{"as_of":"2026-08-08T20:04:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2603aa5f1135986733df2e329cdbe14d0a9af91503720800f5246c1a34413806","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":4,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":4,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:28:10.386222Z","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":"2026-05-13T23:48:27.708624Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2306.14243","last_updated":"2023-10-09T16:02:12Z","snapshot_observed_at":"2026-07-06T15:46:29.060519Z","submitted_at":"2023-06-25T13:29:49Z","title":"Asymptotic behaviour of the $\\text{v}$-number of homogeneous ideals","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.14243","snapshot_observed_at":"2026-08-07T15:28:10.386222Z","title":"Ficarra, E","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.15608","last_updated":"2025-05-21T15:00:57Z","snapshot_observed_at":"2026-08-08T13:04:02.243229Z","submitted_at":"2025-05-21T15:00:57Z","title":"Comparison of stability indices of powers of graded ideals","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T15:28:10.386222Z"},"links":{"cited_paper":"/paper/2306.14243","citing_paper":"/paper/2505.15608"},"observation_digest":"sha256:c1f822ad613133f0b88653cde2e74f2163f8a12e2486f291a2c61d526b658dd6","observation_id":"693c7ca3-6646-4080-8e61-850c10108778","resolution":{"observed_at":"2026-08-07T15:28:10.386222Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.14243","last_updated":"2023-10-09T16:02:12Z","snapshot_observed_at":"2026-07-06T15:46:29.060519Z","submitted_at":"2023-06-25T13:29:49Z","title":"Asymptotic behaviour of the $\\text{v}$-number of homogeneous ideals","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.14243","snapshot_observed_at":"2026-08-07T05:15:08.720349Z","title":"Ficarra and E","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.09051","last_updated":"2025-07-11T03:13:32Z","snapshot_observed_at":"2026-08-07T04:54:21.085150Z","submitted_at":"2025-06-10T17:59:59Z","title":"$\\operatorname{v}$-numbers of integral closure filtrations of monomial ideals","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T05:15:08.720349Z"},"links":{"cited_paper":"/paper/2306.14243","citing_paper":"/paper/2506.09051"},"observation_digest":"sha256:eeff6d89d26cebedb94051309738e956021f30f5860944c4d1ddae820a89132d","observation_id":"a1d97952-8f2e-48d5-ac55-02b63b2eedb1","resolution":{"observed_at":"2026-08-07T05:15:08.720349Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.14243","last_updated":"2023-10-09T16:02:12Z","snapshot_observed_at":"2026-07-06T15:46:29.060519Z","submitted_at":"2023-06-25T13:29:49Z","title":"Asymptotic behaviour of the $\\text{v}$-number of homogeneous ideals","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.14243","snapshot_observed_at":"2026-08-06T19:34:25.557347Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.05700","last_updated":"2025-07-17T18:02:15Z","snapshot_observed_at":"2026-08-06T19:17:40.860452Z","submitted_at":"2025-07-08T06:21:21Z","title":"Comparing the $\\mathrm{v}$-number and $h$-polynomials of edge ideals","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T19:34:25.557347Z"},"links":{"cited_paper":"/paper/2306.14243","citing_paper":"/paper/2507.05700"},"observation_digest":"sha256:51d577b9ab3b196e7c592f718e1d14c430ef5dbb9ba39f86256b1e9daf40d9d9","observation_id":"67b8f7b0-bd36-4836-a6d4-6f7d62162ddd","resolution":{"observed_at":"2026-08-06T19:34:25.557347Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.14243","last_updated":"2023-10-09T16:02:12Z","snapshot_observed_at":"2026-07-06T15:46:29.060519Z","submitted_at":"2023-06-25T13:29:49Z","title":"Asymptotic behaviour of the $\\text{v}$-number of homogeneous ideals","version":4},"cited_work":{"arxiv_id":"2306.14243","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2306.14243","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ficarra and E","venue":null,"work_id":"fdadfe6d-c351-41b2-b4b9-30a1ce181026","year":null},"citing_paper":{"arxiv_id":"2603.29516","last_updated":"2026-04-07T08:03:28Z","snapshot_observed_at":"2026-08-08T18:23:48.803701Z","submitted_at":"2026-03-31T09:59:02Z","title":"The $v$-number of generalized binomial edge ideals of some graphs","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-13T23:47:14.365344Z"},"links":{"cited_paper":"/paper/2306.14243","citing_paper":"/paper/2603.29516"},"observation_digest":"sha256:19ceff92e0b06a53b717e3bb6170fd98ca25dd688721230610695a0803cb23be","observation_id":"64f051f8-c968-4a4e-891f-1fa73f7269fb","resolution":{"observed_at":"2026-05-13T23:48:27.711618Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2306.14243/citation-record","integrity":"/paper/2306.14243/integrity","json":"/paper/2306.14243/citation-record.json","paper":"/paper/2306.14243"},"outbound":[],"paper":{"arxiv_id":"2306.14243","last_updated":"2023-10-09T16:02:12Z","latest_version":4,"primary_category":"math.AC","snapshot_observed_at":"2026-07-06T15:46:29.060519Z","submitted_at":"2023-06-25T13:29:49Z","title":"Asymptotic behaviour of the $\\text{v}$-number of homogeneous ideals"},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:2306.14243."}