{"as_of":"2026-08-08T19:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fd47d13a52a48f71edb9929ffee4c537d9cbbdfe020b6dab3aa40a19b220bdaa","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T08:53:56.751870Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2607.03944/citation-record","integrity":"/paper/2607.03944/integrity","json":"/paper/2607.03944/citation-record.json","paper":"/paper/2607.03944"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T08:53:55.053960Z","title":null,"venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.053960Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:48e95392d41fe89a07b1b57118076d7ad83be2891247bc0cf45d9e0e522160c3","observation_id":"adf846cf-cc39-42cf-8fa8-345008e1b5ac","resolution":{"observed_at":"2026-08-02T08:53:55.053960Z","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":"2026-08-02T08:53:55.131715Z","title":"Beauville","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.131715Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:07be3d2f710fdbe95bafdc274e487c275e7e58fddda2e6bd2cb1777d83533bcc","observation_id":"5a289d03-0245-42d8-99ee-27df437c9733","resolution":{"observed_at":"2026-08-02T08:53:55.131715Z","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":"2026-08-02T08:53:55.174722Z","title":null,"venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.174722Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:9128bf2c459f98fcbea52b2c37ee08a922a115d315fb6cd60096e1550f06fe6f","observation_id":"e831a7e0-9be6-41dc-81b6-5c463dd362ba","resolution":{"observed_at":"2026-08-02T08:53:55.174722Z","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":"2026-08-02T08:53:55.233583Z","title":"Bl\\\"aser, D","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.233583Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:5a11b105a4e0b31886c53df7f46bd78bf97e54b2f3a11dd7e6be2586eb2f94a3","observation_id":"9259cc8f-0177-4121-90d3-ff3fa797ce0a","resolution":{"observed_at":"2026-08-02T08:53:55.233583Z","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":"2026-08-02T08:53:55.293431Z","title":"Ciliberto, F","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.293431Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:ebf998c1c0c891a0d8531110f6fd74c8458fe5b2409ecc68047cd770c4f6e046","observation_id":"526d86eb-9f01-42ac-98fd-7cc161c5f9ff","resolution":{"observed_at":"2026-08-02T08:53:55.293431Z","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":"2026-08-02T08:53:55.329819Z","title":"Casanellas, R","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.329819Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:4dec219375e51a2b038fc1dfe88119565ea9b8dbea503294c5d077792fc18a9a","observation_id":"03edab78-2618-40ac-a5da-faa8c1b95ab8","resolution":{"observed_at":"2026-08-02T08:53:55.329819Z","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":"2026-08-02T08:53:55.350700Z","title":"Costa, R","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.350700Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:cbc87001d8503f4051e16a129f28d760fb8c5549b8a8449874c0d573f4936094","observation_id":"0477c5c7-218c-44ce-8310-cd641bfa4c1b","resolution":{"observed_at":"2026-08-02T08:53:55.350700Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2112.08864","last_updated":"2022-09-26T23:39:44Z","snapshot_observed_at":"2026-07-06T12:19:33.825116Z","submitted_at":"2021-12-16T13:18:24Z","title":"Matrix factorizations of generic polynomials","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2112.08864","snapshot_observed_at":"2026-08-02T08:53:55.409767Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.409767Z"},"links":{"cited_paper":"/paper/2112.08864","citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:bb4d7ad98de3d369d8b6210b1c611dd4dc8a3813e717da5d22aea6d945bcec34","observation_id":"c3e2c135-5a4b-41f6-ae95-dc6abb25f8c3","resolution":{"observed_at":"2026-08-02T08:53:55.409767Z","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":"2026-08-02T08:53:55.476660Z","title":"Eisenbud, F.-O","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.476660Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:253ff2d8a2769e967dcb071fc9cbbb7eec7c4ff9e889aa6904661fdd08ee6735","observation_id":"4b1b9e6f-444f-4e9c-8c5e-c4f8989a3dd8","resolution":{"observed_at":"2026-08-02T08:53:55.476660Z","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":"2026-08-02T08:53:55.528228Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.528228Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:6cc8f83b03e9755b30cc05005dbe1fd37d43a269d1914aa358b3aae993135a2a","observation_id":"a1a0fa55-4384-4ade-9b33-4f9cf2904509","resolution":{"observed_at":"2026-08-02T08:53:55.528228Z","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":"2026-08-02T08:53:55.539050Z","title":"Faenzi, Y","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.539050Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:39ad992033e2c3d9b758d9a5061033c96f4ca532fc56ccface7cf1cf8e87a800","observation_id":"a4216a6d-8a87-45fd-a8dc-5b36a58d9bb1","resolution":{"observed_at":"2026-08-02T08:53:55.539050Z","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":"2026-08-02T08:53:55.596116Z","title":"Herzog, B","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.596116Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:a726f3d2c693ef09ec320a87fdaba18d49bf17fd40fb68fc840472ae2a1a9d21","observation_id":"ced9a580-5b23-45b0-8913-2de3e60f6b3d","resolution":{"observed_at":"2026-08-02T08:53:55.596116Z","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":"2026-08-02T08:53:55.628645Z","title":"Kim, F.-O","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.628645Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:e89fccd8c1f2f89f4efd4e5f99df39ff9017d6ce39436d21e886b05bcbdc0eb4","observation_id":"f57b430e-1e09-4185-be4d-aa0412c079e4","resolution":{"observed_at":"2026-08-02T08:53:55.628645Z","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":"2026-08-02T08:53:55.687274Z","title":"Lazarsfeld","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.687274Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:cb85cb4f8a1d6ac92c27fbe1770b1ab74d9f8d7534d70a64ce89c90f9c1f7346","observation_id":"fa6d41ae-ea45-4e73-a746-b7cd2d4e419a","resolution":{"observed_at":"2026-08-02T08:53:55.687274Z","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":"2026-08-02T08:53:55.736572Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.736572Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:1e2e147cc86409fe59066af9b2eceed79aa121fd70b6b19842ed19aa7ac8bf3f","observation_id":"b5999be3-5c14-4038-81c3-6178e66e423d","resolution":{"observed_at":"2026-08-02T08:53:55.736572Z","resolver_source":null,"status":"parse_uncertain"},"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":"2026-08-02T08:53:55.879519Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:55.879519Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:2e01a1072e6334059adf520c7e77b1936668e8333e037e9d1cbee4e1c2e1a2aa","observation_id":"8f0c7b56-010a-4f70-9ae5-c75cd52e278a","resolution":{"observed_at":"2026-08-02T08:53:55.879519Z","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":"2026-08-02T08:53:56.063215Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:56.063215Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:9c286ce916dca58cd4b6e6dde10fb135f9ae89e9a10f7a008c1aa180053fc38f","observation_id":"ddf056c3-f640-4f22-994e-f9cabe64be0c","resolution":{"observed_at":"2026-08-02T08:53:56.063215Z","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":"2026-08-02T08:53:56.182729Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:56.182729Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:4fd51d124e1025397f7af8aa82ecb9de80e7429be83eeb4eba9d19b57722c3d3","observation_id":"fbfb181a-a851-435f-b431-872a653fd622","resolution":{"observed_at":"2026-08-02T08:53:56.182729Z","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":"2026-08-02T08:53:56.347908Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:56.347908Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:08d4352d95f5551b10a572777fbf4833cbadefdc21bc726ec90485532fd3730f","observation_id":"295526fe-1a97-4159-bafe-f39b1def762d","resolution":{"observed_at":"2026-08-02T08:53:56.347908Z","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":"2026-08-02T08:53:56.490080Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:56.490080Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:e4b543fc6775c7c34a817c786354a92dc2f11d9a322d803827911503e871d9fa","observation_id":"7ce3801f-e95e-4c90-a763-5e6edf07de5d","resolution":{"observed_at":"2026-08-02T08:53:56.490080Z","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":"2026-08-02T08:53:56.644577Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:56.644577Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:d9e75983485c7e5a8403c125286250dcebbdac217eda368b1c90331b46422a55","observation_id":"4d6747f2-cdc6-4b23-b26d-11a63913b634","resolution":{"observed_at":"2026-08-02T08:53:56.644577Z","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":"2026-08-02T08:53:56.751870Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-02T08:53:56.751870Z"},"links":{"citing_paper":"/paper/2607.03944"},"observation_digest":"sha256:8ce10003f590ff83e1c8a96c596a29e927f08685bf89df075970893a02862c22","observation_id":"fb649252-39cb-49d7-b172-f107cf0d2065","resolution":{"observed_at":"2026-08-02T08:53:56.751870Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.03944","last_updated":"2026-07-20T19:11:18Z","latest_version":2,"primary_category":"math.AG","snapshot_observed_at":"2026-08-02T08:53:54.129833Z","submitted_at":"2026-07-04T16:36:42Z","title":"A linear lower bound on the Ulrich complexity of hypersurfaces"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":1,"unresolved":21,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":22},"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 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2607.03944."}