{"as_of":"2026-08-12T20:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8bb81f9cc841fcae6c6efcfc714466fa7ed581e1d4307f5a1d0abb24efc4ac12","coverage":[{"denominator":21,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":21,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T09:03:30.640464Z","state":"measured"},{"denominator":21,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":21,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2510.18024/citation-record","integrity":"/paper/2510.18024/integrity","json":"/paper/2510.18024/citation-record.json","paper":"/paper/2510.18024"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T09:03:28.037327Z","title":"Balog and C","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:28.037327Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:dfc0dadf09f6ea02573dd193d35ead09c871642a5c3d60d160b324673d79d2b2","observation_id":"294075a1-4b9a-4040-bd67-bffdb38e6dce","resolution":{"observed_at":"2026-08-04T09:03:28.037327Z","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":"2026-08-04T09:03:28.144451Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:28.144451Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:93924dd99bd35051d59bebad18b500c0d08e23a0e80d8556054e2f687fe01cd5","observation_id":"d87b4980-c1fc-40fc-a7fc-dcac3bb7cf58","resolution":{"observed_at":"2026-08-04T09:03:28.144451Z","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":"2026-08-04T09:03:28.205018Z","title":"de la Bret` eche and G","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:28.205018Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:8c2ddfb003957e768757845dd90cb3b873bdcbf2f2179fc1b0657576282e16af","observation_id":"a76bcf81-871f-4d0f-9644-4dbfe10aca3c","resolution":{"observed_at":"2026-08-04T09:03:28.205018Z","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":"2026-08-04T09:03:28.338079Z","title":"de la Bret` eche and G","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:28.338079Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:b91007766bbd967cd0b44d7b7d397344cf62331f488107a3bbc4257294beb5fb","observation_id":"c0fe224a-8c67-4af3-99a1-28c24f6dcc76","resolution":{"observed_at":"2026-08-04T09:03:28.338079Z","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":"2026-08-04T09:03:28.496183Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:28.496183Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:efffe17e3fb6525ea9925c9369094ea1c01bdf2eb29bd1fab7890757683cab0b","observation_id":"f7d4c972-aab8-48d3-9c05-ed6d9f0eb47c","resolution":{"observed_at":"2026-08-04T09:03:28.496183Z","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":"2026-08-04T09:03:28.611720Z","title":"Erd˝ os and P","venue":null,"work_id":null,"year":1936},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:28.611720Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:94db5dbc55cfcf8cbbcf85a1a1168ce8e558aac6130d6b9da54628c95ea03227","observation_id":"179aa46f-bdc3-491f-9838-5926f882a183","resolution":{"observed_at":"2026-08-04T09:03:28.611720Z","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":"2026-08-04T09:03:28.751362Z","title":"Fouvry and G","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:28.751362Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:93f185f5446b8f6a187a456decd07917408855cf279dcac5c4f05cea3f1a2614","observation_id":"61d48cc5-8d90-4aa9-a008-2d1b6eab338e","resolution":{"observed_at":"2026-08-04T09:03:28.751362Z","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":"2026-08-04T09:03:28.928948Z","title":null,"venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:28.928948Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:7455cba133ec23a9a2a00ce85d66251b94b02f422d5bf34b326b95828f23cff4","observation_id":"9cb09a7f-983d-4614-95d5-41074e8f9028","resolution":{"observed_at":"2026-08-04T09:03:28.928948Z","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":"2026-08-04T09:03:29.144591Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:29.144591Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:2be39493e323aea71c03dd526c24595db067c4b7c4ee804c8c225f5b708d327f","observation_id":"9cc7ad3c-52e9-4d79-bc14-c945241a3458","resolution":{"observed_at":"2026-08-04T09:03:29.144591Z","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":"2026-08-04T09:03:29.333799Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:29.333799Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:be5e09287e336e4db3874dab2ad0ccba830a002fb4cc9a6c4a1c8ae4557c8619","observation_id":"a1b8fcae-c58c-4042-b24e-c201bd46cc28","resolution":{"observed_at":"2026-08-04T09:03:29.333799Z","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":"2026-08-04T09:03:29.482591Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:29.482591Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:245658f40eff4afd0bba6292550e1008ce20234bc10292595949077611475f81","observation_id":"42cccf77-bba7-4095-a15a-7dae304b29c6","resolution":{"observed_at":"2026-08-04T09:03:29.482591Z","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":"2026-08-04T09:03:29.624854Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:29.624854Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:b736f951ad1f21eaf888231b21af829b9330a546b1824032a33b9e937c45a1da","observation_id":"a6d803ba-0904-4a85-8db3-cb42b39ace97","resolution":{"observed_at":"2026-08-04T09:03:29.624854Z","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":"2026-08-04T09:03:29.701355Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:29.701355Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:21619b08a6ed6aac9ec4b25f2d08ecd1678be2ac444df5e2a3426aeef4136752","observation_id":"88d9f3f3-7b3e-41b4-ac41-ecad1d0c1fdb","resolution":{"observed_at":"2026-08-04T09:03:29.701355Z","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":"2026-08-04T09:03:29.750721Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:29.750721Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:fccdf0a41c38e817ad90d500a8d62fce9305ef0a0bf145f24dcbb73b555d209e","observation_id":"3cd6f954-26a3-442f-aaee-7b17351174e0","resolution":{"observed_at":"2026-08-04T09:03:29.750721Z","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":"2026-08-04T09:03:29.824172Z","title":"Kelley and R","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:29.824172Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:d26f1991f2d28269fd88e11f098f65b83edd7337798a941bdf59bd4e28fb14ac","observation_id":"9fce8cc3-7bb5-4461-b500-b6b3957941d7","resolution":{"observed_at":"2026-08-04T09:03:29.824172Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.17995","last_updated":"2024-02-29T18:22:36Z","snapshot_observed_at":"2026-08-09T04:11:38.226835Z","submitted_at":"2024-02-28T02:19:59Z","title":"Improved Bounds for Szemer\\'{e}di's Theorem","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.17995","snapshot_observed_at":"2026-08-04T09:03:29.931923Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:29.931923Z"},"links":{"cited_paper":"/paper/2402.17995","citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:330d940da3cf093e4bc7e651cd4822ea94095611a85ac2a4ffbf3b1c1d2bc4c4","observation_id":"8e9d2a0a-7c12-419b-99a6-d63f09f42da7","resolution":{"observed_at":"2026-08-04T09:03:29.931923Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2211.16892","last_updated":"2024-10-09T15:18:23Z","snapshot_observed_at":"2026-08-06T04:42:23.216135Z","submitted_at":"2022-11-30T10:45:17Z","title":"Smooth numbers are orthogonal to nilsequences","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.16892","snapshot_observed_at":"2026-08-04T09:03:30.043339Z","title":"Matthiesen and Mengdi Wang, ‘Smooth numbers are orthogonal to nilsequences’,arXiv preprint https://arxiv.org/abs/2211.16892, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:30.043339Z"},"links":{"cited_paper":"/paper/2211.16892","citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:3c13a1fcc69a3cd8cebaf4184739a093921f6cebcfdb4e713438e1d3a1757c99","observation_id":"54f64258-7c36-407c-9d1b-5932a3912a4f","resolution":{"observed_at":"2026-08-04T09:03:30.043339Z","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":"2026-08-04T09:03:30.201347Z","title":null,"venue":null,"work_id":null,"year":1953},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:30.201347Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:892138ce9dd7abc804d66e53a5b6c3bf87b2137a9162f3fa5be31a986881e33e","observation_id":"ba72b390-0659-49c7-b17e-98370ba2af4a","resolution":{"observed_at":"2026-08-04T09:03:30.201347Z","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":"2026-08-04T09:03:30.369602Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:30.369602Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:5cfc8ebe21904ffcd48a19920144619e4f62034590f38e1221c49abc5f934a6c","observation_id":"b7b478f5-c14a-48c8-a016-26185d5b9d83","resolution":{"observed_at":"2026-08-04T09:03:30.369602Z","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":"2026-08-04T09:03:30.501928Z","title":"Soundararajan, ‘The distribution of smooth numbers in arithmetic progressions’,in: Anatomy of Integers, in: CRM Proc","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:30.501928Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:9f2687302298394ec63c0e0a8318c5fa124f8a12e075f49e3ba1a01f41793fc5","observation_id":"87a38903-671a-433b-ba29-f024839ec31e","resolution":{"observed_at":"2026-08-04T09:03:30.501928Z","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":"2026-08-04T09:03:30.640464Z","title":"Szemer´ edi., ‘On sets of integers containing nokelements in arithmetic progression’,Acta Arith.,27, 199–245, 1975","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T09:03:30.640464Z"},"links":{"citing_paper":"/paper/2510.18024"},"observation_digest":"sha256:83eef88026caf5b77d31bfe6dfab2b2c5b0f054279b8d8bfaab15a1f1ea31d8c","observation_id":"8fa1cb1e-b623-46f8-956b-d4c4d1b5e3f5","resolution":{"observed_at":"2026-08-04T09:03:30.640464Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2510.18024","last_updated":"2026-07-03T01:51:16Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-07T10:51:57.658657Z","submitted_at":"2025-10-20T18:55:50Z","title":"Roth's Theorem in Super Smooth Numbers"},"reference_resolution":{"displayed":21,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":21,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":21},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2510.18024."}