{"as_of":"2026-08-13T07:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9869af5eb1703c92955c106f72573ca51192d7c35feac1f92275c434bebb6eb2","coverage":[{"denominator":14,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":14,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T03:10:54.967875Z","state":"measured"},{"denominator":14,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":14,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.25277/citation-record","integrity":"/paper/2607.25277/integrity","json":"/paper/2607.25277/citation-record.json","paper":"/paper/2607.25277"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1063/1.4905202","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Gaunt, D.S., Guttmann, A.J., Whittington, S.G.,","venue":"Chaos An Interdisciplinary Journal of Nonlinear Science","work_id":"b041304d-3873-481e-86ab-46a90370d137","year":null},"citing_paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T03:10:54.930698Z"},"links":{"citing_paper":"/paper/2607.25277"},"observation_digest":"sha256:2653e7b13ae611e7fc1cbe78ede286897dcf3708ddb1e917271442686d5686de","observation_id":"ca3b2944-0e66-441f-b215-7dabc979b1fb","resolution":{"observed_at":"2026-08-01T03:14:14.314958Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-01T03:10:54.967875Z","title":"1016/j.physa.2020.125723, doi:doi:10.1016/j.physa.2020.125723","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T03:10:54.967875Z"},"links":{"citing_paper":"/paper/2607.25277"},"observation_digest":"sha256:3348ccdd453b45c6a888d1d824d3e1cedd97ec7687979d21c929be85fb8135f4","observation_id":"28106f72-d1e8-4e91-8f40-c0e12bd3489c","resolution":{"observed_at":"2026-08-01T03:10:54.967875Z","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":"10.1007/s10955-025-03567-x","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Burton, R.M., Keane, M.,","venue":"Journal of Statistical Physics","work_id":"28624c36-4913-4f26-a0ec-37145cabdff2","year":null},"citing_paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T03:10:54.923238Z"},"links":{"citing_paper":"/paper/2607.25277"},"observation_digest":"sha256:5bacf1b5fe9a40ede0c6a6f73cd2194aa0467afda89e2fd4a6b23762e8efc3d9","observation_id":"76bc7585-aaee-4756-90de-edd5429aee89","resolution":{"observed_at":"2026-08-01T03:14:14.711532Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/19-aap1527","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"The Annals of Applied Probability","work_id":"6e463abb-fca5-4b34-b6f1-d2821cefbc64","year":null},"citing_paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T03:10:54.961348Z"},"links":{"citing_paper":"/paper/2607.25277"},"observation_digest":"sha256:cdded96c3f8c3aefe772dc17d1d0c67a49850aa32bdcc115241486ae48f7b87c","observation_id":"f80b5b8c-7257-4915-8405-3b470c486d23","resolution":{"observed_at":"2026-08-01T03:14:12.268922Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1088/0305-4470/12/1/019","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Gladkov, N.,","venue":"Journal of Physics A Mathematical and General","work_id":"dd4d0c47-2782-4fb6-b8a0-00a5a55fa806","year":null},"citing_paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-01T03:10:54.933952Z"},"links":{"citing_paper":"/paper/2607.25277"},"observation_digest":"sha256:f51e610f29d003de05cab0b8a71dfc36186b0b6076132019638c39c8ae9cb86b","observation_id":"e3a7014f-82d0-4167-8317-130091843640","resolution":{"observed_at":"2026-08-01T03:14:14.013244Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-01T03:10:54.927374Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$","version":1},"reference_index":1989,"source":"pdf_text","source_observed_at":"2026-08-01T03:10:54.927374Z"},"links":{"citing_paper":"/paper/2607.25277"},"observation_digest":"sha256:367cd4a5056fdb47faade7a04da7cda4fac4dfb226040f7acd1d592d2174d254","observation_id":"4af0474e-5d7f-4491-b6b6-7a4f73a0eafb","resolution":{"observed_at":"2026-08-01T03:10:54.927374Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T03:10:54.940744Z","title":"volume 321 ofGrundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$","version":1},"reference_index":1999,"source":"pdf_text","source_observed_at":"2026-08-01T03:10:54.940744Z"},"links":{"citing_paper":"/paper/2607.25277"},"observation_digest":"sha256:ac55ea65603b93407e76c76fb51eadfc9731bf8a85ec65009efb08d04a2e96d5","observation_id":"66827e1e-23b5-4fea-a707-891307d107ec","resolution":{"observed_at":"2026-08-01T03:10:54.940744Z","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":"10.1016/s0167-7152(99)00107-8","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"fkg equality","venue":"Statistics & Probability Letters","work_id":"d247b014-355b-42c0-99a4-1e837f6a05e8","year":null},"citing_paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$","version":1},"reference_index":2000,"source":"pdf_text","source_observed_at":"2026-08-01T03:10:54.964566Z"},"links":{"citing_paper":"/paper/2607.25277"},"observation_digest":"sha256:6077148354206d460d6a2bc77cd31e9ca09684154f1c8110d4c7bdde5fe0ade4","observation_id":"f237a11b-d83c-4798-8306-7adc8c22ef73","resolution":{"observed_at":"2026-08-01T03:14:11.955665Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/rsa.20307","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Random Structures Algorithms 37, 137–175","venue":"Random Structures and Algorithms","work_id":"8fc425f1-b633-4235-a523-443ce0837d6f","year":null},"citing_paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$","version":1},"reference_index":2010,"source":"pdf_text","source_observed_at":"2026-08-01T03:10:54.944391Z"},"links":{"citing_paper":"/paper/2607.25277"},"observation_digest":"sha256:44983c13377d35960c991eabab4bd8d151495cd72ea6d482cd631a158b9fe4e7","observation_id":"c1e0f026-24c2-4c27-a6aa-a7ef615927df","resolution":{"observed_at":"2026-08-01T03:14:13.380454Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-01T03:10:54.954403Z","title":"volume 42 ofCambridge Series in Statistical and Probabilistic Mathematics","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$","version":1},"reference_index":2016,"source":"pdf_text","source_observed_at":"2026-08-01T03:10:54.954403Z"},"links":{"citing_paper":"/paper/2607.25277"},"observation_digest":"sha256:43509d0a902a009acc1c949c5b21ba5f730ecdb6edaa5ab2baac911027448f56","observation_id":"5d31375a-3fe7-4cb7-b641-c640bb1efda6","resolution":{"observed_at":"2026-08-01T03:10:54.954403Z","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":"10.1016/j.spa.2020.03.014","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Stochastic Process","venue":"Stochastic Processes and their Applications","work_id":"8f17db4b-92e9-4504-b4d2-4a1a22195799","year":2020},"citing_paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$","version":1},"reference_index":2020,"source":"pdf_text","source_observed_at":"2026-08-01T03:10:54.951188Z"},"links":{"citing_paper":"/paper/2607.25277"},"observation_digest":"sha256:c0610f8b26404bfa06cfb41b999624499a5f3fd45e36c324067831e3138e21d0","observation_id":"97480251-0c60-42ed-878f-ab7211a11731","resolution":{"observed_at":"2026-08-01T03:14:12.848552Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4171/aihpd/106","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Annales de l’Institut Henri Poincaré D Combinatorics Physics and their Interactions","work_id":"384c61c7-7722-49f7-9b17-d2615f9c9a0a","year":null},"citing_paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$","version":1},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-01T03:10:54.947631Z"},"links":{"citing_paper":"/paper/2607.25277"},"observation_digest":"sha256:07762f910531f2c9e4534f2128c0168fc370d6edab0935e8dc5372972125dfd7","observation_id":"528a9530-a774-4c94-96b1-d7954d93f445","resolution":{"observed_at":"2026-08-01T03:14:13.059840Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/21-aihp1231","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Annales de l Institut Henri Poincaré Probabilités et Statistiques","work_id":"ddaf5ce9-a797-4e98-9258-cf9af28b845d","year":null},"citing_paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-01T03:10:54.957967Z"},"links":{"citing_paper":"/paper/2607.25277"},"observation_digest":"sha256:72ccac3037a8925dd8b6c7bf061b1bc9b419eae84e76ea3fd4102764cb87137a","observation_id":"126eb07c-d8c2-4094-a227-db6fb66991f9","resolution":{"observed_at":"2026-08-01T03:14:12.620030Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1112/blms.13101/","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T03:14:13.579790Z","title":"Bulletin of the London Mathematical Society 56, 2794–2801","venue":null,"work_id":"8dd9832e-7183-4840-8cdb-b2e67e9e960a","year":null},"citing_paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-01T03:10:54.937492Z"},"links":{"citing_paper":"/paper/2607.25277"},"observation_digest":"sha256:7c00723f3a4b5c2ce206899da610f05ba424d87dfabb948461874d7c260ae3f4","observation_id":"4c27da66-24e3-4cf3-b68d-f140853f29d0","resolution":{"observed_at":"2026-08-01T03:14:13.638107Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2607.25277","last_updated":"2026-07-28T04:30:22Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-04T01:46:14.019432Z","submitted_at":"2026-07-28T04:30:22Z","title":"A note on the random constrained-degree percolation model on $\\mathbb{L}^2$"},"reference_resolution":{"displayed":14,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":9,"verified_fuzzy":0},"total_outbound_references":14},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:2607.25277."}