{"as_of":"2026-08-11T14:47:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c72efc92042870011dd3726b2c2b912bd661be120a28aef8a163e8b7ad0bb035","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T04:33:24.636816Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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":"2026-08-07T05:09:49.753340Z","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":"2026-05-22T17:36:52.808061Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"cited_work":{"arxiv_id":"2412.18915","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.18915","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"fdc3cdab-5f3c-48d1-9978-7d2070db9969","year":null},"citing_paper":{"arxiv_id":"2505.01148","last_updated":"2025-05-02T09:46:17Z","snapshot_observed_at":"2026-08-06T05:40:29.787263Z","submitted_at":"2025-05-02T09:46:17Z","title":"The class $\\boldsymbol{Q}$ and mixture distributions with dominated continuous singular parts","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-22T17:35:49.168113Z"},"links":{"cited_paper":"/paper/2412.18915","citing_paper":"/paper/2505.01148"},"observation_digest":"sha256:1277ed1a2e9d91f8889a1d93a05a16edfc1f4d3e7c676cb641d3d9f5219830c2","observation_id":"f500ce97-9ff4-4261-8d97-ef8be6a1ab6d","resolution":{"observed_at":"2026-05-22T17:36:52.811415Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.18915","snapshot_observed_at":"2026-08-07T05:09:49.753340Z","title":"Khartov, On decomposition problem for distribution functions of class Q","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.09012","last_updated":"2025-06-11T10:12:48Z","snapshot_observed_at":"2026-08-07T21:12:55.226388Z","submitted_at":"2025-06-10T17:41:40Z","title":"Invertible Complex Measures on Euclidean Spaces","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T05:09:49.753340Z"},"links":{"cited_paper":"/paper/2412.18915","citing_paper":"/paper/2506.09012"},"observation_digest":"sha256:b6a5e7d9cd51918b5dfa85c6dee1e70d367998cd91e1a8e6cfb3e87a29e49a50","observation_id":"76dbeffa-470f-4afc-a3b6-4db5f2a73cc5","resolution":{"observed_at":"2026-08-07T05:09:49.753340Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2412.18915/citation-record","integrity":"/paper/2412.18915/integrity","json":"/paper/2412.18915/citation-record.json","paper":"/paper/2412.18915"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T04:33:24.240304Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.240304Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:fdba22081548a7af639d54962903e2dbbb8b96157229bd4bdcde68d700abbf50","observation_id":"8d55579e-7ce1-4915-ac22-1064cc9bf916","resolution":{"observed_at":"2026-08-11T04:33:24.240304Z","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":"2026-08-11T04:33:24.245182Z","title":"Applebaum, L´ evy Processes and Stochastic Calculus, Camb","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.245182Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:82810039437d44580b12c67c43f148859298c6de76f288515fe60e5acf770b01","observation_id":"9a1adcec-6cd1-4822-b718-018a7be8044f","resolution":{"observed_at":"2026-08-11T04:33:24.245182Z","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":"2026-08-11T04:33:24.250862Z","title":"Berger, On quasi-infinitely divisible distributions with a point ma ss, Math","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.250862Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:28d8f1bef388a7519253fdc594375251663ea895f7cd6da13597d58cb8f57fc8","observation_id":"c90b7fae-8b55-4b97-9ea0-2476a63fd8c1","resolution":{"observed_at":"2026-08-11T04:33:24.250862Z","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":"2026-08-11T04:33:25.241619Z","title":"Berger, M","venue":null,"work_id":"5da5ce25-bbd0-47df-8e35-6d5d19626427","year":2023},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.256888Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:e8dead8faed8aa144ee0baff5ef302cfdc1dd7d84bf545ca0d3f4888f88b477e","observation_id":"3f21025c-ee23-4cdd-96cb-63c4e81f009c","resolution":{"observed_at":"2026-08-11T04:33:25.245100Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-11T04:33:24.260664Z","title":"Chhaiba, N","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.260664Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:3657ed371e5e369fcad3aee4471770512fc77948a6acd5f46dc94106c6d8d67d","observation_id":"e441155a-a0d9-41c1-bd39-4a9852d99593","resolution":{"observed_at":"2026-08-11T04:33:24.260664Z","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":"2026-08-11T04:33:25.184518Z","title":"Cuppens, Decompositions of Multivariate Probabilities , Academic Press, New-York–London, 1975","venue":null,"work_id":"8f67f315-683e-407b-8b47-38e8e9d86989","year":1975},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.266338Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:23b57c8394619f27c7c23364bce55145bece54c2be0841d04c247be5041ca880","observation_id":"1b5f759b-c09d-4bcc-83d3-59292d5deedc","resolution":{"observed_at":"2026-08-11T04:33:25.199662Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-11T04:33:24.273797Z","title":null,"venue":null,"work_id":null,"year":1954},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.273797Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:c6673afba065b4afa15a065af7a2343db0f8ed495369dbe49759b3c73f92bd3e","observation_id":"8d45bd59-e3db-44f4-97ad-1a2cfebdc476","resolution":{"observed_at":"2026-08-11T04:33:24.273797Z","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":"2026-08-11T04:33:25.126085Z","title":null,"venue":null,"work_id":"1d60c913-2fbe-4ce5-896a-3f276e299c0a","year":1975},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.280516Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:af24989bf22eb6fa52f3fbe1e87655acb7ba917bc39287beb7c65912e274684c","observation_id":"d2639e2f-910e-4881-8acb-76532568ef9e","resolution":{"observed_at":"2026-08-11T04:33:25.147370Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-11T04:33:24.283901Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.283901Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:b2d4ab8bd0b220da973470ef7f74438816ff1bf40f717098f62838a22edfaec8","observation_id":"50ac06b2-0e40-44d7-be17-0a14a8c36d8b","resolution":{"observed_at":"2026-08-11T04:33:24.283901Z","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":"2026-08-11T04:33:24.287386Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.287386Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:dda6daf644f4790537a0c812f8c401604ecaec85ac647e4e697f8f06560cea89","observation_id":"60811e04-28bd-4a2d-8a57-2ddefbc9cdae","resolution":{"observed_at":"2026-08-11T04:33:24.287386Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.14524","last_updated":"2024-09-12T20:20:40Z","snapshot_observed_at":"2026-07-06T15:32:06.975391Z","submitted_at":"2023-05-23T20:56:42Z","title":"Some criteria of rational-infinite divisibility for probability laws","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.14524","snapshot_observed_at":"2026-08-11T04:33:24.291134Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.291134Z"},"links":{"cited_paper":"/paper/2305.14524","citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:d5f8df7999053a03249bff1278ac6f956b59985079795dbca77ad48b2300c3b0","observation_id":"6edf3a79-2076-467b-b0f9-944fcef4456b","resolution":{"observed_at":"2026-08-11T04:33:24.291134Z","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":"2026-08-11T04:33:25.011569Z","title":null,"venue":null,"work_id":"0f8f0919-a44f-4349-91a9-73649ab6e560","year":1938},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.316434Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:66a9f9fd6ee3c4bed48b40ca0590d82a54977eaf411855e8c937663a59790c6a","observation_id":"9fea5285-5ae9-4e8b-a7a5-fd8be8ee8c94","resolution":{"observed_at":"2026-08-11T04:33:25.056994Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-11T04:33:24.346876Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.346876Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:44fe96e0588c05ba90936e8a1000bc786e9d3318f1114bc12bd37a14315a8d24","observation_id":"09f1a204-d49e-4c69-be97-d0f4a379d3eb","resolution":{"observed_at":"2026-08-11T04:33:24.346876Z","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":"2026-08-11T04:33:24.385442Z","title":"Lindner, L","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.385442Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:f93e95e90441a10d67abbeea7ac57fb049b0047c42c522b88bca37b3dc24f1cb","observation_id":"a5bd7f38-6c2b-4e70-a0e0-fdd414e22537","resolution":{"observed_at":"2026-08-11T04:33:24.385442Z","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":"2026-08-11T04:33:24.913151Z","title":null,"venue":null,"work_id":"7aece5c7-0cb7-4ac9-904c-591b861ada8b","year":1977},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.421170Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:ac13e3a111bb3d66adf2192fe7bb8637c1d190db1612343d9ede45c0820f64dd","observation_id":"3e9ecfc0-5616-489d-b012-7d00d2438b62","resolution":{"observed_at":"2026-08-11T04:33:24.960429Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-11T04:33:24.471953Z","title":"Lukacs, Characteristic Functions, Griffin, London, 1970","venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.471953Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:ec0fb958e3c711a8d904556274a9143646172add17b432c919ab77bb285254c5","observation_id":"1bd95d3a-3262-44d6-9f7f-afa838379e20","resolution":{"observed_at":"2026-08-11T04:33:24.471953Z","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":"2026-08-11T04:33:24.488269Z","title":"Nakamura, A complete Riemann zeta distribution and the Riemann hypoth esis, Bernoulli 21 (2015), 1, 604–617","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.488269Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:d60ee48e227ec95600cf1c5e8bc3af5bda88ff7ed96a799f30d6c4973ebd7fdb","observation_id":"9c2d7a3e-18f1-413c-a945-603e1eb9cde0","resolution":{"observed_at":"2026-08-11T04:33:24.488269Z","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":"2026-08-11T04:33:24.814618Z","title":"V.Ostrovskij, P","venue":null,"work_id":"bdeb0ebd-2bf0-4787-85e8-fed4157519aa","year":1981},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.506446Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:a1f3b14f09f2e24b0adbddef8b7849d4090118d702237a2adc4b397f13f3ce55","observation_id":"7c1d412a-0a0a-4c88-aa0e-e1eeb79a56ea","resolution":{"observed_at":"2026-08-11T04:33:24.855636Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-11T04:33:24.779587Z","title":null,"venue":null,"work_id":"aff78adf-bb59-4393-80dc-ba5e6f47e332","year":1995},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.528256Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:86a3f9ef1d3e3bc5347e4aef5a42067f91f6bd0dd61d42a73d68094adffd3444","observation_id":"13fa848e-1622-4b4e-a5ea-817b86f3365c","resolution":{"observed_at":"2026-08-11T04:33:24.789337Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-11T04:33:24.545642Z","title":"Sato, L´ evy Processes and Infinitely Divisible Distributions, Camb","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.545642Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:ebb8e73b50c163ef4c900e174949929c7385eaa1f9bcd8ffe0a215a1a1da07e4","observation_id":"1f75f3b5-9300-4136-a141-3575816df816","resolution":{"observed_at":"2026-08-11T04:33:24.545642Z","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":"2026-08-11T04:33:24.757332Z","title":"Schoutens, L´ evy Processes in Finance: Pricing Financial Derivatives, Wiley, Chichester, 2003","venue":null,"work_id":"33d53ea6-4c1b-4d9d-bd51-04f14ce3321b","year":2003},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.555343Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:6da3d4c870e6a06f4b4a0a96f5959ffcd1d907db29b612a6021d9efae4ae5554","observation_id":"3cdfa41e-a3d3-4597-8b8a-fc3fb26bdf72","resolution":{"observed_at":"2026-08-11T04:33:24.765159Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.11377","last_updated":"2024-06-17T09:53:28Z","snapshot_observed_at":"2026-07-06T18:32:06.826381Z","submitted_at":"2024-06-17T09:53:28Z","title":"Vague and basic convergence of signed measures","version":1},"cited_work":{"arxiv_id":"2406.11377","doi":null,"metadata_source":"pith","pith_arxiv_id":"2406.11377","snapshot_observed_at":"2026-08-11T04:33:24.679715Z","title":"Vague and basic convergence of signed measures","venue":"math.PR","work_id":"ca4eedc5-3139-4c93-b478-0b59adb26d9d","year":2024},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.578321Z"},"links":{"cited_paper":"/paper/2406.11377","citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:e140ac07b6cfd3e5cd3fd094e3a351204d67e98612fefc90cc19116e3708b4cf","observation_id":"663aac47-2f29-456e-8f18-712794ed8ffb","resolution":{"observed_at":"2026-08-11T04:33:24.691069Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-11T04:33:24.746165Z","title":"Zhang, Y","venue":null,"work_id":"929b4cf5-0185-4765-971d-94cf49b169a4","year":2014},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.597966Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:29aa28675dac59550ebc26c1b7a92f93f47e695d12c9e37159951d52377fc0e0","observation_id":"4e12566f-66d4-4578-b55f-2dfa7fcd0959","resolution":{"observed_at":"2026-08-11T04:33:24.749543Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-11T04:33:24.735581Z","title":null,"venue":null,"work_id":"e5f33b49-d602-44c6-bb31-6016dea93c1b","year":1986},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.624474Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:f4532e6d894859b853fb9a385fa0b9749d52154e9713cfc93bd9413f2a9e2394","observation_id":"0abc2cca-a611-45f1-a3b8-0e0d97a5f0f0","resolution":{"observed_at":"2026-08-11T04:33:24.739193Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-11T04:33:24.714174Z","title":null,"venue":null,"work_id":"e82ecb5a-9005-4e2f-b8a8-bde813ba4fec","year":1997},"citing_paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T04:33:24.636816Z"},"links":{"citing_paper":"/paper/2412.18915"},"observation_digest":"sha256:7f20e17b358fe808aaefbf755fed197b60ec83624223dced755866cf4c140fc4","observation_id":"39af5a51-6521-4c77-a8dc-76204d4a607e","resolution":{"observed_at":"2026-08-11T04:33:24.724929Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.18915","last_updated":"2024-12-25T14:18:16Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-11T08:33:40.784879Z","submitted_at":"2024-12-25T14:18:16Z","title":"On decomposition problem for distribution functions of class $\\boldsymbol{Q}$"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":19,"verified_exact":1,"verified_fuzzy":5},"total_outbound_references":25},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 2 inbound Pith citation observations for arXiv:2412.18915."}