{"as_of":"2026-08-12T16:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ffc376e9e4693c8c6cf3c39a15477a5c7de1c78a141cb93d313846b4f2a74641","coverage":[{"denominator":20,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":20,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T01:31:09.288509Z","state":"measured"},{"denominator":20,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":20,"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/2607.28857/citation-record","integrity":"/paper/2607.28857/integrity","json":"/paper/2607.28857/citation-record.json","paper":"/paper/2607.28857"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T01:31:06.981815Z","title":"Baker and G","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:06.981815Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:e8547f7fdbbbceb92900823e4a0748a63ee86f2d17304a6a0143d5b82f3bfa62","observation_id":"38202e14-8864-43f6-8d51-1dab92a63184","resolution":{"observed_at":"2026-08-03T01:31:06.981815Z","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":"2026-08-03T01:31:07.062409Z","title":"1, 135–158","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:07.062409Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:fe75e734f5cd7b3397a2a5001761fda7d91144fba6773c99f29a5c6a74c2f21e","observation_id":"45a6aeaa-6d0c-4bca-8d57-650e0a24a086","resolution":{"observed_at":"2026-08-03T01:31:07.062409Z","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":"2026-08-03T01:31:07.141154Z","title":"2, 195–217","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:07.141154Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:3f93747de7e3bc2e68ea97ea3c4bf610e0b945fb308425c682e4e7e95085c5f0","observation_id":"8d56d355-ebd3-4f39-b257-4583df9830c9","resolution":{"observed_at":"2026-08-03T01:31:07.141154Z","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":"2026-08-03T01:31:07.199482Z","title":"Bilu,Baker’s method and modular curves, A panorama of number theory or the view from Baker’s garden (Z¨ urich, 1999), Cambridge Univ","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:07.199482Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:2f5b115d4de3042d8821d2c660c364b3ee8508cfab4d9f525b5f6300b7262de1","observation_id":"8c99bb80-7f37-463d-bc02-0dbadf882255","resolution":{"observed_at":"2026-08-03T01:31:07.199482Z","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":"2026-08-03T01:31:07.249574Z","title":"Bilu, Yann Bugeaud, and Maurice Mignotte,The problem of Catalan, Springer, Cham, 2014","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:07.249574Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:8faee31c6d9f1d9baf40f191ae2150b986fe3b565c8d8f608dfb6e47ccff6dab","observation_id":"45f5d49a-d552-4e1f-a39b-8b53ef0bd025","resolution":{"observed_at":"2026-08-03T01:31:07.249574Z","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":"2026-08-03T01:31:07.313594Z","title":"Math.144(2005), no","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:07.313594Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:c8fbff799648e2faa8a7db8e968b21d8684faa083fc1915e4427428af3d81178","observation_id":"73bf9e0c-8d09-471e-8230-8561746cd9c4","resolution":{"observed_at":"2026-08-03T01:31:07.313594Z","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":"2026-08-03T01:31:07.368012Z","title":"Elkies,ABCimplies Mordell, Internat","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:07.368012Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:9c6c89714876b8599709a689a3dd9f47cd1e07237e85b17e888944604f5be4a0","observation_id":"2b11dc42-6880-4961-a973-4b7fdef29736","resolution":{"observed_at":"2026-08-03T01:31:07.368012Z","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":"2026-08-03T01:31:07.459111Z","title":"2, 225–244","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:07.459111Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:ab7b601f56e1f7c00ac6e04e412f772f6d81d3cf239e424d7f0391f53b4ca56c","observation_id":"df39f5ed-9cac-4ee3-b12a-b012a55eac9d","resolution":{"observed_at":"2026-08-03T01:31:07.459111Z","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":"2026-08-03T01:31:07.632203Z","title":"Siegel zeros","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:07.632203Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:aa445b7a470f9b20e102896c5a15aaddac6246be7473d66ee1c8cbf0a08adca0","observation_id":"50c14867-82cf-4bf4-9daf-2626b789537c","resolution":{"observed_at":"2026-08-03T01:31:07.632203Z","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":"2026-08-03T01:31:07.843369Z","title":"Math.78(1984), no","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:07.843369Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:8e466f8812a455ad364b665e5de355bd263d263c6a1633c0d71cc1fe318b6c20","observation_id":"0a0b34db-b137-4725-a3f2-117537db8eda","resolution":{"observed_at":"2026-08-03T01:31:07.843369Z","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":"2026-08-03T01:31:07.962660Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:07.962660Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:7a9a5dc2d897200a14aed5a2cb58bccc36c28d35ce4ad6792c27545b9d834b20","observation_id":"a2eb88d0-0893-4322-91de-b1c8e5ee5de3","resolution":{"observed_at":"2026-08-03T01:31:07.962660Z","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":"2026-08-03T01:31:08.110042Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:08.110042Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:9f18103622733d4e1c35c2dc747ce8d12ac20e4ca04fabb14ffcd3af61763e77","observation_id":"e1a7a1be-5d5f-4bae-98d1-c8b56023b2d6","resolution":{"observed_at":"2026-08-03T01:31:08.110042Z","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":"2026-08-03T01:31:08.271100Z","title":"Schinzel,Primitive divisors of the expressionA n −B n in algebraic number fields, J","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:08.271100Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:ccfd81d4dea83611faaa43db7ad0840809750cc323161d404232f71766b98812","observation_id":"6167c13c-9585-4dab-a34d-c067265b37a0","resolution":{"observed_at":"2026-08-03T01:31:08.271100Z","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":"2026-08-03T01:31:08.439889Z","title":"Schinzel and R","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:08.439889Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:22b58b30171c534bfa08fa5731395fea91206d2939e23d4f496ffb67cc2c13d6","observation_id":"59807508-1800-432f-b9cc-ed9b66c8a8dd","resolution":{"observed_at":"2026-08-03T01:31:08.439889Z","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":"2026-08-03T01:31:08.609120Z","title":null,"venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:08.609120Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:b38e43bfbc7bfad33cc2428e4fe99f943b55c73b61d3e8c184ef6cf85dca78b2","observation_id":"da9b6516-5da1-406c-bf98-d80e4d55afd0","resolution":{"observed_at":"2026-08-03T01:31:08.609120Z","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":"2026-08-03T01:31:08.769986Z","title":"Number Theory27(1987), no","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:08.769986Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:a1aaea207b61ebb0ed3422f50617636e62c0ab32c5ab1aa7998be42d0f8b5ada","observation_id":"3a775b08-5e1e-473d-a9cd-dc934bfecffe","resolution":{"observed_at":"2026-08-03T01:31:08.769986Z","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":"2026-08-03T01:31:08.931898Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:08.931898Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:08677773ab8ebfae184f31f270ea3aaf41f3efdf924b75334c84b963b35af800","observation_id":"37001f3e-1f3a-42be-b978-43e0c7962a4c","resolution":{"observed_at":"2026-08-03T01:31:08.931898Z","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":"2026-08-03T01:31:09.079135Z","title":"1239, Springer-Verlag, Berlin, 1987","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:09.079135Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:59b6977a9699f498de3675de4beed69d7908b203e627ab3bc79ddb204d5c8345","observation_id":"d239264e-7d82-4670-914b-e12061e15b89","resolution":{"observed_at":"2026-08-03T01:31:09.079135Z","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":"2026-08-03T01:31:09.197087Z","title":null,"venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:09.197087Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:4ffc4db68d9db0c1c1132bd17de50d754159f057319b4422f6d53fffda94a295","observation_id":"22cdd5e3-22f3-4342-a7ca-4ea7802fd1d6","resolution":{"observed_at":"2026-08-03T01:31:09.197087Z","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":"2026-08-03T01:31:09.288509Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-03T01:31:09.288509Z"},"links":{"citing_paper":"/paper/2607.28857"},"observation_digest":"sha256:9cb94852da9f27c92f2676db95322a582c4bf79661058b56ba4f9aef67dbc634","observation_id":"d14b2e05-2bfa-4e6e-a4fe-1f19a9e97e75","resolution":{"observed_at":"2026-08-03T01:31:09.288509Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.28857","last_updated":"2026-07-30T21:44:54Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-12T11:38:02.030529Z","submitted_at":"2026-07-30T21:44:54Z","title":"Multiplicative dependence in the sumset of multiplicative groups"},"reference_resolution":{"displayed":20,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":20,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":20},"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 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2607.28857."}