{"as_of":"2026-08-05T03:52:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c332cbcab82b045c4ab5952a3eede98c009a7e3c60c802d913140bd143e97826","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-24T23:58:54.340345Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-04T06:34:03.388597+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-10T19:33:37.147779Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-11T19:41:10.704951Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"cited_work":{"arxiv_id":"1907.04559","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1907.04559","snapshot_observed_at":"2026-07-04T23:46:53.602680Z","title":"Balogh, G","venue":null,"work_id":"934d0288-7916-45fe-a9ce-9bd11ad35b9f","year":1907},"citing_paper":{"arxiv_id":"2604.04607","last_updated":"2026-04-06T11:49:30Z","snapshot_observed_at":"2026-08-02T14:49:35.709380Z","submitted_at":"2026-04-06T11:49:30Z","title":"Bootstrap percolation of extension hypergraphs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-10T19:33:37.147779Z"},"links":{"cited_paper":"/paper/1907.04559","citing_paper":"/paper/2604.04607"},"observation_digest":"sha256:1a358ccfcc68b13d15982289e9e9949dea6cd42c8bffbc2bfbecf10bf759574a","observation_id":"9a0f615c-055f-4725-8734-6f1917133a07","resolution":{"observed_at":"2026-07-04T23:46:53.602680Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"cited_work":{"arxiv_id":"1907.04559","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1907.04559","snapshot_observed_at":"2026-07-04T23:46:53.602680Z","title":"Balogh, G","venue":null,"work_id":"934d0288-7916-45fe-a9ce-9bd11ad35b9f","year":1907},"citing_paper":{"arxiv_id":"2604.22630","last_updated":"2026-04-24T15:01:42Z","snapshot_observed_at":"2026-07-06T23:09:01.221922Z","submitted_at":"2026-04-24T15:01:42Z","title":"Upper bounds on the running time of bootstrap percolation","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-08T11:09:40.735819Z"},"links":{"cited_paper":"/paper/1907.04559","citing_paper":"/paper/2604.22630"},"observation_digest":"sha256:f6a5ef9077c916a08f3d1c919aa457de4d91cb3f29c021a48a1773b1271edd98","observation_id":"7c2af944-8e65-4298-b532-97bbda0523ef","resolution":{"observed_at":"2026-07-04T23:46:53.602680Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1907.04559/citation-record","integrity":"/paper/1907.04559/integrity","json":"/paper/1907.04559/citation-record.json","paper":"/paper/1907.04559"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Metastability effects in bootstrap percolation","venue":null,"work_id":"7580538f-8766-475e-9141-88feb3b4f460","year":1988},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:a218e86f7a105f254851bff296df8f17c05ed47cc02f6562f9ec66d576f8d953","observation_id":"63e448e2-c62d-4f35-9b4c-1192bef1d093","resolution":{"observed_at":"2026-05-25T00:00:08.573257Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"An extremal problem for sets with applications to graph theory","venue":null,"work_id":"f039821b-c640-4790-b6c3-13a7521a4f53","year":1985},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:a9994adeae06607f7daa2b57162047bb7927672a068d9b4d4ed7aaf48c28f009","observation_id":"f995396a-e12c-4f08-bcb9-481187d94249","resolution":{"observed_at":"2026-05-25T00:00:08.581694Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Sharp thresholds for contagi ous sets in random graphs","venue":null,"work_id":"857bf0e0-a6ab-4cf8-aaf8-5a399123f736","year":2018},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:e464f27be0f5930099540b3267982bb0edd7305c6fc335b4cc01300f7be2c138","observation_id":"40c2bde7-6598-4579-8c8c-438f947cb940","resolution":{"observed_at":"2026-05-25T00:00:08.577550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"The sharp threshold for bootstrap percolation in all dimensions","venue":null,"work_id":"de383ff7-1c7a-4624-a752-dcc583bd76c9","year":2012},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:39ad28933dfb66f37f21f13aa4de3cb5a47d59a973273cad2c644c6af6333b33","observation_id":"bcccc14a-c5f1-4009-b665-b49e5014d69a","resolution":{"observed_at":"2026-05-25T00:00:08.608570Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Graph bootstrap percolation","venue":null,"work_id":"b7043511-09ec-42eb-aa6b-b75a9e48a62e","year":2012},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:42066b7a6d998bf306b2edde3ebbfa34b722ecb3ea4bcfde380d1c01b0905345","observation_id":"b7f58f59-a91a-47af-a6af-9680ff2035a2","resolution":{"observed_at":"2026-05-25T00:00:08.612670Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Line ar algebra and bootstrap percolation","venue":null,"work_id":"08657e79-4467-4457-bdbb-0312c8ba0032","year":2012},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:83159a2f7b13278bc56e1bfb1315f275ceb78e10090b4190fc672b0adcc197b1","observation_id":"76afb575-51e5-47e8-88e7-e6375e49dc92","resolution":{"observed_at":"2026-05-25T00:00:08.651933Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Random disease on the square grid","venue":null,"work_id":"2742618f-1ea0-4093-8636-fe42c4e19b25","year":1998},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:b0756e74c4cd57c513c880ecc51878541fd93e5717a652b14406f53a0813f702","observation_id":"8991a187-1c14-4264-b2d3-06340371da5f","resolution":{"observed_at":"2026-05-25T00:00:08.616731Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"On sets of integers which contain no three terms in arithmetical progression","venue":null,"work_id":"97611f59-87c7-4cdf-8727-c0d29454b5f3","year":1946},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:d2ef86d5e579ba577546a503e832ae12cd6acccecf7c551a61e4074b7e0b1070","observation_id":"bea7db4b-bacf-4110-88d4-f52fedc2c6f5","resolution":{"observed_at":"2026-05-25T00:00:08.603909Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"On slowly percolating s ets of minimal size in bootstrap percolation","venue":null,"work_id":"c68c03a7-6d8f-4d83-a8e1-32dbeacc4e46","year":2013},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:6a6b5726865e97508c853cb7057f71c7d05294e1251f9b8f9a75a845db996757","observation_id":"2eac8988-0f95-40ac-a491-ddcb7a308a5c","resolution":{"observed_at":"2026-05-25T00:00:08.620976Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Maximum percolation t ime in two-dimensional bootstrap percolation","venue":null,"work_id":"64ee6bc6-cc10-4abc-b22f-0cf32c27e423","year":2015},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:159edf151b00fcee15e89291f272c766b592ee1f2bf1330c36b23b6fdad9a2cc","observation_id":"cb56eaf6-5f8c-4f24-a59d-6119bacc9956","resolution":{"observed_at":"2026-05-25T00:00:08.625161Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Weakly k-saturated graphs","venue":null,"work_id":"3cda56c2-c55c-4d3f-8605-b6795e358d3c","year":1967},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:cc0121d82e6fa40c32fa30b50556da5d4f120362c5efe90a0ffe6a8457d481a0","observation_id":"76369529-5c90-4153-953e-085922325c89","resolution":{"observed_at":"2026-05-25T00:00:08.647374Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"On the maximum running time in graph bootstrap percolation","venue":null,"work_id":"4bc3697f-87bc-45e7-9759-71f9848817d3","year":2017},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:7acc993abd415466ea04f5897cf6afac4b97f3891b2a6340c230e4b0161db8b6","observation_id":"318c9c28-fd82-4739-962c-33f78b9be52e","resolution":{"observed_at":"2026-05-25T00:00:08.599779Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Bootstrap perc olation on a Bethe lattice","venue":null,"work_id":"a834437c-abc8-4792-a239-2ab7b45297e2","year":1979},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:f487b2fffb9cb3d5227d96406609d09590b944cb6fd72727d5fd44b1960d8893","observation_id":"6e0093a6-d5b7-41bd-bd20-bb054d750afe","resolution":{"observed_at":"2026-05-25T00:00:08.634109Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"On random graphs I","venue":null,"work_id":"3216d3cc-931f-48b3-9d9f-d6547ef51fc8","year":1959},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:e6c3f08ed182dbd0d3ed2527ae20c0aa256393e7795f9b181d51180fec1d03c6","observation_id":"2a22325f-5c33-40de-bb99-088a4a8fe775","resolution":{"observed_at":"2026-05-25T00:00:08.638999Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"An extremal problem for two families of sets","venue":null,"work_id":"3780a4a5-e3c2-427c-af41-1e8a4363bd0a","year":1982},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:15e224cde359357bf9a83d39af688090577635fcf74554f6ce3e9db6bf30514c","observation_id":"335b0622-7903-41d7-a819-43673c1f4c38","resolution":{"observed_at":"2026-05-25T00:00:08.643116Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"The time of gra ph bootstrap percolation","venue":null,"work_id":"d83daa6a-c399-4e6e-a86e-455c733e0494","year":2017},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:11540be1da3608f4550fee0df1062782e94b6ad97a0f8f8f8304aeaacaf4d518","observation_id":"3bbd7e82-02e0-45b9-b4c1-2519dacf64c1","resolution":{"observed_at":"2026-05-25T00:00:08.595352Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Weakly saturated graphs are rigid","venue":null,"work_id":"d815bfbf-9780-47ef-910c-cfaaf59b5904","year":1984},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:731d0d2b71188704f99ca602d9d26b765b7f18fac056865d9c7d8463ac28b378","observation_id":"e3357ae7-f558-4f4d-93f4-a002f544bee2","resolution":{"observed_at":"2026-05-25T00:00:08.629749Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"1705.08882","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Sharp threshold for K4-percolation","venue":null,"work_id":"0050b0da-b0aa-477e-9743-38e7567b54d3","year":2017},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:d2d3b9d6a4e723be0097ab65afb38d51413518a0f1d2745be1efe65271c977e1","observation_id":"be575831-a6ff-41cf-8d22-81db70843c61","resolution":{"observed_at":"2026-05-25T00:00:08.132592Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1510.06156","last_updated":"2015-11-19T14:38:12Z","snapshot_observed_at":"2026-08-05T02:05:05.025719Z","submitted_at":"2015-10-21T07:40:43Z","title":"The Saturation Time of Graph Bootstrap Percolation","version":2},"cited_work":{"arxiv_id":"1510.06156","doi":null,"metadata_source":"pith","pith_arxiv_id":"1510.06156","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"The Saturation Time of Graph Bootstrap Percolation","venue":"math.CO","work_id":"7d3289f0-816b-4b7f-9447-9abe1fb9530a","year":2015},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"cited_paper":"/paper/1510.06156","citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:cdaa7c561c58c9da16a42e8123d981899b9222c69defa013bf93dffadc2b3151","observation_id":"1edf27ea-13f0-4e61-9707-b4058e760d32","resolution":{"observed_at":"2026-05-25T00:00:08.119376Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Extremal bounds for bootst rap percolation in the hypercube","venue":null,"work_id":"dc0474aa-7c09-4e2f-8ac0-fa31d5cf8bbe","year":2018},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:5c75dcabd12ba97afb7abe7c16022690186b63ee6871c92a06f79bd10f89d3f4","observation_id":"1ada0af3-8a03-434c-adc9-9652cd3aaa5c","resolution":{"observed_at":"2026-05-25T00:00:08.591007Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1806.02903","last_updated":"2020-10-07T00:31:47Z","snapshot_observed_at":"2026-07-30T16:50:59.146936Z","submitted_at":"2018-06-07T21:01:54Z","title":"A Sharp Threshold for Bootstrap Percolation in a Random Hypergraph","version":2},"cited_work":{"arxiv_id":"1806.02903","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1806.02903","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"A Sharp Threshold for Boots trap Percolation in a Random Hypergraph","venue":null,"work_id":"dce3012d-d1d3-4d7d-b7df-46c87d2e4b48","year":2018},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"cited_paper":"/paper/1806.02903","citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:f7da5dcb53196768f0a0f7d21d62f12b53b55d371bc07647f67e7e0f68fb4af1","observation_id":"3b1dd2b9-3c17-4b78-92d4-1e21b780f939","resolution":{"observed_at":"2026-05-25T00:00:08.126194Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Maximal Percolation Time in Hypercubes Under 2-Bootstrap Percolation","venue":null,"work_id":"b0676534-a3c3-4d21-966c-92f709ef07a5","year":2012},"citing_paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-24T23:58:54.340345Z"},"links":{"citing_paper":"/paper/1907.04559"},"observation_digest":"sha256:96f913001a1b55fa6070ebb5a4338f2b355815c37a4384161b01f9f98a056afc","observation_id":"5e053555-c380-429a-a6c1-64061e8bc6a8","resolution":{"observed_at":"2026-05-25T00:00:08.586461Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1907.04559","last_updated":"2019-07-10T08:05:49Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-07-06T08:06:44.034117Z","submitted_at":"2019-07-10T08:05:49Z","title":"The maximum length of $K_r$-Bootstrap Percolation"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":3,"verified_fuzzy":19},"total_outbound_references":22},"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":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"thesis":"As of 5 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 2 inbound Pith citation observations for arXiv:1907.04559."}