{"as_of":"2026-08-11T20:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ce78728f10d88d0dd66c42f33b906f514ac3a95dfc1d3df0d4153a4a3434399c","coverage":[{"denominator":34,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":34,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T23:19:02.887510Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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/2607.15510/citation-record","integrity":"/paper/2607.15510/integrity","json":"/paper/2607.15510/citation-record.json","paper":"/paper/2607.15510"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T23:18:59.954772Z","title":"Skolem, Ein Verfahren zur Behandlung gewisser exponentialer Gle- ichungen, in: Comptes rendus du congrès des mathématiciens scandi- naves, 1934","venue":null,"work_id":null,"year":1934},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T23:18:59.954772Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:6408184980606ede868fa448350b9acb298e4a338060db2589cfc9377a296003","observation_id":"84fd3887-0b4b-4162-bbc9-87f9e2715869","resolution":{"observed_at":"2026-08-01T23:18:59.954772Z","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":"2026-08-01T23:19:00.084186Z","title":"Mahler, Eine arithmetische Eigenschaft der Taylor Koeffizienten ra- tionaler Funktionen, Proc","venue":null,"work_id":null,"year":1935},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:00.084186Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:d5f520f1a0c3e256c9ede57ccd6dc1e36ef141b27ce8e2390affa187f050d993","observation_id":"e8601d0e-648f-417b-8220-6d20ecd0fb2e","resolution":{"observed_at":"2026-08-01T23:19:00.084186Z","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":"2026-08-01T23:19:00.191455Z","title":"Lech, A note on recurring series, Ark","venue":null,"work_id":null,"year":1953},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:00.191455Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:bf1b0ff151a715a81d8b21829b722b9da5cf436b74f5361efa9e5cac780d3e17","observation_id":"0b41d685-03a4-4706-8978-a108db3ee54d","resolution":{"observed_at":"2026-08-01T23:19:00.191455Z","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":"2026-08-01T23:19:00.271376Z","title":"Everest, A","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:00.271376Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:a5a47a213a74ae94a5bbbd5a64f9258b654f32f0b2c46a68ace2129427b6dcc1","observation_id":"bf056337-2e52-4009-8d1b-ab7ac4302eb9","resolution":{"observed_at":"2026-08-01T23:19:00.271376Z","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":"2026-08-01T23:19:00.392014Z","title":"Kauers, P","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:00.392014Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:e70a7eb2d378836d33684f414dc2b2d80b4f5e6485efc94ca75fd474f6668834","observation_id":"4553a405-24a4-49ed-92d8-d8ce56171501","resolution":{"observed_at":"2026-08-01T23:19:00.392014Z","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":"2026-08-01T23:19:00.553609Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:00.553609Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:16efda3300d7d98a101082e4b4a82551a0f050fce2fe87ce312f316feb4de2c5","observation_id":"0c5fa648-e1fe-4316-862a-553c3527031a","resolution":{"observed_at":"2026-08-01T23:19:00.553609Z","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":"2026-08-01T23:19:00.651534Z","title":"Berstel, C","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:00.651534Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:fc10ad5e1b5429bbc8e6101c9ddd02dac69ce9dbc908403d5ad7968ce4acb123","observation_id":"9c455805-906d-499b-858a-e09d0418a013","resolution":{"observed_at":"2026-08-01T23:19:00.651534Z","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":"2026-08-01T23:19:00.811495Z","title":"Tao, Structure and randomness: pages from year one of a mathemat- ical blog, American Mathematical Society, 2008","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:00.811495Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:a3f39481f8d5a4b770bc531967ad2c48277d30729eba60ef727358b1783384cb","observation_id":"f1756d6d-7fcb-439d-ad57-5397726b694b","resolution":{"observed_at":"2026-08-01T23:19:00.811495Z","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":"2026-08-01T23:19:00.933148Z","title":"Rozenberg, A","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:00.933148Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:b22a4c76d88233e1c85b77b6973e109d53b933adf97b5ba1a885d59740b14238","observation_id":"ee2e4cea-b5ed-4ac1-a5a1-7c18492af878","resolution":{"observed_at":"2026-08-01T23:19:00.933148Z","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":"2026-08-01T23:19:01.061455Z","title":"Beauquier, A","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:01.061455Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:ecd6ae8fc55e681e975a8213c5c41a0e35badec4b5501895d2f7749533a96d4c","observation_id":"663d533a-ffb7-4491-9b04-6850af72c7ff","resolution":{"observed_at":"2026-08-01T23:19:01.061455Z","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":"2026-08-01T23:19:01.184664Z","title":"Piribauer, C","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:01.184664Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:88936e1ced5517fbd8024f6d94936865baaad67ac4d452f348bc03f02fe4780f","observation_id":"6efb556f-e63b-4065-9cc8-78b4ac204137","resolution":{"observed_at":"2026-08-01T23:19:01.184664Z","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":"2026-08-01T23:19:01.217215Z","title":"Blondel, J","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:01.217215Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:c21bc4ad095e18e1f279acea71ca641cabf255de87acb285e0e543dd1964a59b","observation_id":"2b72d8cd-3525-4c4d-9490-88d65b858095","resolution":{"observed_at":"2026-08-01T23:19:01.217215Z","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":"2026-08-01T23:19:01.287742Z","title":"Fijalkow, J","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:01.287742Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:d8da25c7b582e974c99a49edea20132d15c6d8d7b13df85e3d72ff6d351b5119","observation_id":"bffcebf6-bf33-4a9b-ad8c-3c8005f86f18","resolution":{"observed_at":"2026-08-01T23:19:01.287742Z","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":"2026-08-01T23:19:01.344221Z","title":"Ouaknine, J","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:01.344221Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:2c678faf3b2477a0877c7c33dba3fc57440745dafac96befaf3a2b9bb3670ae5","observation_id":"40b4fe5b-3915-4132-94b8-aee82e7c7cc1","resolution":{"observed_at":"2026-08-01T23:19:01.344221Z","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":"2026-08-01T23:19:01.429799Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:01.429799Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:ee911fc7d8ebbc18fd0579c8068c247cd8f816908fada972b763222489423e9f","observation_id":"c2549b31-5839-4887-b1af-1641c67e4f75","resolution":{"observed_at":"2026-08-01T23:19:01.429799Z","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":"2026-08-01T23:19:01.493610Z","title":"Kannan, R","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:01.493610Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:3c3e81929bccb44c83566ebb2ffb53a5a0429f56b40ab353af782f3c62d9822e","observation_id":"06126983-de39-461b-aa98-5601cd418d4e","resolution":{"observed_at":"2026-08-01T23:19:01.493610Z","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":"2026-08-01T23:19:01.571806Z","title":"Mignotte, T","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:01.571806Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:39ed618792d8a89c943dc98619889721c4e05a37a0251027c627e051dbf5259c","observation_id":"52307996-1eb7-454a-895a-32f025f1f599","resolution":{"observed_at":"2026-08-01T23:19:01.571806Z","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":"2026-08-01T23:19:01.651189Z","title":null,"venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:01.651189Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:a0c89d6c3c6f05880f34370e6ad63c015891c342e3953852f2247f89f39b3544","observation_id":"5bed1708-6fc3-4ac2-ab81-6ea132bb773b","resolution":{"observed_at":"2026-08-01T23:19:01.651189Z","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":"2026-08-01T23:19:01.721718Z","title":"Akshay, N","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:01.721718Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:6eff34fa040572cf57a220eec269f59a8a508e3153a6a2a6bc5984f520c07814","observation_id":"e9de6048-aa39-45b4-863e-dd827b8eed05","resolution":{"observed_at":"2026-08-01T23:19:01.721718Z","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":"2026-08-01T23:19:01.796155Z","title":"Lipton, F","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:01.796155Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:b5c7dd8d2872c59991817bb1c9b16937d503353e230e4d0a3aa8ce47c9329cfb","observation_id":"c29dbe92-b195-439f-8397-afc671a51c9b","resolution":{"observed_at":"2026-08-01T23:19:01.796155Z","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":"2026-08-01T23:19:01.872699Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:01.872699Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:6da964e635e7600fe379b7ea6772c599e6e54edbd4febae0682034813f21be1e","observation_id":"fbf91bef-3f47-49e1-8b94-2ae20055682c","resolution":{"observed_at":"2026-08-01T23:19:01.872699Z","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":"2026-08-01T23:19:01.933082Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:01.933082Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:fc05c98b8f7511b2bae7d1ceb2bb7873d740df7a33543e6b0b4b56b179e496f3","observation_id":"10ed8758-0223-4eaa-af46-a2ad5de1c366","resolution":{"observed_at":"2026-08-01T23:19:01.933082Z","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":"2026-08-01T23:19:02.010301Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:02.010301Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:5b9c2e21c1816c70c6d45b991d917e3ffa308af4407eb432004c77b365b4a5e1","observation_id":"da2879f8-4c72-445a-9bea-13c8f72b5ecf","resolution":{"observed_at":"2026-08-01T23:19:02.010301Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2308.01152","last_updated":"2026-08-05T03:25:17Z","snapshot_observed_at":"2026-08-11T06:40:50.204254Z","submitted_at":"2023-08-02T13:57:01Z","title":"Skolem Meets Bateman-Horn","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.01152","snapshot_observed_at":"2026-08-01T23:19:02.108978Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:02.108978Z"},"links":{"cited_paper":"/paper/2308.01152","citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:f52af3f2b8d7ba0ad4a68ca000fd7a1c856c78e7bc5277ec6cc96378b5f464aa","observation_id":"8144c0cf-27a9-4672-968f-97512dedd115","resolution":{"observed_at":"2026-08-01T23:19:02.108978Z","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":"2026-08-01T23:19:02.178244Z","title":"Cramér, On the order of magnitude of the difference between consec- utive prime numbers, Acta Arith","venue":null,"work_id":null,"year":1936},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:02.178244Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:74d1718088c04bf63329afc9969ec9a56c502c3983601e2da054685d87a32810","observation_id":"940fe748-6da7-4543-a1cd-37fd8ae9a0ad","resolution":{"observed_at":"2026-08-01T23:19:02.178244Z","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":"2026-08-01T23:19:02.253293Z","title":"Oliveira e Silva, S","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:02.253293Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:a434d8251ae70e54fe422ff3cf79dd96b3b2cfdd007b13488481bdd845ae76bc","observation_id":"cf01c430-ce0d-4460-bb8f-193284f59ebe","resolution":{"observed_at":"2026-08-01T23:19:02.253293Z","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":"2026-08-01T23:19:02.330794Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:02.330794Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:5ba0810abb66c0859e27b0bd3ed449da597a630a055350e5187eb1ca904ed07c","observation_id":"451c6022-039c-493f-98e4-e2a8b72caa2c","resolution":{"observed_at":"2026-08-01T23:19:02.330794Z","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":"2026-08-01T23:19:02.401499Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:02.401499Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:a9d755a97e5fc1ec92e2b10e8d87bb29c1015a07b423a4cd31f3dcfc7f33a24e","observation_id":"63e4e52b-6a47-4407-ae0e-609f8ea4bc21","resolution":{"observed_at":"2026-08-01T23:19:02.401499Z","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":"2026-08-01T23:19:02.479401Z","title":"Granville, Harald Cramér and the distribution of prime numbers, Scandinavian Actuarial Journal 1995 (1) (1995) 12–28","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:02.479401Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:9993bf21665483b86756e860baefd0c72246beb165c74636a1c1f99f32e346e9","observation_id":"1e734501-8c2d-4057-841d-a60ff57020b7","resolution":{"observed_at":"2026-08-01T23:19:02.479401Z","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":"2026-08-01T23:19:02.565867Z","title":"Fröhlich, M","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:02.565867Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:ef3cb18a546c8de450c7844697c9fa90110293401d9b109801b90a5195199544","observation_id":"1577932e-858e-4c6a-9f29-1ed61c37725b","resolution":{"observed_at":"2026-08-01T23:19:02.565867Z","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":"2026-08-01T23:19:02.638221Z","title":"Odlyzko, M","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:02.638221Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:b497e1ef915445b50557b0c7e7c5fd97da4b5fea94dd73e9b92a22e59560bf63","observation_id":"c3b2545c-c96d-4745-955c-652d7587746c","resolution":{"observed_at":"2026-08-01T23:19:02.638221Z","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":"2026-08-01T23:19:02.707531Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:02.707531Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:8b0461bb17dd6c8b8880ca8af44fcc43cf1f9ff0d060e1d9c766bcf28180c0e9","observation_id":"429b480c-3c5f-4149-8bb6-6ea54b584cec","resolution":{"observed_at":"2026-08-01T23:19:02.707531Z","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":"2026-08-01T23:19:02.793216Z","title":"Amoroso, E","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:02.793216Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:7b8bca64329ff57239eee04753ce04b08587d86ffd52b1327276988bcf7327a7","observation_id":"c78608e6-10d9-43a1-a4d1-3d5a5f283072","resolution":{"observed_at":"2026-08-01T23:19:02.793216Z","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":"2026-08-01T23:19:02.887510Z","title":"Jia, Almost all short intervals containing prime numbers, Acta Arith","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-01T23:19:02.887510Z"},"links":{"citing_paper":"/paper/2607.15510"},"observation_digest":"sha256:f25057c700bfd10f59b508f15eaa6fc621c45503cddc37c133b7b09abab01c94","observation_id":"358b81bb-dbb2-4a5c-b317-47e5c287f60d","resolution":{"observed_at":"2026-08-01T23:19:02.887510Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.15510","last_updated":"2026-07-16T23:45:15Z","latest_version":1,"primary_category":"cs.DM","snapshot_observed_at":"2026-08-06T08:34:12.041865Z","submitted_at":"2026-07-16T23:45:15Z","title":"Conjectural Decidability of the Skolem Problem"},"reference_resolution":{"displayed":34,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":34,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":34},"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 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2607.15510."}