{"as_of":"2026-08-19T15:02:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0e91c0783332252098d0c7eac312926a2afa4747887528ac6a73d5b800890e04","coverage":[{"denominator":33,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":33,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T19:49:27.139927Z","state":"measured"},{"denominator":33,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":33,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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/2507.05027/citation-record","integrity":"/paper/2507.05027/integrity","json":"/paper/2507.05027/citation-record.json","paper":"/paper/2507.05027"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:49:35.498444Z","title":"An upper bound for the generalised greatest common divisor of rational points","venue":null,"work_id":"34d07449-3445-4daf-a3a7-03f495eac0e7","year":2025},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:22.186030Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:2864a8d5af6b7449121c004cdf69fdbb40468bd57e23e45687cd1fbc57d2229c","observation_id":"01847e5d-5a96-47db-becb-328d4b30283b","resolution":{"observed_at":"2026-08-06T19:49:35.643057Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:35.255844Z","title":null,"venue":null,"work_id":"a1e76942-0890-48a2-819b-473434490ce5","year":2014},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:22.308105Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:be68796927c159bb5d5af469fb79c7b02d682410f327e74f91c7a176ffbcc1d9","observation_id":"7eb4d55f-7b13-4316-b63f-d4b124fdbc2e","resolution":{"observed_at":"2026-08-06T19:49:35.399405Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:34.949087Z","title":"Dynamical degrees of (pseudo)-automorphisms fixing cubic hypersurfaces","venue":null,"work_id":"7da3f633-2a3e-4356-a0e6-5bb4b334e4e8","year":2013},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:22.446853Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:0bba6adb723a3cee21a7624904032ffafa02111cb7ede68c25b6980ba19e6966","observation_id":"12946773-fd3f-4f2a-999b-6e2533cf0ab1","resolution":{"observed_at":"2026-08-06T19:49:35.078853Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:34.608443Z","title":"4 of New Mathematical Monographs","venue":null,"work_id":"b16035b5-b6c7-4d3d-a9ce-64a945cc813b","year":2006},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:22.591327Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:38a55418165f4fc861f2939892718eb06f76fb8a4d368fc24392b63636ba60a7","observation_id":"18b25800-3edf-4b37-a6a0-9a6939baac20","resolution":{"observed_at":"2026-08-06T19:49:34.734732Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:34.311330Z","title":"of an´ 1 and bn´ 1","venue":null,"work_id":"293e4157-b48d-4298-bfc1-dd2fa94335da","year":2003},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:22.776953Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:fa76921907c8d8b1ea3093fc1d24b280777a9be65231775b7209132b5947417e","observation_id":"b3f57eee-e9a2-4e6c-b473-c2796b6db3a6","resolution":{"observed_at":"2026-08-06T19:49:34.481970Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:34.045181Z","title":"Degrees of iterates of rational maps on normal projective varieties","venue":null,"work_id":"1e2f2a77-6a3b-4176-99ea-b2d51a97ca34","year":2020},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:22.981767Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:a87bfd5570bf5f65580e221cee5426ee57c7b11d4664757aff6e4a64fafefd96","observation_id":"120a71ea-60e3-4371-89b8-7e1bbd5a0c96","resolution":{"observed_at":"2026-08-06T19:49:34.155451Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:33.806451Z","title":"Springer Monographs in Mathematics","venue":null,"work_id":"fc8b8f65-6788-47c4-a435-147eb62b2348","year":1999},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:23.150540Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:0f0c04224eaa4e5566b50e5e9022dcd8c4033224c1d8d76118cc570e9fdde06d","observation_id":"e239e4a7-8266-4583-8f6b-c9cb7ab6bc25","resolution":{"observed_at":"2026-08-06T19:49:33.904051Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:33.553603Z","title":"2 of Ergebnisse der Mathematik und ihrer Gren- zgebiete","venue":null,"work_id":"375c6a24-e2b8-474b-be34-a77a47400625","year":1998},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:23.358919Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:350d9dbb5f3e83170b2479360459f0a5bccc0872dc10e79b8aa70b3898cdb21e","observation_id":"3cdd88a3-ea83-42a0-a5db-89ca42aab683","resolution":{"observed_at":"2026-08-06T19:49:33.696408Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:33.261255Z","title":"Bulletin of the London Mathematical Society 56 , 6 (2024), 1939–1950","venue":null,"work_id":"014a431a-3f43-4e60-a635-a7af02836eb4","year":2024},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:23.548263Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:9596c0d3c48f89bf175733fd0935a6dfcd14ed9db8bdcfc72cfdd28ad0325d92","observation_id":"b938cb2c-ac6c-499f-921a-c8638602c32d","resolution":{"observed_at":"2026-08-06T19:49:33.429372Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:33.035716Z","title":"Algebraic geometry, vol","venue":null,"work_id":"eb0bf86c-ef62-4765-ad82-bff0e04e585b","year":1977},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:23.697062Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:6c448130708a4526e71095ad05663059aface8fb77edc5914b16b24d4a5dd75a","observation_id":"e5d2ef1c-f109-4293-b34d-db7df389887f","resolution":{"observed_at":"2026-08-06T19:49:33.127122Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:32.772904Z","title":"H.Diophantine geometry, vol","venue":null,"work_id":"bd97ed36-6ede-4298-b1d3-1ee80769d50b","year":2000},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:23.852010Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:7cadd559e26067b8aadd776aa12f4a994e6c13536008500930b946c4414ed2ff","observation_id":"5462abfa-dfd0-4744-ae33-b44bed31dcd3","resolution":{"observed_at":"2026-08-06T19:49:32.885040Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:32.521567Z","title":"Generalized greatest common divisors for orbits under rational functions","venue":null,"work_id":"99d1fa81-fa90-4a06-8ea8-27937f1eb7fe","year":2020},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:24.069542Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:28b3e466ca2eba642168a4a1729fa790f603f8b73bd6fd27863087b93102c76b","observation_id":"18297074-ea34-401e-8e4e-49ca9fd67405","resolution":{"observed_at":"2026-08-06T19:49:32.633173Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:32.265982Z","title":"H.Dynamical canonical heights for Jordan blocks, arith- metic degrees of orbits, and nef canonical heights on abelian varieties","venue":null,"work_id":"c53b6695-1a4f-4b5f-bc05-ac8966576bf2","year":2016},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:24.303897Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:8e39420d8726d8a81f88d153c7b9a64fdac8cac17b35800e880c5c7002c40bd9","observation_id":"afe4cfc5-5d02-4ba4-85fe-8692b0fe66b2","resolution":{"observed_at":"2026-08-06T19:49:32.424509Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:31.996385Z","title":"Springer-Verlag, New York, 1983","venue":null,"work_id":"b391edc6-262b-4a53-95d7-6d49701c35d5","year":1983},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:24.483173Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:0391398bf6c5a69b97458830122188098a2979f34437cc0f3b723e27df131f8a","observation_id":"d4fca4b4-78ed-4938-91d5-a9bacdfeb93a","resolution":{"observed_at":"2026-08-06T19:49:32.134637Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:31.730035Z","title":"Positivity in algebraic geometry","venue":null,"work_id":"9a8c0de8-33fa-48d3-90dc-81735919d8e7","year":2004},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:24.639324Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:42478a2c71a9730274976f167f785d587583b4de8df3bade24879515b845e29f","observation_id":"99ad3812-2f83-47d8-a6fa-a9ef73f2e547","resolution":{"observed_at":"2026-08-06T19:49:31.843998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:31.470148Z","title":"Positivity in algebraic geometry","venue":null,"work_id":"f9e33b09-bb2f-4b73-b836-e8bd6beacc9e","year":2004},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:24.872118Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:1c44b67bb27a099b009048d58fea082d6823d5daa1891ec148cbcc390be4c78f","observation_id":"e4e073e7-36da-4161-8f22-cd8af75f728a","resolution":{"observed_at":"2026-08-06T19:49:31.595107Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:31.211741Z","title":null,"venue":null,"work_id":"4bf602b6-96f8-47ee-ab11-2ebe253d90ba","year":2012},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:25.017572Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:c3f8c166fdf6a020aa97dadca01947fb662930b964c01a04ca23a1328e70e22d","observation_id":"c1f6d012-b09b-4ba8-91a5-9f85f418666a","resolution":{"observed_at":"2026-08-06T19:49:31.339728Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:30.985910Z","title":"6 of Oxford Graduate Texts in Mathemat- ics","venue":null,"work_id":"9aaef127-fd21-4d26-bff8-275af825d300","year":2002},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:25.105813Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:5260267a553caae826326bad966bca9bead11a01f4cc048eae6a706ba5cb0102","observation_id":"b003f924-f800-4c7d-af6f-765a8c11526e","resolution":{"observed_at":"2026-08-06T19:49:31.119100Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:30.717425Z","title":"8 of Cambridge Studies in Advanced Mathematics","venue":null,"work_id":"2d0d48cb-b7c6-494c-bfcd-bb55b31b2db4","year":1989},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:25.193961Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:79e494737667235865e289ae2a954c34e99a1360d34bdbe1eaf72c01afaaa942","observation_id":"38eda247-6ec5-4e1a-aa8d-59c1f227274f","resolution":{"observed_at":"2026-08-06T19:49:30.807115Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2008.08153","last_updated":"2020-11-19T03:07:51Z","snapshot_observed_at":"2026-07-06T09:48:12.550290Z","submitted_at":"2020-08-18T20:42:16Z","title":"Height functions associated with closed subschemes","version":2},"cited_work":{"arxiv_id":"2008.08153","doi":null,"metadata_source":"pith","pith_arxiv_id":"2008.08153","snapshot_observed_at":"2026-08-06T19:49:27.869105Z","title":"Height functions associated with closed subschemes","venue":"math.NT","work_id":"4ec78f20-2d53-429f-bc82-b2ba54cd815c","year":2020},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:25.330568Z"},"links":{"cited_paper":"/paper/2008.08153","citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:a7dd08d4c3b453f0c4a6c1d7f3b02367a47a5434f67fefaf27a1c77cc878dc9d","observation_id":"68fdb1ba-1229-4915-a85f-2bac095ab34e","resolution":{"observed_at":"2026-08-06T19:49:27.997256Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:30.491694Z","title":null,"venue":null,"work_id":"dcbd65f3-b002-480c-999a-f3e5c4aa642e","year":2020},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:25.436788Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:1a375c2d60c20df2c8366e9ee7c21b7692e4ede82e698152d23c259720b34ae6","observation_id":"d68aa431-ce38-4ab6-8966-78ce15c04235","resolution":{"observed_at":"2026-08-06T19:49:30.618426Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.04693","last_updated":"2020-12-08T19:27:53Z","snapshot_observed_at":"2026-08-19T04:55:20.500845Z","submitted_at":"2020-12-08T19:27:53Z","title":"Vojta's conjecture, heights associated with subschemes, and primitive prime divisors in arithmetic dynamics","version":1},"cited_work":{"arxiv_id":"2012.04693","doi":null,"metadata_source":"pith","pith_arxiv_id":"2012.04693","snapshot_observed_at":"2026-08-06T19:49:27.628588Z","title":"Vojta's conjecture, heights associated with subschemes, and primitive prime divisors in arithmetic dynamics","venue":"math.NT","work_id":"43b8133a-19b1-46eb-8dc5-abaf84aac1d1","year":2020},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:25.578719Z"},"links":{"cited_paper":"/paper/2012.04693","citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:fd76da459f51dc52c9e4364175bf17d10448fbf3ae1abf73f9b8c6f475f1e3c6","observation_id":"1d83827c-8a29-4e0e-99f6-a923860da952","resolution":{"observed_at":"2026-08-06T19:49:27.735773Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.15489","last_updated":"2023-11-27T02:16:21Z","snapshot_observed_at":"2026-08-19T13:02:48.458104Z","submitted_at":"2023-11-27T02:16:21Z","title":"Recent advances on Kawaguchi-Silverman conjecture","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.15489","snapshot_observed_at":"2026-08-06T19:49:25.720882Z","title":"Recent advances on kawaguchi-silverman conjecture","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:25.720882Z"},"links":{"cited_paper":"/paper/2311.15489","citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:daec1c6aace6c38886c3523247815b6ff0bd0c40be1ee2e04a03cf767b75f866","observation_id":"e4dbf953-5d0c-41aa-a144-1923a11487d8","resolution":{"observed_at":"2026-08-06T19:49:25.720882Z","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":"2026-08-06T19:49:30.173212Z","title":"Journal f¨ ur die reine und angewandte Mathematik (Crelles Journal) (2025)","venue":null,"work_id":"da0963d4-cefa-4e47-a980-bfa7083feb81","year":2025},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:25.881968Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:d8d09f781c0f6d311aea8d397d7ec14742252618e8c795390264b8374d78a7a3","observation_id":"17d3a7a0-9d90-49f5-9688-baadcdeb2411","resolution":{"observed_at":"2026-08-06T19:49:30.306294Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:29.872210Z","title":"to appear in Trans","venue":null,"work_id":"9b19e32d-0ed1-4ea8-ada9-8e1064813d54","year":2022},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:26.030890Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:32c724e728b11b37cd8125889ad6b2c583833385308226824aa1bb9524bba88d","observation_id":"f60c191b-9d62-4f10-98f0-8e5e68afceae","resolution":{"observed_at":"2026-08-06T19:49:30.018749Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:29.566464Z","title":"T.Explicit examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy","venue":null,"work_id":"c4f9747e-de1c-4de8-a8b1-d1837ec18598","year":2015},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:26.156039Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:7c890c4f7a35ac37a03167f8b8fb6c17f1c188cea2310872f81e8015fbf447a7","observation_id":"1596744f-3b65-41db-82c9-09c0a10dfb62","resolution":{"observed_at":"2026-08-06T19:49:29.729998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:29.254362Z","title":null,"venue":null,"work_id":"a0ca8a4f-bb8f-407c-9e88-40507346e1ac","year":2014},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:26.318137Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:7bcbea75505fa78bb5cd06dcb366fb3323fd780efe38c427dda669c73ca2838f","observation_id":"e96af1de-02b7-42d7-9e15-1d3b81b96e0e","resolution":{"observed_at":"2026-08-06T19:49:29.399220Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:29.013692Z","title":"H.Arithmetic distance functions and height functions in Diophantine geometry","venue":null,"work_id":"5037e7e3-aa00-45e8-8155-ee002cca55a7","year":1987},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:26.471797Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:738806bdd8de841d975fc926d72e7c8a70927e2f2b719351a991a47925735ca8","observation_id":"fd6f3402-ae6e-4f75-aec1-98b08638672f","resolution":{"observed_at":"2026-08-06T19:49:29.183051Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:28.789497Z","title":"H.Dynamical degree, arithmetic entropy, and canonical heights for dominant rational self-maps of projective space","venue":null,"work_id":"b6e28519-24c6-4d47-bb43-bc50d020c896","year":2012},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:26.623837Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:e2849ad1eaa1f445594e304c7905855ff7e878a52b77b47939af32c790ffb9cd","observation_id":"626a1291-2f0a-4b63-8f35-f1344fd40ef1","resolution":{"observed_at":"2026-08-06T19:49:28.909429Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.01559","last_updated":"2024-08-02T20:16:43Z","snapshot_observed_at":"2026-08-19T07:30:30.294449Z","submitted_at":"2024-08-02T20:16:43Z","title":"Dynamical Degrees, Arithmetic Degrees, and Canonical Heights: History, Conjectures, and Future Directions","version":1},"cited_work":{"arxiv_id":"2408.01559","doi":null,"metadata_source":"pith","pith_arxiv_id":"2408.01559","snapshot_observed_at":"2026-08-06T19:49:27.340947Z","title":"Dynamical Degrees, Arithmetic Degrees, and Canonical Heights: History, Conjectures, and Future Directions","venue":"math.NT","work_id":"172f291a-c3c4-4d2f-b857-c726d505e949","year":2024},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:26.749997Z"},"links":{"cited_paper":"/paper/2408.01559","citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:26612fee7cb634e218deaa84e4cc6031efa24e67fa20667cfd5c1ba8e7b1b0e0","observation_id":"33150412-3ae0-4a03-919e-167d1db18ddb","resolution":{"observed_at":"2026-08-06T19:49:27.457251Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:28.474823Z","title":"T.Relative dynamical degrees of correspondences over a field of arbitrary charac- teristic","venue":null,"work_id":"5d853fda-47b1-429a-8f58-3cd38c485ba3","year":2020},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:26.871151Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:d3074f3e9ec0049288501ed3493c86f682e215cb344639d29d9927e5a9fbb5df","observation_id":"3d4b7b9e-daca-43f1-bd95-791ee2922f97","resolution":{"observed_at":"2026-08-06T19:49:28.627304Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:49:28.190799Z","title":"Ast´ erisque, 394 (2017), vi+110","venue":null,"work_id":"f0dac99d-f05f-4a37-9dc6-604fe21b05c3","year":2017},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:26.995923Z"},"links":{"citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:a0699f8e57c6c37016a29b742561259e1313cca523332cdffae225dfe4a0fa58","observation_id":"6a72f2e5-c038-4579-a870-f2e1529174fa","resolution":{"observed_at":"2026-08-06T19:49:28.322392Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.12678","last_updated":"2025-03-29T17:19:08Z","snapshot_observed_at":"2026-08-19T07:41:56.599732Z","submitted_at":"2024-02-20T02:55:30Z","title":"Algebraic dynamics and recursive inequalities","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.12678","snapshot_observed_at":"2026-08-06T19:49:27.139927Z","title":"arXiv preprint arXiv:2402.12678 (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T19:49:27.139927Z"},"links":{"cited_paper":"/paper/2402.12678","citing_paper":"/paper/2507.05027"},"observation_digest":"sha256:09d4da61d5ecaf6ef2208d470a6e7f8b272fc81635b430dadabb42b961a03e6d","observation_id":"6af47cef-7bf4-46b6-b0d8-4f2843911901","resolution":{"observed_at":"2026-08-06T19:49:27.139927Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.05027","last_updated":"2025-07-07T14:10:01Z","latest_version":1,"primary_category":"math.AG","snapshot_observed_at":"2026-08-10T06:42:24.669857Z","submitted_at":"2025-07-07T14:10:01Z","title":"Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties"},"reference_resolution":{"displayed":33,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":3,"verified_fuzzy":24},"total_outbound_references":33},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2507.05027."}