{"as_of":"2026-08-07T16:28:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0385b8e6ae0aec097128bd3cde1a8527d0337175327ef8a3706e095f2ca56ee1","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T00:46:14.847287Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+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/2607.26167/citation-record","integrity":"/paper/2607.26167/integrity","json":"/paper/2607.26167/citation-record.json","paper":"/paper/2607.26167"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T00:46:12.413489Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:12.413489Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:89e347e0f325d83512b4d70cd158c131969c09b0e7867126775825a3e4ad0709","observation_id":"20e3fb50-fc4a-4080-8756-95bbbdaf495b","resolution":{"observed_at":"2026-08-01T00:46:12.413489Z","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":"2026-08-01T00:46:12.492511Z","title":"K., On the discrete Safronov-Dubovski ˇi coagulation equations: well- posedness, mass conservation, and asymptotic behavior,Math","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:12.492511Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:237875ec6a762fdc5da9481c74807be2224c98bb54aa5ec33033924eb588ee68","observation_id":"a0b11102-f5b9-403f-9796-71a85135d9e9","resolution":{"observed_at":"2026-08-01T00:46:12.492511Z","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":"2026-08-01T00:46:12.585623Z","title":"K., Global existence of solutions to the discrete Safronov-Dubovski ˇi coagulation equations and failure of mass-conservation,J","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:12.585623Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:3b4a4bf2655e20359558191dcc07925c299a817875d2e7dd2cf10821d047956b","observation_id":"8c15f1e6-d3de-472e-ad14-871fc1738c49","resolution":{"observed_at":"2026-08-01T00:46:12.585623Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2308.10232","last_updated":"2025-08-07T12:07:29Z","snapshot_observed_at":"2026-07-06T16:08:08.552117Z","submitted_at":"2023-08-20T11:37:10Z","title":"Gelation in cluster coagulation processes","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.10232","snapshot_observed_at":"2026-08-01T00:46:12.710612Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:12.710612Z"},"links":{"cited_paper":"/paper/2308.10232","citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:d25abee5fb71436c32168bc5f553fb188eaa99577a8cd669e1555fa6f74bcc27","observation_id":"fbac1133-0e3a-4629-9c08-a90f25f33497","resolution":{"observed_at":"2026-08-01T00:46:12.710612Z","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":"2026-08-01T00:46:12.823812Z","title":"Methods Appl","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:12.823812Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:6771e9da02f0eb9f61000ed359aa8c6e1b09b6c60a9b8214715b011ae05716a3","observation_id":"b9ca08b9-7ee5-48b1-aaa4-c9f9b114fb40","resolution":{"observed_at":"2026-08-01T00:46:12.823812Z","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":"2026-08-01T00:46:12.911385Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:12.911385Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:380b491fe4863b1616525866b1c4a6f9baf711ec904625b516c3028bc6a9e28c","observation_id":"27342f71-26ea-4b67-a997-cf5c52ec4796","resolution":{"observed_at":"2026-08-01T00:46:12.911385Z","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":"2026-08-01T00:46:13.017813Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:13.017813Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:849528f345b864ccce716a73623c6d87a1a6223549a5097db86152900dd23dff","observation_id":"c6d799a6-bf6d-4ab0-bcd3-909df0c01ab9","resolution":{"observed_at":"2026-08-01T00:46:13.017813Z","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":"2026-08-01T00:46:13.128470Z","title":"K., Rai, P., Giri, A","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:13.128470Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:cacfffc57cea3ede678634edcd47c78ec77386a5fa5ab1249147e27c07633fd5","observation_id":"3d81940c-89d6-41fd-bad9-45b28b189b9f","resolution":{"observed_at":"2026-08-01T00:46:13.128470Z","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":"2026-08-01T00:46:13.272247Z","title":"P., On the positivity of solutions to the Smoluchowski equations,Mathematika,42, 406–412, 1995","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:13.272247Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:f2cc4ab993ca302e06e0cf8f9252c39c4396801988bfc135affcdc03703f06c4","observation_id":"ad2c288b-80db-4d0b-a97e-058a2ab1c2a1","resolution":{"observed_at":"2026-08-01T00:46:13.272247Z","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":"2026-08-01T00:46:13.410628Z","title":"P., Mathematical aspects of coagulation-fragmentation equations, inMathematics of Energy and Climate Change, Springer International Publishing, Cham, 83–162, 2015","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:13.410628Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:c1dc16da717fa0f7006ebe2c137da330069b2b4fa5cbf8c5ae55271db73e00cc","observation_id":"942c9d76-fad4-4197-a180-b3b6cbfe7bf2","resolution":{"observed_at":"2026-08-01T00:46:13.410628Z","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":"2026-08-01T00:46:13.509801Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:13.509801Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:c22411a6f3bed30b8441fd76bc600373cee52b142eb62c2d0d038e8850cb4fe5","observation_id":"e397d69d-4015-42f7-8db3-e3126206a45e","resolution":{"observed_at":"2026-08-01T00:46:13.509801Z","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":"2026-08-01T00:46:13.620431Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:13.620431Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:858d4ad77a33a5587b03776805afb0fa51496a54550c5d1839b72e0fca6d6e8e","observation_id":"d3017fa6-88d5-48d9-b315-3e7e4db9da49","resolution":{"observed_at":"2026-08-01T00:46:13.620431Z","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":"2026-08-01T00:46:13.766627Z","title":null,"venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:13.766627Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:00106962a9a656bc1ab98806980bd56ad6fd9e4877c739ba58885b2deadcbe0f","observation_id":"35b4ed27-248f-4b83-a8b7-7a69f1475e87","resolution":{"observed_at":"2026-08-01T00:46:13.766627Z","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":"2026-08-01T00:46:13.914747Z","title":"B., Structural stability of disperse systems and finite nature of a coagulation front,J","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:13.914747Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:5e8baee90e775b3872fc1c609a12d40a84e56178b07d5b1ff951038b2398765f","observation_id":"7d51e81c-be1c-4fba-9cb1-89d3b44db362","resolution":{"observed_at":"2026-08-01T00:46:13.914747Z","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":"2026-08-01T00:46:14.059887Z","title":"B., A ‘triangle’ of interconnected coagulation models,J","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:14.059887Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:2a9bdd6e5dcb4b42a2f61eaeb320982e69fae0368458f753197a61f6149d5acd","observation_id":"7b400777-736c-46da-b7cd-687a1c0b850b","resolution":{"observed_at":"2026-08-01T00:46:14.059887Z","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":"2026-08-01T00:46:14.163901Z","title":"Math´ ematique,363(G6), 583–591, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:14.163901Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:f67891f1dd2d19d337702e1ff271909e94988ef138d373f2a95637ab985cb3ab","observation_id":"7ab4e9c1-d517-45a3-8a41-2947db61ade4","resolution":{"observed_at":"2026-08-01T00:46:14.163901Z","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":"2026-08-01T00:46:14.222517Z","title":"P., Theoretical analysis of a discrete population balance model with sum kernel,Port","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:14.222517Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:1b7600ef1f4a874b774246dc11feae79ad5e212cf63588fc6363cc27775a462a","observation_id":"256df456-4af8-4b82-85d4-fe1069c41fb1","resolution":{"observed_at":"2026-08-01T00:46:14.222517Z","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":"2026-08-01T00:46:14.336664Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:14.336664Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:6f59d47ec87432e3449c34bccebc16492b51755be420ab2cc1dd724af16f0b0c","observation_id":"c6403658-4d52-400f-a6f6-f4a896d3c2f9","resolution":{"observed_at":"2026-08-01T00:46:14.336664Z","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":"2026-08-01T00:46:14.465049Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:14.465049Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:30c8399fc0bce33a2c6ad3ed21c12147739d70ff80ab8efe2e95a5b986798e53","observation_id":"c498ac79-80a7-4e62-ad77-58f2ff47c738","resolution":{"observed_at":"2026-08-01T00:46:14.465049Z","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":"2026-08-01T00:46:14.570950Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:14.570950Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:0ad5c178f26d696ddf62d40d30676d71166cba56cc4acd9c822d31c3c6878731","observation_id":"072e2ca7-9b80-4148-bda1-1531c4452cdc","resolution":{"observed_at":"2026-08-01T00:46:14.570950Z","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":"2026-08-01T00:46:14.661826Z","title":"H., Van de Hulst, H","venue":null,"work_id":null,"year":1946},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:14.661826Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:2f2ff6f78a8ebef978618aae71cbc1a2d4449a0c6af4bc5bb5d81dfdeb3ab812","observation_id":"8a3d98bd-22b1-494c-beae-ec9fa73dc9a5","resolution":{"observed_at":"2026-08-01T00:46:14.661826Z","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":"2026-08-01T00:46:14.764796Z","title":"Probab.,41(3B), 1806–1830, 2013","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:14.764796Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:1034cdacec60407b8c50b2ac23633378819618dec66973a424619837a38bb742","observation_id":"bd2e4920-7cbc-4df9-8452-8a171b392c59","resolution":{"observed_at":"2026-08-01T00:46:14.764796Z","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":"2026-08-01T00:46:14.847287Z","title":"S.,Evolution of the Protoplanetary Cloud and Formation of the Earth and the Planets, Israel Program for Scientific Translations, Jerusalem, 1972","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T00:46:14.847287Z"},"links":{"citing_paper":"/paper/2607.26167"},"observation_digest":"sha256:5b2c2783d48609398f3a82a5401181a2a39c23fe49f576e5f9ad4e83b3b24c43","observation_id":"3e7165a8-06d0-4d8b-865f-d9cd5d639e0a","resolution":{"observed_at":"2026-08-01T00:46:14.847287Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.26167","last_updated":"2026-07-28T18:16:50Z","latest_version":1,"primary_category":"math.CA","snapshot_observed_at":"2026-08-06T19:43:19.602191Z","submitted_at":"2026-07-28T18:16:50Z","title":"Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":23,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":23},"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 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2607.26167."}