{"as_of":"2026-08-13T05:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c6b7acac00a50634ec12ae417bc7193ae0a0314104fb068a612f75071a9dd602","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T21:53:16.334340Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"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/2412.04253/citation-record","integrity":"/paper/2412.04253/integrity","json":"/paper/2412.04253/citation-record.json","paper":"/paper/2412.04253"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.18774","last_updated":"2025-01-30T21:56:25Z","snapshot_observed_at":"2026-08-12T09:30:06.095399Z","submitted_at":"2025-01-30T21:56:25Z","title":"Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.18774","snapshot_observed_at":"2026-08-11T21:53:16.233482Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.233482Z"},"links":{"cited_paper":"/paper/2501.18774","citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:f8a745922e3846ab642d9e1bcc83dddb5a571a8e12b75a34956f619b69970e41","observation_id":"95f31f90-79ef-4abe-af6e-180e1a41ea96","resolution":{"observed_at":"2026-08-11T21:53:16.233482Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2210.10730","last_updated":"2024-10-19T18:46:20Z","snapshot_observed_at":"2026-08-12T04:39:06.960924Z","submitted_at":"2022-10-19T17:14:03Z","title":"Integers expressible as the sum of two rational cubes","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2210.10730","snapshot_observed_at":"2026-08-11T21:53:16.239253Z","title":"Alp\\\"oge, M","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.239253Z"},"links":{"cited_paper":"/paper/2210.10730","citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:74a68a1a44d0a12fa0e93aa16ef58c69232dd2168c1d3a5dc70e942498d44db0","observation_id":"c9a744bd-91f2-474f-88a2-81d2330581f2","resolution":{"observed_at":"2026-08-11T21:53:16.239253Z","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":"2026-08-11T21:53:16.733851Z","title":null,"venue":null,"work_id":"e3f6c421-9f98-4c89-88f5-4cb293e7ffad","year":2017},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.244375Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:6d1766c6242b50656ef8e139e4bdb8c8f41c03379e72f9f3b7bdbdb45f986aa8","observation_id":"eede168f-7d04-478b-b62d-2aafccb82bb4","resolution":{"observed_at":"2026-08-11T21:53:16.738070Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.720855Z","title":"London Math","venue":null,"work_id":"98bdd881-6b3a-4347-bce5-6ea2ee8d87d7","year":1978},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.249286Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:f40469b6b9a2e70be0da890c941ed151bb7cc5e1b67ac27ce2c124ecb555a7a4","observation_id":"540048b7-9734-4ce6-9c8c-d0b6c7e501fe","resolution":{"observed_at":"2026-08-11T21:53:16.725179Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.707996Z","title":null,"venue":null,"work_id":"b6739824-4b1b-4ce9-9e2d-1c48a9c50100","year":1961},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.254700Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:87623c68d895ba509506563464eeebf64dc6e2fa99dedf82d797d4270f1406da","observation_id":"162cc7d4-95b6-4fe8-8b52-d2b371d112fd","resolution":{"observed_at":"2026-08-11T21:53:16.712282Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.695211Z","title":null,"venue":null,"work_id":"f6ad50c1-253a-4389-b094-6a2e6ca943e9","year":1961},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.259910Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:a03d5579808ce1ff5e2bef58f4313a8adfe1d744c844e2ef179df1ebaaa4f6fd","observation_id":"bf6c8447-e30e-4f8e-b3af-d1c455815985","resolution":{"observed_at":"2026-08-11T21:53:16.699661Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.681669Z","title":null,"venue":null,"work_id":"d0f7c2f4-887f-4bb9-a2da-85a3a41c983d","year":2018},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.265594Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:90a794546fb4a588352fec0c362a993b456dd096635f6c84aed975220a2a97c9","observation_id":"8a564e85-d246-4d05-ac48-363c782350e3","resolution":{"observed_at":"2026-08-11T21:53:16.685733Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.668676Z","title":null,"venue":null,"work_id":"139111b1-5b01-463d-bc73-324f10976fea","year":2020},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.270624Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:faf8d1130a5a3d5ff64de6fa5575ba9ec2926c15f13071bc33384b3ab9cbce95","observation_id":"f742f7c4-1b77-4a0d-a82c-e3ae5758a2b0","resolution":{"observed_at":"2026-08-11T21:53:16.673013Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.655498Z","title":null,"venue":null,"work_id":"5241b47b-b928-497b-8377-5fa27b2dd61e","year":2019},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.275527Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:98b66e4d33a8d51cdf00839edf38ad3663f7c32962fe0436d05694200cbbee5b","observation_id":"b3aed0ab-0d65-4499-8fd8-3abf04892476","resolution":{"observed_at":"2026-08-11T21:53:16.659893Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2207.12487","last_updated":"2025-01-21T15:33:52Z","snapshot_observed_at":"2026-08-12T19:51:21.089340Z","submitted_at":"2022-07-25T19:26:28Z","title":"$3$-Selmer group, ideal class groups and cube sum problem","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2207.12487","snapshot_observed_at":"2026-08-11T21:53:16.281099Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.281099Z"},"links":{"cited_paper":"/paper/2207.12487","citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:f43fac23e34e1de05c837bb22c1096e2d6d1fdef6ad5bb8c750cb06e980bb0e0","observation_id":"920eea1a-e076-4972-a655-7c3aea8bca41","resolution":{"observed_at":"2026-08-11T21:53:16.281099Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2301.06970","last_updated":"2024-05-31T07:55:53Z","snapshot_observed_at":"2026-08-07T06:03:34.218256Z","submitted_at":"2023-01-17T15:44:20Z","title":"Binary Cubic Forms and Rational Cube Sum Problem","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2301.06970","snapshot_observed_at":"2026-08-11T21:53:16.286254Z","title":"Sury, Binary cubic forms and rational cube sum problem, 2023, arXiv preprint arXiv:2301.06970","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.286254Z"},"links":{"cited_paper":"/paper/2301.06970","citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:57966b3f5a6fb69814da78243d91b09ab9a162ff8b0a87cfe36b10665adbc41a","observation_id":"5955ae59-417f-4ae3-bc66-57d80dee8d04","resolution":{"observed_at":"2026-08-11T21:53:16.286254Z","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":"2026-08-11T21:53:16.641472Z","title":null,"venue":null,"work_id":"ec215a78-a10b-41bd-981b-de36fa62f50e","year":2024},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.291053Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:6ded7f12cdbfc3c863f9e81e20823aee069e0bc51ecf49f95d9a27d6e12d4271","observation_id":"fe8ac3b5-081b-4412-8845-1d9727fd7632","resolution":{"observed_at":"2026-08-11T21:53:16.645976Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.295868Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.295868Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:f5825f747e7005e4ce2e05aee2dd19328cafa3f0eef4a9944f6d007b9acdc9cd","observation_id":"d68c75ec-b5c8-4943-bd9b-ef90ed784faa","resolution":{"observed_at":"2026-08-11T21:53:16.295868Z","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":"2026-08-11T21:53:16.628377Z","title":"Dokl., vol","venue":null,"work_id":"8b354f76-4d2c-415d-b1a7-2877d18bb09a","year":1970},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.300104Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:e546eaeb95bd7e941e41f9b4a36d64ea3babae52bf3e66a3ef2acfa3fb358852","observation_id":"31888d81-e974-4631-80a8-603723b052e1","resolution":{"observed_at":"2026-08-11T21:53:16.632670Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.614971Z","title":null,"venue":null,"work_id":"02984b86-901b-4a11-95a9-1d07d7479245","year":2010},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.304384Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:7dc11df24bbe0e5311fb1a9aa08a747872ceadde37dbeb85e9277891ed265bce","observation_id":"716274ea-632b-4139-aa7f-364bf063f868","resolution":{"observed_at":"2026-08-11T21:53:16.619441Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.600914Z","title":null,"venue":null,"work_id":"0789e19b-30b2-46a1-a19c-5cdb7e118d24","year":2023},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.308842Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:52ad08732c2070db45c2127dd59b379c41caede307591ee8888a8f280985da59","observation_id":"bd2e04a4-2e9e-4860-9a9f-9394db75f3f0","resolution":{"observed_at":"2026-08-11T21:53:16.605896Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.587015Z","title":null,"venue":null,"work_id":"f1d34af8-5a7b-490d-a69f-091ab484825c","year":2002},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.313010Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:2e0f3dac3bc29bb568b7483c413df497804a693d2ab3041a6a8fe357f9da82ba","observation_id":"b65f7140-a8a9-477e-a8e5-0b5bdbccd035","resolution":{"observed_at":"2026-08-11T21:53:16.591253Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.571689Z","title":"Perelli and J","venue":null,"work_id":"8d051227-f405-41b1-b3d7-74ef22c69601","year":1997},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.317295Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:3d915a2b96e24d62824fd9663e950754cf84528ee0e3401fb8d10caf6f40dd4e","observation_id":"c9c1ba3f-4989-413a-a039-7b3551418d1a","resolution":{"observed_at":"2026-08-11T21:53:16.576293Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.557302Z","title":null,"venue":null,"work_id":"7051be0d-0be6-4664-8eb9-cc85156f7989","year":1969},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.321556Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:a5cddc9c8d82a3a5f36483b42386a8ba22219c65f0294bbcd32add99bd81593a","observation_id":"30c02815-d181-4a92-b72d-a53ed5bc0368","resolution":{"observed_at":"2026-08-11T21:53:16.562038Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.543240Z","title":null,"venue":null,"work_id":"15beed7b-d616-489b-8e70-c39134bd7edf","year":2008},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.325836Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:9b7fd9c3e390f3f777c768f37af26723898bd7c7126829bc4a169a8615fd55ca","observation_id":"c2cd549e-bb19-445c-9c58-adf29828a272","resolution":{"observed_at":"2026-08-11T21:53:16.547923Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.529318Z","title":null,"venue":null,"work_id":"71a64c3d-8408-4418-9a68-87070e314bcc","year":2023},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.330490Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:8022cc7092f1f1e916c2eee0f2ca3197d58465624ee1b2ffe87deb97c9c44b2c","observation_id":"b7862091-67c5-4618-8500-0dbd61108256","resolution":{"observed_at":"2026-08-11T21:53:16.533757Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:53:16.513578Z","title":null,"venue":null,"work_id":"4d429b4c-a007-407f-87cd-f3aa8a725bbd","year":null},"citing_paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-11T21:53:16.334340Z"},"links":{"citing_paper":"/paper/2412.04253"},"observation_digest":"sha256:576438b94d8c4ce7038bd88dfa2c7a2bb3899dad6af209d6e500037e746cb46f","observation_id":"982f5c99-6619-425a-93cd-c90a89afc208","resolution":{"observed_at":"2026-08-11T21:53:16.519146Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.04253","last_updated":"2025-02-19T03:59:39Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-12T22:42:29.089030Z","submitted_at":"2024-12-05T15:33:54Z","title":"Hilbert's 10th Problem via Mordell curves"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":19,"verified_exact":0,"verified_fuzzy":3},"total_outbound_references":22},"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 13 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2412.04253."}