{"as_of":"2026-08-19T14:49:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e82149fb3b7db9bfcc9441acacb07408d358bcf415431dadc450083102539e4d","coverage":[{"denominator":21,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":21,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T14:56:19.862913Z","state":"measured"},{"denominator":21,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":21,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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/2507.17643/citation-record","integrity":"/paper/2507.17643/integrity","json":"/paper/2507.17643/citation-record.json","paper":"/paper/2507.17643"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:56:20.066044Z","title":null,"venue":null,"work_id":"bcbee940-2340-4854-b791-bc0404a74e0a","year":2016},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.797581Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:2b971de10727c4c459dc2ec8e2bbb35345cbfcb9db17d43017de6ff2024f894e","observation_id":"39d288a6-4642-4942-8ee8-62cffd44f373","resolution":{"observed_at":"2026-08-06T14:56:20.069676Z","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":"1701.07760","last_updated":"2019-07-16T12:55:53Z","snapshot_observed_at":"2026-08-14T21:19:20.813573Z","submitted_at":"2017-01-26T16:23:18Z","title":"Degrees of Iterates of Rational Maps on Normal Projective Varieties","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1701.07760","snapshot_observed_at":"2026-08-06T14:56:19.801630Z","title":"Degrees of iterates of rational maps on normal projective varieties","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.801630Z"},"links":{"cited_paper":"/paper/1701.07760","citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:308a085c40b2f2573bf27b4f8a05441d3a7499768ae2ce5f53f88cacce31e128","observation_id":"88d3a384-2f43-4e87-91df-a95a37319300","resolution":{"observed_at":"2026-08-06T14:56:19.801630Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:56:19.805448Z","title":"Degrees of iterates of rational maps on normal projective varieties","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.805448Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:95bf2482f4914b8442dda682910f623be0303525638e6582255b76a1d4e849ce","observation_id":"44949281-514d-41b9-9105-5dc8bcc4ccb5","resolution":{"observed_at":"2026-08-06T14:56:19.805448Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:56:19.809222Z","title":"Comparison of dynamical degrees for semi-conjugate meromorphic maps","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.809222Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:6fc20afe8f4c2e0372a97129aa5040b6494d888d78c71ea2a8bb8933520624a5","observation_id":"2dec40a8-1f82-4e81-af33-6c194a67edbc","resolution":{"observed_at":"2026-08-06T14:56:19.809222Z","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":"2026-08-06T14:56:20.047993Z","title":"Une borne sup\\'erieure pour l'entropie topologique d'une application rationnelle","venue":null,"work_id":"cf7a0fd2-da20-48da-ba07-628ad76d7326","year":2005},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.813156Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:7aa4c43180f1024fbcba8d5bd713073fabd650975cdac4c48ec400f9bbf3e37b","observation_id":"a39943be-e1f8-4c60-a20e-60a5c249bf3b","resolution":{"observed_at":"2026-08-06T14:56:20.051151Z","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":"2026-08-06T14:56:20.039354Z","title":"Silverman","venue":null,"work_id":"c978fc92-850c-4e44-acb8-c5014f6f3fcf","year":2016},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.816579Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:76bb0d3cbed1a254251c75bf166d028b463b08d6482b88a91e0ce00e1cd95ff7","observation_id":"6f72ffb4-5f14-4304-a63d-9186dd8aa847","resolution":{"observed_at":"2026-08-06T14:56:20.042390Z","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":"2026-08-06T14:56:20.030055Z","title":"Silverman","venue":null,"work_id":"cf9c789f-07c7-4029-a799-69d8a3de62be","year":2016},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.819766Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:49eb43f640234492e7941b7c275568fb69b6050776bc73292aa80d0907a827e5","observation_id":"5a307764-5f29-41d6-bd16-6d516ed37e26","resolution":{"observed_at":"2026-08-06T14:56:20.033001Z","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":"2026-08-06T14:56:20.021764Z","title":"A note on K awaguchi- S ilverman conjecture","venue":null,"work_id":"3a9fd631-4184-428f-90d8-4edc50f8433a","year":2021},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.822851Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:3da478ee386d530e088c30db8316eb61e28ef699bb9e1932bcfb3c32f4aa60ee","observation_id":"13a802f5-a124-411b-bd43-8d0e6c99407c","resolution":{"observed_at":"2026-08-06T14:56:20.024820Z","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":"2401.11982","last_updated":"2025-07-26T13:12:33Z","snapshot_observed_at":"2026-08-16T14:25:33.870042Z","submitted_at":"2024-01-22T14:34:58Z","title":"Arithmetic degrees of dynamical systems over fields of characteristic zero","version":3},"cited_work":{"arxiv_id":"2401.11982","doi":null,"metadata_source":"pith","pith_arxiv_id":"2401.11982","snapshot_observed_at":"2026-08-06T14:56:19.944271Z","title":"Arithmetic degrees of dynamical systems over fields of characteristic zero","venue":"math.NT","work_id":"1a13dbd4-ce3b-47d4-9f11-0f8897702cc6","year":2024},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.825758Z"},"links":{"cited_paper":"/paper/2401.11982","citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:bb3ebf75b2c339724a4b9cd80fe032d6384eacf33ebd45b46382b242cdc682fd","observation_id":"a9b76659-0ecf-426f-b97f-2140f244a97d","resolution":{"observed_at":"2026-08-06T14:56:19.947799Z","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":"2026-08-06T14:56:20.013298Z","title":"On upper bounds of arithmetic degrees","venue":null,"work_id":"a2e91b25-04e2-4958-b726-e8d934877e7f","year":2020},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.829095Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:57f0cc50fe100b9ee3404e0e9d197f632aea758371ddb5c8907d4e73335c0609","observation_id":"9de4e15c-3a44-419f-a62c-0c1eb0a47d80","resolution":{"observed_at":"2026-08-06T14:56:20.016424Z","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":"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":"2311.15489","doi":null,"metadata_source":"pith","pith_arxiv_id":"2311.15489","snapshot_observed_at":"2026-08-06T14:56:19.932865Z","title":"Recent advances on Kawaguchi-Silverman conjecture","venue":"math.AG","work_id":"51967b4a-daa4-48a2-80e1-9614880e4501","year":2023},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.832069Z"},"links":{"cited_paper":"/paper/2311.15489","citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:a6e1235343fdf81b541801b45988848f59b2c06dd35770e038fe4ec29d222bad","observation_id":"b878b9ab-08df-49e6-9a48-d75cf18b7939","resolution":{"observed_at":"2026-08-06T14:56:19.936101Z","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":"10.1515/crelle-2025-0038","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Existence of arithmetic degrees for generic orbits and dynamical L ang-- S iegel problem","venue":"Journal für die reine und angewandte Mathematik (Crelles Journal)","work_id":"3f6e8933-bc56-42e7-be28-656562e13b9b","year":2025},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.835262Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:e2e85be99aa1204b6b98496aa5da80b401596e9536e32bf58f12e4e68be43551","observation_id":"f48f05ce-bd85-482e-89a3-cd4ed9287291","resolution":{"observed_at":"2026-08-06T14:56:19.891969Z","resolver_source":"doi","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":"2026-08-06T14:56:20.004407Z","title":"Arithmetic height functions over finitely generated fields","venue":null,"work_id":"84b08542-fbe5-46b4-8505-0b78254ea358","year":2000},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.838439Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:450a6ec9a199c9512ce7db92e4960e62eedebc21215999099a9f7c92fad9675a","observation_id":"078c7a33-1a42-4afa-8627-842008bc0da7","resolution":{"observed_at":"2026-08-06T14:56:20.007805Z","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":"2026-08-06T14:56:19.995188Z","title":"Arakelov geometry over an adelic curve and dynamical systems","venue":null,"work_id":"2f93743f-3865-4a65-986d-a3c4a05f2675","year":2022},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.841267Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:83c94edd1bfaeb7282d165f0a0680a33f98c7e71e68b888f51e7838dc48ac564","observation_id":"8e6bcbe8-cef1-4a74-a505-51f950d06196","resolution":{"observed_at":"2026-08-06T14:56:19.998289Z","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":"2026-08-06T14:56:19.985820Z","title":"Silverman","venue":null,"work_id":"0f20430a-b392-4f9d-a855-b02159b77d6e","year":2017},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.844139Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:eb6061b4445880c0e6ed7457ed375370d16e00f5f0ef3440885071b3fdf5ca55","observation_id":"9227b98a-cda9-4966-a8d7-77982071409f","resolution":{"observed_at":"2026-08-06T14:56:19.989779Z","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":"2026-08-06T14:56:19.977493Z","title":"Relative dynamical degrees of correspondences over a field of arbitrary characteristic","venue":null,"work_id":"0eab5741-69ff-4554-9b97-d2c7dda1e641","year":2020},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.847070Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:e3bfe5dd9a1502bb690028ce29dd67c090bf880f49cf99298b63f4642b2f57ca","observation_id":"afb69526-b4a4-4ba8-92cb-51de6cbb5396","resolution":{"observed_at":"2026-08-06T14:56:19.980585Z","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":"2026-08-06T14:56:19.969293Z","title":"Relations between dynamical degrees, W eil's riemann hypothesis and the standard conjectures","venue":null,"work_id":"ae666dd3-2292-4ec7-b606-e0362f649fba","year":2025},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.849744Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:91a725a0d8b3f53ef106056543eeba5f928ed0a16839f3af3cd760c693a65e73","observation_id":"7c756235-dda9-4a5c-b55b-48aabdf8ac1c","resolution":{"observed_at":"2026-08-06T14:56:19.972330Z","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":"2026-08-06T14:56:19.852432Z","title":"Algebraic dynamics and recursive inequalities","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.852432Z"},"links":{"cited_paper":"/paper/2402.12678","citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:5c587ec191f9d64985c4735034b0564eac0ea9ec64b723689134bfafe1878e87","observation_id":"a14886ee-7e30-4933-b627-478d9aa50d2f","resolution":{"observed_at":"2026-08-06T14:56:19.852432Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.04779","last_updated":"2025-02-07T09:33:40Z","snapshot_observed_at":"2026-08-08T21:27:58.725732Z","submitted_at":"2025-02-07T09:33:40Z","title":"Numerical action for endomorphisms","version":1},"cited_work":{"arxiv_id":"2502.04779","doi":null,"metadata_source":"pith","pith_arxiv_id":"2502.04779","snapshot_observed_at":"2026-08-06T14:56:19.913708Z","title":"Numerical action for endomorphisms","venue":"math.DS","work_id":"c1f5bc37-c2eb-4b15-b21b-03ef25d35498","year":2025},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.856090Z"},"links":{"cited_paper":"/paper/2502.04779","citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:d313d003225cb841c3d0dc36215bad6e3518a7f03394221a232e2b610a55c474","observation_id":"78f4fdae-1204-4f14-8f28-37d9c976909c","resolution":{"observed_at":"2026-08-06T14:56:19.917040Z","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":"2026-08-06T14:56:19.960484Z","title":"Around the dynamical M ordell-- L ang conjecture","venue":null,"work_id":"9bac3be4-1f29-4269-9615-de76078eb5c1","year":2023},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.859526Z"},"links":{"citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:7756bd18000b05f6d51bc82d0bd4cc6425c88085545529f5233c3ceadcb7062d","observation_id":"1b7b6511-ec5c-44f8-9d9a-3c40d5765db0","resolution":{"observed_at":"2026-08-06T14:56:19.963701Z","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":"2504.01563","last_updated":"2026-07-09T14:17:24Z","snapshot_observed_at":"2026-08-18T17:59:52.835922Z","submitted_at":"2025-04-02T10:04:14Z","title":"Height arguments toward the dynamical Mordell-Lang problem in arbitrary characteristic","version":4},"cited_work":{"arxiv_id":"2504.01563","doi":null,"metadata_source":"pith","pith_arxiv_id":"2504.01563","snapshot_observed_at":"2026-08-06T14:56:19.901442Z","title":"Height arguments toward the dynamical Mordell-Lang problem in arbitrary characteristic","venue":"math.DS","work_id":"3287d6c5-98fe-4db2-b558-f9a4c8d97f69","year":2025},"citing_paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T14:56:19.862913Z"},"links":{"cited_paper":"/paper/2504.01563","citing_paper":"/paper/2507.17643"},"observation_digest":"sha256:cc7ba1dba6b3a3256d352b098fc09855d734f4fbdd854caa332079771f1cf1a3","observation_id":"2b63dddc-d7e4-420c-b65d-1f7f91aacf4b","resolution":{"observed_at":"2026-08-06T14:56:19.905023Z","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"}}],"paper":{"arxiv_id":"2507.17643","last_updated":"2025-07-23T16:07:20Z","latest_version":1,"primary_category":"math.DS","snapshot_observed_at":"2026-08-17T22:09:01.828305Z","submitted_at":"2025-07-23T16:07:20Z","title":"Arithmetic Degrees are Cohomological Lyapunov Multipliers"},"reference_resolution":{"displayed":21,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":5,"verified_fuzzy":11},"total_outbound_references":21},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-19T06:32:44.657259+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 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2507.17643."}