-4095-82e4-e7e0477ac7f5","resolution":{"observed_at":"2026-08-06T19:41:02.030904Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2306.10375","last_updated":"2024-03-10T11:13:17Z","snapshot_observed_at":"2026-08-04T03:51:34.577925Z","submitted_at":"2023-06-17T15:23:13Z","title":"Weak saturation numbers in random graphs","version":3},"cited_work":{"arxiv_id":"2306.10375","doi":null,"metadata_source":"pith","pith_arxiv_id":"2306.10375","snapshot_observed_at":"2026-08-06T19:41:01.597533Z","title":"Weak saturation numbers in random graphs","venue":"math.CO","work_id":"8eb8e267-5917-4c25-a1ac-03761462748d","year":2023},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.460319Z"},"links":{"cited_paper":"/paper/2306.10375","citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:ace7309a895341346116ab77bdc23c7e248604a9dc82fe756fa070679d331c8a","observation_id":"1800d65e-c99a-4bc4-b250-c2410dc2b3d0","resolution":{"observed_at":"2026-08-06T19:41:01.601159Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.017305Z","title":"Kalinichenko, M","venue":null,"work_id":"78de9f65-3532-4892-9d21-e7ce32be22b6","year":2023},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.464334Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:6fe13580d293e81dfbc42a3134d0448a2c30f40692a8a0dbe13b832c04885797","observation_id":"6ed682d5-147e-4b5b-b664-3430ada4e4a8","resolution":{"observed_at":"2026-08-06T19:41:02.020473Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:02.006655Z","title":"Koml´ os, E","venue":null,"work_id":"4f198b5b-8e16-4278-8ac6-d5c42d4fe759","year":1983},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.467556Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:9448fda714560c28b584448513ad1cd00ee322ffec93e2dc98790b92b00981d3","observation_id":"592f01a3-4e4e-4e17-97eb-e8300f388bbe","resolution":{"observed_at":"2026-08-06T19:41:02.009945Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.995792Z","title":"Kor´ andi, Y","venue":null,"work_id":"e5c8d369-663f-45b5-86c1-840f4c51b9fc","year":2016},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.470380Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:5f4bd5c013e27cf37eb737ade6033ee6dc0da39689cf798fec0b16f4c3db3570","observation_id":"2c1c89f3-43aa-4739-8228-1f0434f694b7","resolution":{"observed_at":"2026-08-06T19:41:01.999409Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.985517Z","title":"Kor´ andi, B","venue":null,"work_id":"d50312e6-86b4-4fb3-9196-988eb0397502","year":2017},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.473472Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:dc5b3fa83f4549a3f17782cd04afcc9930ec57e24dc4204ec3d050756c0853c3","observation_id":"4dd2d87f-bfa5-4d32-b6e7-68537e9dc1f9","resolution":{"observed_at":"2026-08-06T19:41:01.988696Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.975013Z","title":null,"venue":null,"work_id":"1ed564e9-8081-430a-9c6b-ebb79fd2f2df","year":1976},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.476488Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:a040acf849bd80ac12efe13a708ac002fa537f85dfdddf975c6d3b38a3c739a0","observation_id":"8a24bcff-67a3-45bb-b03f-b96df245f302","resolution":{"observed_at":"2026-08-06T19:41:01.978245Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.964746Z","title":"Krivelevich, G","venue":null,"work_id":"0d14cf30-6f2b-4ca8-b56c-5771a9a8af15","year":2023},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.479621Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:c723121bacba40b74ce4cce20f1b3f1e5e399eb60ebd33b22fdbbfefbe05bdd2","observation_id":"d6f1318c-0aa2-47b8-ba3c-d69a2c691159","resolution":{"observed_at":"2026-08-06T19:41:01.967919Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.954249Z","title":"Kronenberg, T","venue":null,"work_id":"f2b87644-e8e9-4a49-a4a8-2bdc11655c58","year":2021},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.482923Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:31c3bd04a72f2b48ed490553c1d099bda8b321a37cbc30db8a8b913e0f615dd6","observation_id":"d7dc59a5-3143-4a15-8092-12876043ca5b","resolution":{"observed_at":"2026-08-06T19:41:01.957581Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.943807Z","title":"Morris, Bootstrap percolation, and other automata, European Journal of Combinatorics, 66 (2017) 250–263","venue":null,"work_id":"8b244604-a731-49db-9d75-86dee682698f","year":2017},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.485959Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:230c0ec8cf8eecb8c9107e9425d029ab7109a1856fe83ff852905dbb749796c6","observation_id":"0ba8adc2-9e13-456e-a0df-22cf0ccd5509","resolution":{"observed_at":"2026-08-06T19:41:01.947064Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.932857Z","title":"Morris, Zero-temperature Glauber dynamics on Zd, Probab","venue":null,"work_id":"df0ad874-fa09-402a-847f-ec38b86e6d08","year":2011},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.488940Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:745f50a6f085759a898b52c93b6266b4f21b95a864094ae988383c14483cb4dd","observation_id":"53b74345-7607-4ffa-8995-11e45df3183f","resolution":{"observed_at":"2026-08-06T19:41:01.936715Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.921906Z","title":"Morrison, J","venue":null,"work_id":"41fabd8e-237f-408f-a1e2-dbebe93c36f2","year":2018},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.491910Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:50e6445eb96bb773feb49f5198be43a7837b9a61c7e5842df93421d57537153b","observation_id":"bd810cae-70ea-44f6-91bf-78a9da045d28","resolution":{"observed_at":"2026-08-06T19:41:01.925494Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.911631Z","title":"Morrison, J","venue":null,"work_id":"4329d4be-6090-41fb-8f1b-1f0970719532","year":2017},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.495099Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:46b5f984e1367e533b49969e801e190e8871a4e9a73f18b13446641b5f6b3167","observation_id":"09db5ef4-66f9-4d94-b725-49b9945ca65c","resolution":{"observed_at":"2026-08-06T19:41:01.914815Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.900487Z","title":"Moshkovitz, A","venue":null,"work_id":"f401a5eb-0fee-4e75-8eca-9457703f2eca","year":2015},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.498445Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:d30fa25b9a408fb89ab6d050b27cfc515e44e6044823f5b64bcb12eaff1c67c5","observation_id":"bc1c9ba1-3bd4-4ca6-bd49-ccaa8c7a9610","resolution":{"observed_at":"2026-08-06T19:41:01.903904Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.888526Z","title":"O’Connell, Some large deviation results for sparse random graphs , Probab","venue":null,"work_id":"d13736ae-bbe7-4a41-9b52-3a0d59ca437d","year":1998},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.501504Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:b04004f17f47aba63e837c1e189a0f55fc06a0c61d8aff8ffffbed5dddde382c","observation_id":"f03b07cc-2dca-48b9-92d6-076e37554210","resolution":{"observed_at":"2026-08-06T19:41:01.892845Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.877893Z","title":"Pikhurko, Extremal hypergraphs, PhD thesis, University of Cambridge, 1999","venue":null,"work_id":"1f138a9c-bffd-45f7-bccb-e69a6ed4ad8d","year":1999},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.505085Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:b94ab4c1abbb8403c81ba7d0b4d29915cc9aa7fa60903d46c835287cb6f03f2c","observation_id":"6d72bc03-395a-4c2f-8955-977f8cabdd63","resolution":{"observed_at":"2026-08-06T19:41:01.881201Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.867183Z","title":"Pikhurko, Weakly saturated hypergraphs and exterior algebra , Combin","venue":null,"work_id":"1e71a6e3-fff0-4803-8091-3a2c66b6c313","year":2001},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.508225Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:5c0c2e46f66c192efba62cf6c3079d67169d8ae5808b8d026347b13a4cf223b5","observation_id":"4a082663-88c4-493c-92cc-48278ccad138","resolution":{"observed_at":"2026-08-06T19:41:01.870489Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.855875Z","title":"Schacht, Extremal results for random discrete structures , Annals of Mathematics, 184:2 (2016) 333–365","venue":null,"work_id":"b933e25d-ddf7-4de1-8664-698f29429d4e","year":2016},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.511269Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:3edfa6eb57a7727b7d3a08e8da780e119a1043e28783bca0fafa84c809e936d7","observation_id":"202b2f9c-5661-43dd-a8b7-2d0acb3731cc","resolution":{"observed_at":"2026-08-06T19:41:01.859255Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.845116Z","title":"Shapira, M","venue":null,"work_id":"cf8f18c8-4f91-4d8d-8543-36b9243d9de5","year":2023},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.514255Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:d97ab58ea036c869ca44a1fc2047731bed7a3b426967ebe3e6046d21c840544a","observation_id":"8c8d6181-c915-408c-94ad-1b818665ef71","resolution":{"observed_at":"2026-08-06T19:41:01.848519Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.832716Z","title":"Spencer, Counting extensions, Journal of Combinatorial Theory, Series A, 55:2 (1990) 247– 255","venue":null,"work_id":"015599ec-5415-4f21-99df-b94be1958966","year":1990},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.517487Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:98af8538d707322097244c45e17503f0a19adf09a88be008b72914a65ecc6909","observation_id":"0f84e7f1-7c6a-48fa-9e25-e681356116d9","resolution":{"observed_at":"2026-08-06T19:41:01.836797Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.03816","last_updated":"2026-07-06T12:54:29Z","snapshot_observed_at":"2026-08-07T16:08:43.998874Z","submitted_at":"2025-04-04T15:39:40Z","title":"A short proof of Tuza's conjecture for weak saturation in hypergraphs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.03816","snapshot_observed_at":"2026-08-06T19:41:01.520618Z","title":"Terekhov, A short proof of Tuza’s conjecture for weak saturation in hypergraphs , arXiv preprint (2025) arXiv:2504.03816","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.520618Z"},"links":{"cited_paper":"/paper/2504.03816","citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:addf884f2c48839059cb3572cc5af0ce567b3f337d713d05372e0d985e24e624","observation_id":"d208afee-2e1b-401d-8d5a-6bf3bd9b7c43","resolution":{"observed_at":"2026-08-06T19:41:01.520618Z","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":"2026-08-06T19:41:01.821111Z","title":"Terekhov, M","venue":null,"work_id":"31750d32-97b7-4d8f-96ec-8830058172bd","year":2025},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.523794Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:04d8d897be904175429440602b22e883df113811ce7f70575f6642e3df347dc1","observation_id":"ba7bec13-6ff2-4b9f-a70d-6f8e38e478a7","resolution":{"observed_at":"2026-08-06T19:41:01.824350Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.17857","last_updated":"2024-06-13T20:38:42Z","snapshot_observed_at":"2026-07-06T18:21:05.410042Z","submitted_at":"2024-05-28T06:16:12Z","title":"Weak saturation rank: a failure of linear algebraic approach to weak saturation","version":2},"cited_work":{"arxiv_id":"2405.17857","doi":null,"metadata_source":"pith","pith_arxiv_id":"2405.17857","snapshot_observed_at":"2026-08-06T19:41:01.567049Z","title":"Weak saturation rank: a failure of linear algebraic approach to weak saturation","venue":"math.CO","work_id":"22fbb369-c408-4aca-9de0-b01d63909c0b","year":2024},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.526978Z"},"links":{"cited_paper":"/paper/2405.17857","citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:9ba8afae730b67c06515ff0ad1097b81b04ea8514e3e9cf639cc5d5017ffd684","observation_id":"7689d68e-0a16-42b2-821b-9ff286ad17e6","resolution":{"observed_at":"2026-08-06T19:41:01.572364Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.809788Z","title":null,"venue":null,"work_id":"aa8256be-e5ae-453a-831e-5a2a2fad54c6","year":1962},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.530213Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:c4f434f8a8c763baefeb3094152ca75fac46eda689db30e521755f7384ec27a0","observation_id":"2d54cca2-0da8-4d60-baa1-0ad861120c2a","resolution":{"observed_at":"2026-08-06T19:41:01.813035Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.798311Z","title":"von Neumann, Theory of Self-Reproducing Automata , Univ","venue":null,"work_id":"80a09602-9a59-47a8-a0f3-48a1d5657612","year":1966},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.533364Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:4c6cf0e710f4eaf359d179345111b75db29b0e9259a8340e10e5050a7ee47158","observation_id":"477b3d3a-e46e-4a43-93f5-c104b5317554","resolution":{"observed_at":"2026-08-06T19:41:01.801843Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.787311Z","title":"Tuza, Asymptotic growth of sparse saturated structures is locally determined, Discrete Math- ematics, 108:1-3 (1992) 397–402","venue":null,"work_id":"ace96e62-2d71-49f6-a2c1-453cfaa9a89e","year":1992},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.536466Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:0adb1d9efb46af72cf7ae4a307cfe5d5717d9730ad692f6ddb4434248ac519fe","observation_id":"389eaf59-8111-44e5-a982-d190dac2f17c","resolution":{"observed_at":"2026-08-06T19:41:01.790858Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T19:41:01.776092Z","title":"Ulam, Random processes and transformations, Proc","venue":null,"work_id":"8a46f5af-64d6-4f5d-92e2-33c48876648f","year":1950},"citing_paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.539676Z"},"links":{"citing_paper":"/paper/2507.05697"},"observation_digest":"sha256:2c83d40df4e28afb139343eb3e13dbdeeb6b364959246b4624d81b1d2288939f","observation_id":"ad1a21f4-da51-4978-9986-5d15932e9ebf","resolution":{"observed_at":"2026-08-06T19:41:01.779712Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.05697","last_updated":"2025-07-08T06:09:01Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-06T19:17:42.569446Z","submitted_at":"2025-07-08T06:09:01Z","title":"When does a tree activate the random graph?"},"reference_resolution":{"displayed":67,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":7,"verified_fuzzy":54},"total_outbound_references":67},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 67 of 67 outbound references and 1 inbound Pith citation observation for arXiv:2507.05697."}