{"as_of":"2026-08-12T03:27:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:25afa6c1557b11d5244d21499abd452c6651d3087f0e13402b312d723134caf3","coverage":[{"denominator":13,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":13,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T10:51:55.740647Z","state":"measured"},{"denominator":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"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/2412.16308/citation-record","integrity":"/paper/2412.16308/integrity","json":"/paper/2412.16308/citation-record.json","paper":"/paper/2412.16308"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:51:55.946757Z","title":"Boucksom and D","venue":null,"work_id":"f0e3be2f-8e07-4a6a-9574-3170b9447998","year":2021},"citing_paper":{"arxiv_id":"2412.16308","last_updated":"2026-07-17T15:25:15Z","snapshot_observed_at":"2026-08-11T10:41:09.383263Z","submitted_at":"2024-12-20T19:42:36Z","title":"Heights of complete intersections in toric varieties","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T10:51:55.681455Z"},"links":{"citing_paper":"/paper/2412.16308"},"observation_digest":"sha256:481b269afd165adc2457913fbd9d7553bb62c46bdd231e52d2204bf0025da679","observation_id":"a1b1eae5-a9df-4357-a6d5-450935cc93d6","resolution":{"observed_at":"2026-08-11T10:51:55.951000Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:51:55.868259Z","title":"Maillot, G´ eom´ etrie d’Arakelov des vari´ et´ es toriques et ﬁbr´ es en droites int´ egrables, M´ em","venue":null,"work_id":"c51abab3-0e7b-4919-9846-fe49d1faa331","year":2000},"citing_paper":{"arxiv_id":"2412.16308","last_updated":"2026-07-17T15:25:15Z","snapshot_observed_at":"2026-08-11T10:41:09.383263Z","submitted_at":"2024-12-20T19:42:36Z","title":"Heights of complete intersections in toric varieties","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T10:51:55.725126Z"},"links":{"citing_paper":"/paper/2412.16308"},"observation_digest":"sha256:c48d8e14034c6953759d77616d38db5144c5b1c48372d50048778d6b4b1d82e8","observation_id":"207d27e1-ad88-4eb6-97c4-9372307c1c14","resolution":{"observed_at":"2026-08-11T10:51:55.872904Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:51:55.840597Z","title":"Stoll, The multiplicity of a holomorphic map , Invent","venue":null,"work_id":"1588a06e-5721-4e70-8106-22ae107a9687","year":1966},"citing_paper":{"arxiv_id":"2412.16308","last_updated":"2026-07-17T15:25:15Z","snapshot_observed_at":"2026-08-11T10:41:09.383263Z","submitted_at":"2024-12-20T19:42:36Z","title":"Heights of complete intersections in toric varieties","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T10:51:55.740647Z"},"links":{"citing_paper":"/paper/2412.16308"},"observation_digest":"sha256:28d080bcc42a001470c0587007e8ddeef728e8a95947572221a066614e887bfd","observation_id":"480fb1d8-b0ca-425d-8d97-b2823433899e","resolution":{"observed_at":"2026-08-11T10:51:55.844862Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.24088","last_updated":"2024-10-31T16:20:31Z","snapshot_observed_at":"2026-07-06T19:43:00.571297Z","submitted_at":"2024-10-31T16:20:31Z","title":"$p$-adic equidistribution and an application to $S$-units","version":1},"cited_work":{"arxiv_id":"2410.24088","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.24088","snapshot_observed_at":"2026-08-11T10:51:55.775409Z","title":"$p$-adic equidistribution and an application to $S$-units","venue":"math.NT","work_id":"944ed70d-0dfa-4afe-b39e-e64ef13929a5","year":2024},"citing_paper":{"arxiv_id":"2412.16308","last_updated":"2026-07-17T15:25:15Z","snapshot_observed_at":"2026-08-11T10:41:09.383263Z","submitted_at":"2024-12-20T19:42:36Z","title":"Heights of complete intersections in toric varieties","version":2},"reference_index":1970,"source":"pdf_text","source_observed_at":"2026-08-11T10:51:55.734703Z"},"links":{"cited_paper":"/paper/2410.24088","citing_paper":"/paper/2412.16308"},"observation_digest":"sha256:c24a906803b97cf13e002b0daa4129977f28f2081b3de066aa71928419db410c","observation_id":"02f0f023-109b-4378-9fec-d4c782761d18","resolution":{"observed_at":"2026-08-11T10:51:55.781936Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:51:55.932847Z","title":"Bilu, Limit distribution of small points on algebraic tori , Duke Math","venue":null,"work_id":"be19c1fd-cd0f-4b00-9a9f-4aab2dee4fab","year":1997},"citing_paper":{"arxiv_id":"2412.16308","last_updated":"2026-07-17T15:25:15Z","snapshot_observed_at":"2026-08-11T10:41:09.383263Z","submitted_at":"2024-12-20T19:42:36Z","title":"Heights of complete intersections in toric varieties","version":2},"reference_index":1984,"source":"pdf_text","source_observed_at":"2026-08-11T10:51:55.687180Z"},"links":{"citing_paper":"/paper/2412.16308"},"observation_digest":"sha256:251c6bbf8457dbfcad2c8b14d8ba72433cb36067925375910f710f5cc0749d9a","observation_id":"d8ac1cde-80d8-449a-be60-78bd58da36d7","resolution":{"observed_at":"2026-08-11T10:51:55.936943Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2304.01966","last_updated":"2023-04-04T17:24:45Z","snapshot_observed_at":"2026-08-11T20:52:06.358648Z","submitted_at":"2023-04-04T17:24:45Z","title":"Limit heights and special values of the Riemann zeta function","version":1},"cited_work":{"arxiv_id":"2304.01966","doi":null,"metadata_source":"pith","pith_arxiv_id":"2304.01966","snapshot_observed_at":"2026-08-11T10:51:55.813260Z","title":"Limit heights and special values of the Riemann zeta function","venue":"math.NT","work_id":"f0ac8fdd-0e26-40e0-8161-2f8ff034f4b4","year":2023},"citing_paper":{"arxiv_id":"2412.16308","last_updated":"2026-07-17T15:25:15Z","snapshot_observed_at":"2026-08-11T10:41:09.383263Z","submitted_at":"2024-12-20T19:42:36Z","title":"Heights of complete intersections in toric varieties","version":2},"reference_index":1998,"source":"pdf_text","source_observed_at":"2026-08-11T10:51:55.711220Z"},"links":{"cited_paper":"/paper/2304.01966","citing_paper":"/paper/2412.16308"},"observation_digest":"sha256:23e5f1fe65b4830d15bf9fb7da03231c8a40e2b3fa863d03078b52018ea1a661","observation_id":"d5849489-89c3-4091-b37b-839fba8477b0","resolution":{"observed_at":"2026-08-11T10:51:55.818032Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:51:55.854489Z","title":"Ostrowski, Zur arithmetischen Theorie der algebraischen Gr¨ oßen , G¨ ott","venue":null,"work_id":"c2afb2ce-20fd-47e4-9a86-9635099142a6","year":1919},"citing_paper":{"arxiv_id":"2412.16308","last_updated":"2026-07-17T15:25:15Z","snapshot_observed_at":"2026-08-11T10:41:09.383263Z","submitted_at":"2024-12-20T19:42:36Z","title":"Heights of complete intersections in toric varieties","version":2},"reference_index":1999,"source":"pdf_text","source_observed_at":"2026-08-11T10:51:55.729876Z"},"links":{"citing_paper":"/paper/2412.16308"},"observation_digest":"sha256:9df9f1ea93971565ebf633fd5bb9891cb1f8e9f3f177113ff1a60b902d06669b","observation_id":"62c5cc97-e45d-4b7d-bc6f-8d927b13992f","resolution":{"observed_at":"2026-08-11T10:51:55.858715Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.11156","last_updated":"2024-12-15T11:27:30Z","snapshot_observed_at":"2026-08-11T22:08:20.937667Z","submitted_at":"2024-12-15T11:27:30Z","title":"Galois orbits of torsion points over polytopes near atoral sets","version":1},"cited_work":{"arxiv_id":"2412.11156","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.11156","snapshot_observed_at":"2026-08-11T10:51:55.795681Z","title":"Galois orbits of torsion points over polytopes near atoral sets","venue":"math.NT","work_id":"2913574a-24e2-4acb-b422-bd254fc418d4","year":2024},"citing_paper":{"arxiv_id":"2412.16308","last_updated":"2026-07-17T15:25:15Z","snapshot_observed_at":"2026-08-11T10:41:09.383263Z","submitted_at":"2024-12-20T19:42:36Z","title":"Heights of complete intersections in toric varieties","version":2},"reference_index":2002,"source":"pdf_text","source_observed_at":"2026-08-11T10:51:55.720279Z"},"links":{"cited_paper":"/paper/2412.11156","citing_paper":"/paper/2412.16308"},"observation_digest":"sha256:da1d16073b40a47fbcf9ef5c5fe52cb99763a45f362510ea8f6d733925e8377b","observation_id":"765a366b-cb36-45f2-bc24-2e5cd9e2b58b","resolution":{"observed_at":"2026-08-11T10:51:55.800368Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:51:55.907250Z","title":"Chambert-Loir and A","venue":null,"work_id":"c7f42728-488c-40a3-9e8e-83f60106a9a3","year":2009},"citing_paper":{"arxiv_id":"2412.16308","last_updated":"2026-07-17T15:25:15Z","snapshot_observed_at":"2026-08-11T10:41:09.383263Z","submitted_at":"2024-12-20T19:42:36Z","title":"Heights of complete intersections in toric varieties","version":2},"reference_index":2011,"source":"pdf_text","source_observed_at":"2026-08-11T10:51:55.702515Z"},"links":{"citing_paper":"/paper/2412.16308"},"observation_digest":"sha256:2eb3b0505ce6a50daf1cb5f066612d517a2f562f306aeb74148ea984b0caba17","observation_id":"74156820-98b5-4d1e-939b-42743e36f9c0","resolution":{"observed_at":"2026-08-11T10:51:55.911700Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:51:55.920544Z","title":"Chambert-Loir, Mesures et ´ equidistribution sur les espaces de Berkovich, J","venue":null,"work_id":"b447bd5e-ac71-4306-a34d-6579e51039cf","year":2006},"citing_paper":{"arxiv_id":"2412.16308","last_updated":"2026-07-17T15:25:15Z","snapshot_observed_at":"2026-08-11T10:41:09.383263Z","submitted_at":"2024-12-20T19:42:36Z","title":"Heights of complete intersections in toric varieties","version":2},"reference_index":2012,"source":"pdf_text","source_observed_at":"2026-08-11T10:51:55.697838Z"},"links":{"citing_paper":"/paper/2412.16308"},"observation_digest":"sha256:bad233c45b5c29c2528bbda6b07257c28c6d346a9212d499a7c9983320e33051","observation_id":"caadd886-a10c-48e0-9e5b-252d5531e60a","resolution":{"observed_at":"2026-08-11T10:51:55.924758Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1204.6277","last_updated":"2025-07-25T19:25:07Z","snapshot_observed_at":"2026-08-11T11:47:17.477342Z","submitted_at":"2012-04-27T17:34:26Z","title":"Formes diff\\'erentielles r\\'eelles et courants sur les espaces de Berkovich","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1204.6277","snapshot_observed_at":"2026-08-11T10:51:55.692182Z","title":"Chambert-Loir and A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.16308","last_updated":"2026-07-17T15:25:15Z","snapshot_observed_at":"2026-08-11T10:41:09.383263Z","submitted_at":"2024-12-20T19:42:36Z","title":"Heights of complete intersections in toric varieties","version":2},"reference_index":2014,"source":"pdf_text","source_observed_at":"2026-08-11T10:51:55.692182Z"},"links":{"cited_paper":"/paper/1204.6277","citing_paper":"/paper/2412.16308"},"observation_digest":"sha256:2a65f42dca8361b9b4fdca2285b36c11837ad5d6403739417bef90017bb4ae0d","observation_id":"a2ff4ff8-a376-436c-91f9-6ac562fc8ae2","resolution":{"observed_at":"2026-08-11T10:51:55.692182Z","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":"2026-08-11T10:51:55.881063Z","title":"10, 2403–2443","venue":null,"work_id":"da181822-380b-4dae-9936-eb4206536d96","year":2018},"citing_paper":{"arxiv_id":"2412.16308","last_updated":"2026-07-17T15:25:15Z","snapshot_observed_at":"2026-08-11T10:41:09.383263Z","submitted_at":"2024-12-20T19:42:36Z","title":"Heights of complete intersections in toric varieties","version":2},"reference_index":2018,"source":"pdf_text","source_observed_at":"2026-08-11T10:51:55.716097Z"},"links":{"citing_paper":"/paper/2412.16308"},"observation_digest":"sha256:24e5930a9fbe0201a76840161c7055e1e544908d9c1a20ff7acdef59435970c8","observation_id":"9a8796e3-309d-44f6-bd11-b8df03e24457","resolution":{"observed_at":"2026-08-11T10:51:55.885322Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:51:55.893634Z","title":"D’Andrea and M","venue":null,"work_id":"17d70358-1822-45ff-bb66-2b909fabf15a","year":2015},"citing_paper":{"arxiv_id":"2412.16308","last_updated":"2026-07-17T15:25:15Z","snapshot_observed_at":"2026-08-11T10:41:09.383263Z","submitted_at":"2024-12-20T19:42:36Z","title":"Heights of complete intersections in toric varieties","version":2},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-11T10:51:55.706954Z"},"links":{"citing_paper":"/paper/2412.16308"},"observation_digest":"sha256:64b6257862778efc4901217f4184ab034cdb70f4ad26a26024a6888d0a96d3c5","observation_id":"a3df25a2-7977-4ce1-8fc8-40b66b9e45f1","resolution":{"observed_at":"2026-08-11T10:51:55.897959Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.16308","last_updated":"2026-07-17T15:25:15Z","latest_version":2,"primary_category":"math.AG","snapshot_observed_at":"2026-08-11T10:41:09.383263Z","submitted_at":"2024-12-20T19:42:36Z","title":"Heights of complete intersections in toric varieties"},"reference_resolution":{"displayed":13,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":3,"verified_fuzzy":9},"total_outbound_references":13},"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 12 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2412.16308."}