{"as_of":"2026-08-19T02:44:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9d97435a81e7658b9626676cbfa40b7dcb36ffe68a16c0b5cd435e939d0e54f7","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":"2026-08-18T06:34:40.430872+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":"2026-08-16T01:14:14.636812Z","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":"2026-05-15T01:38:27.663367Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2405.07000","last_updated":"2024-05-11T12:31:49Z","snapshot_observed_at":"2026-08-18T18:30:01.449087Z","submitted_at":"2024-05-11T12:31:49Z","title":"Multidegrees, families, and integral dependence","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.07000","snapshot_observed_at":"2026-08-07T10:33:18.563244Z","title":"Cid-Ruiz, C","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.05248","last_updated":"2025-06-05T17:09:06Z","snapshot_observed_at":"2026-08-07T10:19:42.805971Z","submitted_at":"2025-06-05T17:09:06Z","title":"Degree functions of graded families of ideals","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T10:33:18.563244Z"},"links":{"cited_paper":"/paper/2405.07000","citing_paper":"/paper/2506.05248"},"observation_digest":"sha256:a0bb85a8978c9cc5f6abe7cee127f418d52b0670df788e631a336661628d0335","observation_id":"94be01cb-e9c9-4b40-aa48-2ba5f353bc24","resolution":{"observed_at":"2026-08-07T10:33:18.563244Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.07000","last_updated":"2024-05-11T12:31:49Z","snapshot_observed_at":"2026-08-18T18:30:01.449087Z","submitted_at":"2024-05-11T12:31:49Z","title":"Multidegrees, families, and integral dependence","version":1},"cited_work":{"arxiv_id":"2405.07000","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2405.07000","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Cid-Ruiz, C","venue":null,"work_id":"2b3ebc04-e107-4667-8308-74805d450805","year":2024},"citing_paper":{"arxiv_id":"2605.14203","last_updated":"2026-05-13T23:40:28Z","snapshot_observed_at":"2026-08-01T15:28:43.777373Z","submitted_at":"2026-05-13T23:40:28Z","title":"Numerical characterizations for integral dependence of graded modules","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-15T01:35:18.546193Z"},"links":{"cited_paper":"/paper/2405.07000","citing_paper":"/paper/2605.14203"},"observation_digest":"sha256:8f4d616384f126b1d9d98a291ed4cd03ed5c9df5de42ca83d21c336afa3219d9","observation_id":"4039f82b-db4c-4f64-9286-d6309d534e40","resolution":{"observed_at":"2026-05-15T01:38:27.664920Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.07000","last_updated":"2024-05-11T12:31:49Z","snapshot_observed_at":"2026-08-18T18:30:01.449087Z","submitted_at":"2024-05-11T12:31:49Z","title":"Multidegrees, families, and integral dependence","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.07000","snapshot_observed_at":"2026-08-16T01:14:14.636812Z","title":"Multidegrees, families, and integral dependence.arXiv preprint:2405.07000, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.12731","last_updated":"2026-08-13T02:23:26Z","snapshot_observed_at":"2026-08-18T11:50:23.278100Z","submitted_at":"2026-08-13T02:23:26Z","title":"The multiplicity sequence of monomial ideals","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T01:14:14.636812Z"},"links":{"cited_paper":"/paper/2405.07000","citing_paper":"/paper/2608.12731"},"observation_digest":"sha256:abc8d42535ce273579d766f9f5572cf9c335f7b81fabc135113410de8eaf3c81","observation_id":"b866fb0d-1ad8-4995-a6e7-037a0870b43e","resolution":{"observed_at":"2026-08-16T01:14:14.636812Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2405.07000/citation-record","integrity":"/paper/2405.07000/integrity","json":"/paper/2405.07000/citation-record.json","paper":"/paper/2405.07000"},"outbound":[],"paper":{"arxiv_id":"2405.07000","last_updated":"2024-05-11T12:31:49Z","latest_version":1,"primary_category":"math.AC","snapshot_observed_at":"2026-08-18T18:30:01.449087Z","submitted_at":"2024-05-11T12:31:49Z","title":"Multidegrees, families, and integral dependence"},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 3 inbound Pith citation observations for arXiv:2405.07000."}