{"as_of":"2026-08-15T10:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cace897c7e40201570633cd0a8183718b88e0c3f6bf6c33bae962c29c0c76b49","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":3,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":3,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T22:02:00.976419Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-10T06:01:13.290371Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2204.11443","last_updated":"2022-04-26T12:20:01Z","snapshot_observed_at":"2026-08-15T00:23:23.151675Z","submitted_at":"2022-04-25T05:28:54Z","title":"On the monotonicity of the generalized Markov numbers","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.11443","snapshot_observed_at":"2026-08-10T20:12:38.051589Z","title":"Huang On the monotonicity of the generalized Markov numbers arXiv:2204.11443","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2501.09435","last_updated":"2025-01-16T10:07:18Z","snapshot_observed_at":"2026-08-14T20:32:25.605192Z","submitted_at":"2025-01-16T10:07:18Z","title":"A cluster theory approach from mutation invariants to Diophantine equations","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-10T20:12:38.051589Z"},"links":{"cited_paper":"/paper/2204.11443","citing_paper":"/paper/2501.09435"},"observation_digest":"sha256:e6183ddcf79984422122d4c4ab65c4b55c52f9f17d33bdf044793f8761581632","observation_id":"c0e7bd74-441f-49f9-9801-696446b085fc","resolution":{"observed_at":"2026-08-10T20:12:38.051589Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2204.11443","last_updated":"2022-04-26T12:20:01Z","snapshot_observed_at":"2026-08-15T00:23:23.151675Z","submitted_at":"2022-04-25T05:28:54Z","title":"On the monotonicity of the generalized Markov numbers","version":2},"cited_work":{"arxiv_id":"2204.11443","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2204.11443","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b52728b6-d21d-46b9-96f3-cbd2ca0f9de4","year":2022},"citing_paper":{"arxiv_id":"2604.17445","last_updated":"2026-04-19T13:52:56Z","snapshot_observed_at":"2026-07-06T23:04:32.734175Z","submitted_at":"2026-04-19T13:52:56Z","title":"Orderings of Generalized k-Markov Numbers","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-10T06:00:03.812477Z"},"links":{"cited_paper":"/paper/2204.11443","citing_paper":"/paper/2604.17445"},"observation_digest":"sha256:8dc3c0fb6d04b96429ac9c6232bdc0747a671291a5ff5a38855504bb62d3c5d9","observation_id":"cd4545fa-0aa4-415d-837c-622b369717a5","resolution":{"observed_at":"2026-05-10T06:01:13.291721Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2204.11443","last_updated":"2022-04-26T12:20:01Z","snapshot_observed_at":"2026-08-15T00:23:23.151675Z","submitted_at":"2022-04-25T05:28:54Z","title":"On the monotonicity of the generalized Markov numbers","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.11443","snapshot_observed_at":"2026-08-12T22:02:00.976419Z","title":"Huang On the monotonicity of the generalized Markov numbers arXiv:2204.11443","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.10551","last_updated":"2026-08-11T06:40:58Z","snapshot_observed_at":"2026-08-14T23:10:51.711971Z","submitted_at":"2026-08-11T06:40:58Z","title":"Mutation-preserving generalized cluster algebras and Laurent mutation invariants","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-12T22:02:00.976419Z"},"links":{"cited_paper":"/paper/2204.11443","citing_paper":"/paper/2608.10551"},"observation_digest":"sha256:df153179fb1cb7544196d0ecb3b27d0f2f0aa879eff4c03201ebfd0a43563bcf","observation_id":"b2f2edfb-5aba-46a6-9126-00630fed4fe3","resolution":{"observed_at":"2026-08-12T22:02:00.976419Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2204.11443/citation-record","integrity":"/paper/2204.11443/integrity","json":"/paper/2204.11443/citation-record.json","paper":"/paper/2204.11443"},"outbound":[],"paper":{"arxiv_id":"2204.11443","last_updated":"2022-04-26T12:20:01Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-15T00:23:23.151675Z","submitted_at":"2022-04-25T05:28:54Z","title":"On the monotonicity of the generalized Markov numbers"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 3 inbound Pith citation observations for arXiv:2204.11443."}