{"as_of":"2026-08-13T16:23:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:63bae64e19da057dd6b686ed1cda77ced26e9dd4e8bf28a4186c9a7bbd4ac3f8","coverage":[{"denominator":29,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":29,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T05:31:41.813910Z","state":"measured"},{"denominator":31,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":31,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T19:34:47.297127Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-07T04:54:36.293233Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"cited_work":{"arxiv_id":"2412.00399","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.00399","snapshot_observed_at":"2026-08-07T04:54:36.293233Z","title":"The linkage class of a grade three complete intersection","venue":"math.AC","work_id":"4e11a413-b4c2-4a75-bb48-d31bf947f444","year":2024},"citing_paper":{"arxiv_id":"2506.09598","last_updated":"2025-06-11T10:56:55Z","snapshot_observed_at":"2026-08-11T21:21:14.603649Z","submitted_at":"2025-06-11T10:56:55Z","title":"Generic models of licci ideals parametrized by Schur functors","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T04:54:34.642004Z"},"links":{"cited_paper":"/paper/2412.00399","citing_paper":"/paper/2506.09598"},"observation_digest":"sha256:9eec3513ddbb8b265abe5ea2b5fe38ba57d234988d60ad89b4de8118f5c8e61f","observation_id":"3d62461b-683a-4999-8207-5717a1ec7ed0","resolution":{"observed_at":"2026-08-07T04:54:36.300422Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.00399","snapshot_observed_at":"2026-08-07T19:34:47.297127Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.06019","last_updated":"2026-08-06T13:24:31Z","snapshot_observed_at":"2026-08-13T11:06:17.253375Z","submitted_at":"2026-08-06T13:24:31Z","title":"Restrictions on the Betti tables of licci ideals","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T19:34:47.297127Z"},"links":{"cited_paper":"/paper/2412.00399","citing_paper":"/paper/2608.06019"},"observation_digest":"sha256:b714561aa318d530c63bc4c93bef5d962af3df11c211bba8624498eff498e54b","observation_id":"45c85f11-070f-4a61-944b-579f846f62de","resolution":{"observed_at":"2026-08-07T19:34:47.297127Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2412.00399/citation-record","integrity":"/paper/2412.00399/integrity","json":"/paper/2412.00399/citation-record.json","paper":"/paper/2412.00399"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:41.692285Z","title":"Po incar´ e series of mod- ules over local rings of small embedding codepth or small linking numbe r","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.692285Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:abd8a11a7f478959b078d984f8074cc023db7443243d4d7fae3ebdd740b4fd3b","observation_id":"995a0cac-4b60-4aa9-9496-437e8097b842","resolution":{"observed_at":"2026-08-12T05:31:41.692285Z","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":"2026-08-12T05:31:41.697339Z","title":"A structure theorem for a class of grade thre e perfect ideals","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.697339Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:865ddc6178d9cdb1dac0c9267ce66f2e4d9450a21b1ab7c1ab25164ef988e1cf","observation_id":"d5db66c4-4bcb-485f-8d56-8b446e3d82f0","resolution":{"observed_at":"2026-08-12T05:31:41.697339Z","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":"10.7146/math.scand.a-12064","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:42.028855Z","title":"The existence of generic free resolutions and r elated ob- jects","venue":null,"work_id":"6b84c871-76a4-4f27-9a13-34f6e897a989","year":1984},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.701717Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:9a4b3c552f2c623d0ec0812aee6dce9acbd14e547564cb8322a919425150d1bf","observation_id":"ab67b4a6-ddd1-4e30-ac4e-80f4e1f0e759","resolution":{"observed_at":"2026-08-12T05:31:42.034446Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:41.706276Z","title":"Algebra structures fo r finite free resolu- tions, and some structure theorems for ideals of codimension 3","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.706276Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:423af6c9842597491f28dd43320e57853682a4317cec23af56d959c412140b5f","observation_id":"9e58a88f-972d-46c8-9d82-d45596cdddb8","resolution":{"observed_at":"2026-08-12T05:31:41.706276Z","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":"10.1016/s0001-8708(74)80019-8","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:42.000458Z","title":"Some structure theor ems for finite free resolutions","venue":null,"work_id":"3f4eeabf-156a-49e6-8884-68e1f45c784a","year":1974},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.710653Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:8dfe13aec153e2ae17b01de913d2e22f49e5b88ff627103370965dead63f0f7e","observation_id":"2c01e9cd-743a-4bef-9c0e-fa7d72dd3ae2","resolution":{"observed_at":"2026-08-12T05:31:42.007175Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0021-8693(73)90044-6","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:41.986217Z","title":"What makes a complex ex act?","venue":null,"work_id":"a406c04b-3e93-4dda-a109-c58f6f55f94d","year":1973},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.715284Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:6f6a4c153540b21c4645ddbc6af83012d4717c463f2bc16632f7ddf57fc0ebdf","observation_id":"04446cc4-0c0c-484d-b7a7-42c0c11796af","resolution":{"observed_at":"2026-08-12T05:31:41.990456Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/s0305004100043620","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:41.972064Z","title":"On ideals of finite homological dimension in local ring s","venue":null,"work_id":"2c72f58a-74a7-4f82-8bb4-2fc5bfd9fe98","year":1968},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.719695Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:2a612326238e69cf289e7ec342afe5913f0a06264e3a1a491a36337bd496cef7","observation_id":"11352b30-2ffc-4b27-aa0c-58184fd09e1a","resolution":{"observed_at":"2026-08-12T05:31:41.976345Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T05:31:42.313822Z","title":"On the Buchsbaum-Eisenbud theory of fi- nite free resolutions","venue":null,"work_id":"8662bf12-c30e-4e33-b3ad-540774f64a9f","year":1973},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.723799Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:3bd42f14fd446423e17288e7fbfb0a37015cbe549045c29e11fa964f99114051","observation_id":"190cddf5-4b3a-453e-97e7-c4f6f7edea1d","resolution":{"observed_at":"2026-08-12T05:31:42.318165Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T05:31:42.299434Z","title":"A note on perfect ideals","venue":null,"work_id":"80fe1606-b51f-4122-a1a7-570acc289607","year":1980},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.731821Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:7f1d008529081b30a6c5b608850961375d6c34dd7465dcbe3f20ec3f32a1f976","observation_id":"8a3012de-ed90-4444-a747-8bcf64536ebd","resolution":{"observed_at":"2026-08-12T05:31:42.304526Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2208.05934","last_updated":"2023-03-15T13:26:15Z","snapshot_observed_at":"2026-08-13T14:47:02.612608Z","submitted_at":"2022-08-11T17:11:44Z","title":"Higher structure maps for free resolutions of length 3 and linkage","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2208.05934","snapshot_observed_at":"2026-08-12T05:31:41.735964Z","title":"Higher structure maps for free resolutions of length 3 and linkage","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.735964Z"},"links":{"cited_paper":"/paper/2208.05934","citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:5fc2237304c9f01fe4999a0e7d2ef00aef1fd68e1980be4a01a6076b01a74079","observation_id":"7d605573-56a2-45f2-a8d6-9adb2c17a821","resolution":{"observed_at":"2026-08-12T05:31:41.735964Z","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":"2026-08-12T05:31:41.740364Z","title":"Ueber die Theorie der algebraischen Formen","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.740364Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:bbfda411fb7a845d73db240b28cb061bc69dbbda9a87ba5336c956992b88a412","observation_id":"c27bd511-e076-40f9-8d6f-498c8bb468a7","resolution":{"observed_at":"2026-08-12T05:31:41.740364Z","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":"2026-08-12T05:31:42.283477Z","title":"Topics in the homological theory of modules over commutativ e rings","venue":null,"work_id":"fdd9a831-be68-4a5c-917d-cae2976e1a34","year":1975},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.744680Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:a0a0e981a9b482402c67c3dbcb18ec972f606f941c0d9198a2a00e6f008bff57","observation_id":"80636a2d-9b80-4cd0-b29b-2720830f77cb","resolution":{"observed_at":"2026-08-12T05:31:42.289355Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T05:31:42.270334Z","title":"Humphreys","venue":null,"work_id":"0b04399a-4054-4b6c-ae27-2e91cedcea3f","year":1972},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.748804Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:3b6ed2a6a8eabdeb7b53f20dc9018c42947912dc4261e715676e4d43eb8f528e","observation_id":"d7803e5f-1dd9-4e4f-9af5-365aac36aa9d","resolution":{"observed_at":"2026-08-12T05:31:42.274907Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2307/1998491","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:41.936550Z","title":"The arithmetic perfection of Buchsbaum-Eisen bud varieties and generic modules of projective dimension two","venue":null,"work_id":"9cda76fd-7a34-46fb-836d-fe64beb9176f","year":1981},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.752986Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:a44f2a3076a38f509756582f09fcb607e362b7a88e2270c257ca0d693ebbc64d","observation_id":"0e2b7146-8a4e-42a5-a1ea-970e78e03d94","resolution":{"observed_at":"2026-08-12T05:31:41.941155Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:41.757283Z","title":"Kac-Moody groups, their flag varieties and representation t he- ory","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.757283Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:34510100d64b7d9c1bfcc702dcec6e1bebfed7c3ac2ea7ace18251247c1a8e65","observation_id":"e7f408b2-89b8-40ab-8849-f640680cdd99","resolution":{"observed_at":"2026-08-12T05:31:41.757283Z","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":"2026-08-12T05:31:42.256118Z","title":"The resolution of the universal ring for mod ules of rank zero and projective dimension two","venue":null,"work_id":"89b34cc9-4ec4-4f4b-8df4-77bedbadad16","year":2007},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.761530Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:cc721e4206cad7f198a50fd5e9b6a079a1d88d515561efd076b79c76c4221b22","observation_id":"b07442c6-b43c-451d-9ad6-87fc4c19a2ea","resolution":{"observed_at":"2026-08-12T05:31:42.260592Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4134/ckms.c180373","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:41.900180Z","title":"Some branching formulas fo r Kac-Moody Lie algebras","venue":null,"work_id":"79b8ee64-c89e-4cc4-a0b4-ef46cedc5b2a","year":2019},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.770450Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:0d7b8272718ecb853881556eff9196aa95f7533bd171e09f2ddb9f1a201a4dde","observation_id":"cad4ccd9-632b-4b61-beb5-d6ffed5014a6","resolution":{"observed_at":"2026-08-12T05:31:41.904901Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T05:31:42.242509Z","title":"ADEPerfectIdeals","venue":null,"work_id":"6310c6b2-dec9-482d-ae46-8b06dfc43e0f","year":null},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.775188Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:951f008773e4fd4f7ad45aa5349bb24ea525c249a43123e869055e14d9103f6d","observation_id":"2e40c47e-b7aa-437e-b8d0-3f80a924f51c","resolution":{"observed_at":"2026-08-12T05:31:42.246943Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T05:31:42.228547Z","title":"Free resolutions, linkage, and representation th eory","venue":null,"work_id":"d928f456-1b9d-4e80-80ee-8a466b8f1eb5","year":2024},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.779433Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:73fd91693fb333d792febd1a385aad61471e4bad59a7cd47d46fee2753aaa2e4","observation_id":"20535560-a214-4804-9528-d0560bc5afa8","resolution":{"observed_at":"2026-08-12T05:31:42.233316Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T05:31:42.215082Z","title":"Parametrizing higher structure maps for resolutions of len gth three","venue":null,"work_id":"3199b11c-fad1-439a-b569-4112bf8a3645","year":2023},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.784052Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:3fbf232895bfd4e4cdcd05bfa1e23e17f361c66a3b105200d81c3a54db645196","observation_id":"5bcc8799-6999-4bab-bdb7-34407e15201f","resolution":{"observed_at":"2026-08-12T05:31:42.219805Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T05:31:42.201036Z","title":null,"venue":null,"work_id":"edc9f570-ae33-4f06-99e8-4808956b8904","year":null},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.788267Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:9536519f9fadb48b11fadf9d0b6401896139040c690c9156c5bfb0c487eab578","observation_id":"cdf8052e-835c-495b-ac52-ce03b28c4535","resolution":{"observed_at":"2026-08-12T05:31:42.206019Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01425554","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:41.885568Z","title":"Liaison des vari´ et´ es alg´ ebriques . I","venue":null,"work_id":"b7b85c2d-eed0-4de5-8699-1f2f741079ba","year":1974},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.792448Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:a9d80731566eb243cd1aff45d2a23f25cebe4cb10fc7237db2b8ab92d3d202f8","observation_id":"860880f2-9571-483d-95d7-78377a8d1afe","resolution":{"observed_at":"2026-08-12T05:31:41.889913Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0021-8693(90)90042-m","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:41.869926Z","title":"On the generic free resolut ions","venue":null,"work_id":"1e037143-2049-4a2f-9493-c9eaf81eab0b","year":1990},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.796647Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:896df2f5fe082449d8081f6d1ad4daebd89df2e52574979e12e5c2236d0cd232","observation_id":"6cd394f3-49c5-4289-8173-94ed9a1f8caf","resolution":{"observed_at":"2026-08-12T05:31:41.874904Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:41.801379Z","title":"A structure theorem for type 3, grade 3 perfect ideals","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.801379Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:aa095b09c5dc29738570cab6fbe17ea308c1cefe84d1f1874a3211100d0e6bf7","observation_id":"308ae8fd-d749-4e69-8a79-aac4034f9de0","resolution":{"observed_at":"2026-08-12T05:31:41.801379Z","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":"2026-08-12T05:31:41.805492Z","title":"Universal complexes and the generic structure of free resolu- tions","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.805492Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:7a630524e71e140ce7bd1eab260ef36f1354c6fa9453fb7ce827df01910e2a5a","observation_id":"e18b4f5b-8224-4cd5-8c91-3d322aa71f27","resolution":{"observed_at":"2026-08-12T05:31:41.805492Z","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":"2026-08-12T05:31:42.186218Z","title":"Generic free resolutions and root systems","venue":null,"work_id":"46fc3c0b-7d37-4387-abfe-52ac32c632c8","year":2018},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.809995Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:f4b486723b9ce328560a9b343e135a67b06c192b3d46201d398f5c2efa2c89f2","observation_id":"1042c13c-45e4-415b-be32-5a73693bf946","resolution":{"observed_at":"2026-08-12T05:31:42.190977Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0021-8693(89)90318-9","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:41.843742Z","title":"On the structure of free resolutions of lengt h 3","venue":null,"work_id":"9ea3e7e3-0816-4bbb-80d3-1e41f999233b","year":1989},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.813910Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:d6f2d6112ee32a38f5eea1808521b9f8c649c0417a85ddba5280cd2c32b953d6","observation_id":"c868be4b-5e1b-419e-8516-1f108a61ffbd","resolution":{"observed_at":"2026-08-12T05:31:41.850404Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1515/crll.1973.262-263.205","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:41.958337Z","title":"doi: 10.1515/crll.1973.262-263.205","venue":null,"work_id":"5b49b402-9cf7-4133-bfde-b99a7df13cb9","year":1973},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":219,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.727863Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:d5b3719956d8504195ad1a6c7a05643fcfb201ab7fc8841b872bb852c6011d22","observation_id":"e9b926fa-fad0-44af-b0b6-33b4bc8bd7cc","resolution":{"observed_at":"2026-08-12T05:31:41.963167Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jalgebra.2006.11.013","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:31:41.914517Z","title":"doi: 10.1016/j.jalgebra.2006.11.013","venue":null,"work_id":"5b956adb-3227-4953-88b0-ea8fbeaaa673","year":2006},"citing_paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection","version":2},"reference_index":289,"source":"pdf_text","source_observed_at":"2026-08-12T05:31:41.765824Z"},"links":{"citing_paper":"/paper/2412.00399"},"observation_digest":"sha256:47c80bd27cc83a884b4cee5d028adeba464b7931f37173f61cb1eb9083c71d68","observation_id":"81d0a877-32a1-4d62-b2cf-56091caead51","resolution":{"observed_at":"2026-08-12T05:31:41.919173Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.00399","last_updated":"2026-06-23T22:47:53Z","latest_version":2,"primary_category":"math.AC","snapshot_observed_at":"2026-08-13T05:57:12.180180Z","submitted_at":"2024-11-30T08:45:00Z","title":"The linkage class of a grade three complete intersection"},"reference_resolution":{"displayed":29,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":11,"verified_fuzzy":9},"total_outbound_references":29},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 2 inbound Pith citation observations for arXiv:2412.00399."}