{"as_of":"2026-08-13T21:33:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9c165380ccdbeec2bfd558f5f143c46dae9568a1d5ffad22a3438f3b2cc52d81","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-09T16:48:00.281318Z","state":"measured"},{"denominator":39,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":39,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-19T11:38:45.685674Z","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":"2026-05-19T11:42:15.961601Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"cited_work":{"arxiv_id":"2502.01133","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.01133","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"9d044b02-c387-41f5-9516-40688d447299","year":2025},"citing_paper":{"arxiv_id":"2506.04899","last_updated":"2026-04-28T06:04:55Z","snapshot_observed_at":"2026-08-02T05:35:23.763525Z","submitted_at":"2025-06-05T11:30:52Z","title":"Canonical traces of graded fiber products: applications to disconnected Stanley--Reisner rings","version":5},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-19T11:38:45.685674Z"},"links":{"cited_paper":"/paper/2502.01133","citing_paper":"/paper/2506.04899"},"observation_digest":"sha256:9f571109925c2778ef28727f43ecae4afd39febc5127fee555c487b4a4fca113","observation_id":"a22dc6b8-e225-4b84-84b5-d3a9c5dfb4cc","resolution":{"observed_at":"2026-05-19T11:42:15.963168Z","resolver_source":"arxiv_id","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"}}],"links":{"evidence":"/evidence","html":"/paper/2502.01133/citation-record","integrity":"/paper/2502.01133/integrity","json":"/paper/2502.01133/citation-record.json","paper":"/paper/2502.01133"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T16:48:01.034286Z","title":"Aoyama,Some basic results on canonical modules, Journal of Mathematics of Kyoto University23(1983), no","venue":null,"work_id":"9d9da303-04a4-4415-987e-8b95f765ccff","year":1983},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.120975Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:d4b3108907b5cb2b6745733db5834ff7e5cec73b44c1035b8b5b375e5a52ec38","observation_id":"ea41c993-3133-4984-9e43-78ebe2d79dba","resolution":{"observed_at":"2026-08-09T16:48:01.039064Z","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":"2026-08-09T16:48:01.020394Z","title":"Aoyama and S","venue":null,"work_id":"356ee02b-f4cc-4608-a321-f8fca679f343","year":1985},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.127644Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:d4a2b2e7d2f4f5d3d9de3abf9ffe9212c989acad3f0b9e9687355cdf9eb4804a","observation_id":"6b797cc5-d342-4ef3-8259-c39ba6a96d37","resolution":{"observed_at":"2026-08-09T16:48:01.024722Z","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":"2026-08-09T16:48:01.007487Z","title":"Bagherpoor and A","venue":null,"work_id":"2b7a7a00-6747-46a5-8d96-9e2e621ee560","year":2023},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.132299Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:7a4dc426c5b2a52e8aad4d907dea4abbae0e15882ae789e2e9246f55a3da34d8","observation_id":"88249fe3-66e8-45dd-995e-2da93ff3d00f","resolution":{"observed_at":"2026-08-09T16:48:01.011404Z","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":"2026-08-09T16:48:00.994075Z","title":"Barucci and R","venue":null,"work_id":"d7f803ad-3804-4ee7-ba90-bb271f4df76e","year":1997},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.136594Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:b9bba86f60bc901685f7058b4ac597271f337f0b9701be6e67b3553607891355","observation_id":"b7d972d1-ff61-4631-a20b-0160d689e000","resolution":{"observed_at":"2026-08-09T16:48:00.998258Z","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":"2026-08-09T16:48:00.979949Z","title":"Bruns and J","venue":null,"work_id":"5d9c3932-dd41-4c25-9644-b0e0066c7231","year":1998},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.141479Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:380fe670d3bd334f78b9d9f7bbffbc9b78c648543ec7087911f80717b2628431","observation_id":"8bbf1d16-7154-4378-b708-6b345b42aa4d","resolution":{"observed_at":"2026-08-09T16:48:00.984642Z","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":"2026-08-09T16:48:00.965964Z","title":"Caminata and F","venue":null,"work_id":"91a77e1b-851a-4039-bcd9-7476113d8504","year":2021},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.145994Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:9ee6a18d273b043ee9ff5715e92b4961b5350717422c3b68ac62f0f059aaef74","observation_id":"ea139684-865b-43b2-89fe-4941df62ba91","resolution":{"observed_at":"2026-08-09T16:48:00.970401Z","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":"2505.14961","last_updated":"2025-05-20T22:41:57Z","snapshot_observed_at":"2026-08-07T15:24:15.506421Z","submitted_at":"2025-05-20T22:41:57Z","title":"Full-Trace Modules","version":1},"cited_work":{"arxiv_id":"2505.14961","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.14961","snapshot_observed_at":"2026-08-09T16:48:00.634750Z","title":"Full-Trace Modules","venue":"math.AC","work_id":"914eb9d8-1287-4c8e-a12d-3b4f8f55f4a2","year":2025},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.150652Z"},"links":{"cited_paper":"/paper/2505.14961","citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:3bc6a4b46f2cde5ece223658dcfdc3e319be7dc0c4754b7c32e12c411e396fe1","observation_id":"f803a0e7-26fc-4b64-b442-37347445f459","resolution":{"observed_at":"2026-08-09T16:48:00.639516Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T16:48:00.950641Z","title":null,"venue":null,"work_id":"b4c1d3d9-b03c-4ec0-b1c8-9d6995c4653f","year":2021},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.155458Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:0fccba81c7527743382d2d651d4c180aefcc27e8b3e869c2ac9e50431e533e61","observation_id":"aec8c16e-42f4-4caa-944d-53f17e781e83","resolution":{"observed_at":"2026-08-09T16:48:00.955773Z","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":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T16:48:00.935882Z","title":"Eisenbud and S","venue":null,"work_id":"97070914-e4d3-4eff-aede-4090f73821f9","year":1984},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.159533Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:acac99ef8b6e6ad433a13859d02f21c8c5b80bfb175d24531d183f566b0a276c","observation_id":"fbdfbd61-92a8-49e4-8730-c3b2f050cae9","resolution":{"observed_at":"2026-08-09T16:48:00.940508Z","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":"2026-08-09T16:48:00.921833Z","title":null,"venue":null,"work_id":"3ef3c0a6-799b-4c18-9217-615c3e818fe5","year":2015},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.163757Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:8ab0a606caf14d4a62195688388984f543072f82540c45884447010c8a9dc90d","observation_id":"4b88d89a-f5e0-42e3-bf1e-67c3d76da301","resolution":{"observed_at":"2026-08-09T16:48:00.926259Z","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":"10.1090/proc/17250","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Ficarra,The canonical trace of Cohen–Macaulay algebras of codimension 2, Proceedings of the American Mathematical Society, posted on 2015, DOI 10.1090/proc/17250.↑2 12 S","venue":"Proceedings of the American Mathematical Society","work_id":"83f60dbd-394a-499c-8e44-de7f79853d57","year":2015},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.167979Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:8281556a65d87f050872b45fca6ea73583c369bd6b9215c08ed3f531d8350482","observation_id":"092a9a21-79f3-4854-91ad-4b889b07de0f","resolution":{"observed_at":"2026-08-09T16:48:00.317924Z","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":"2026-08-09T16:48:00.908014Z","title":"Ficarra, J","venue":null,"work_id":"0d5d2b06-68fb-4ce3-9981-e1b9aa466907","year":2024},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.172350Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:94874d9d36452e6514cc3cb1af0a8407407f38d42ed7643c1996ec627ec34309","observation_id":"aae16ac6-ad7e-4d0d-8611-dd8df54c0f4f","resolution":{"observed_at":"2026-08-09T16:48:00.912387Z","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":"2026-08-09T16:48:00.894736Z","title":null,"venue":null,"work_id":"edd3fc9b-efa5-4f0d-a9e9-87c2fada8d9e","year":2013},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.176589Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:c5c9064a0b71d9435e343dff267a498c72eb80e7fb6353bc6635bcda4581098f","observation_id":"1eba8636-6767-4352-83e5-d71e34d62595","resolution":{"observed_at":"2026-08-09T16:48:00.898625Z","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":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T16:48:00.882325Z","title":null,"venue":null,"work_id":"ff001827-a5a0-499b-8d3f-c66e5fcdecd0","year":2015},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.180540Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:ef131fede82fed14f44ba2c849828c699e717a06efe510dc29db6a744b0dd6a6","observation_id":"d2a2fddc-976f-4501-bdf7-ded2fb6170cd","resolution":{"observed_at":"2026-08-09T16:48:00.886020Z","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":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T16:48:00.869892Z","title":"Goto and K","venue":null,"work_id":"01143bf7-3fbd-473e-9f7c-8e12e266c54d","year":1978},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.184794Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:765b9e5839b6e27c9da785b2bf345c3360d2c3628fe6d511944c8983db896bd3","observation_id":"9ddfd60b-02e3-400a-bc6b-493a2d3ba077","resolution":{"observed_at":"2026-08-09T16:48:00.873700Z","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":"2026-08-09T16:48:00.857702Z","title":null,"venue":null,"work_id":"a518bdc4-9ed8-42d2-97f7-9e9e032577c1","year":null},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.188932Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:f0e6b1b16f4216c12c5db43f958c05135624ee1cec448d6d70ec4b2c9188b4db","observation_id":"3323d48e-d186-4849-9e92-7ae50450e781","resolution":{"observed_at":"2026-08-09T16:48:00.861562Z","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":{"arxiv_id":"2306.14523","last_updated":"2023-06-26T08:56:37Z","snapshot_observed_at":"2026-08-13T11:09:29.667828Z","submitted_at":"2023-06-26T08:56:37Z","title":"Indecomposability of graded modules over a graded ring","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.14523","snapshot_observed_at":"2026-08-09T16:48:00.193275Z","title":"Hashimoto and Y","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.193275Z"},"links":{"cited_paper":"/paper/2306.14523","citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:94a42e04d4c626e04b205cfb8eef21726c321fb56971d05caca6528ef38dcb29","observation_id":"acb6005c-7980-4eaa-b905-64f506d6ea58","resolution":{"observed_at":"2026-08-09T16:48:00.193275Z","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":"2026-08-09T16:48:00.844005Z","title":null,"venue":null,"work_id":"13c6b686-c24f-44ac-9790-90d385303e44","year":2023},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.197964Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:5e30fea1d17c675d5ec0d2dfb6ac2752c2e3ce20a16155831033a694746a14b1","observation_id":"e82756cc-be60-49f7-9375-288ce449db5b","resolution":{"observed_at":"2026-08-09T16:48:00.848585Z","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":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T16:48:00.829915Z","title":"Hatasa, N","venue":null,"work_id":"0e77c7a3-2f7c-481f-83c0-6e1a81d339e5","year":2025},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.202051Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:7c7623f4f4f05257d5c5d10a8292b2a5a90f9ad4ff178289840d0bed0812749d","observation_id":"50976d13-1e2f-4324-850f-6e6bf12f03a6","resolution":{"observed_at":"2026-08-09T16:48:00.834336Z","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":"2026-08-09T16:48:00.816826Z","title":"Herzog, T","venue":null,"work_id":"8c868ca4-090d-4011-b85b-78a1775c79af","year":2019},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.205615Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:6354a4ba51dacd7b511e32a810bc9dfcf02331b7a58b5951126fe72a6ff32937","observation_id":"14eb407e-6bf7-466e-8986-ec493eabacee","resolution":{"observed_at":"2026-08-09T16:48:00.821092Z","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":"2026-08-09T16:48:00.803098Z","title":"Higashitani,Almost Gorenstein homogeneous rings and theirh-vectors, Journal of Algebra456(2016), 190–206.↑2, 4","venue":null,"work_id":"4de34347-eedf-4f38-b820-e0cdd81ed79a","year":2016},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.209510Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:5be0ec13f4808a31e574865cf0e8ca71e3a720b1f55882f8c012b90be39d07ae","observation_id":"bd321d90-bcd8-408f-bfd3-5b0979ecdf3a","resolution":{"observed_at":"2026-08-09T16:48:00.807536Z","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":"2026-08-09T16:48:00.789289Z","title":"Higashitani and K","venue":null,"work_id":"799fa225-7be9-4629-9121-e531b4764498","year":2022},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.213225Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:47cde6d71ad1af3f1cadcaae31f704b5c7efa868de08dc7885fecf6fffdbd5a2","observation_id":"655dd3da-d3d5-49ff-afb9-f842445b3834","resolution":{"observed_at":"2026-08-09T16:48:00.793760Z","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":"2411.12081","last_updated":"2024-11-18T21:44:56Z","snapshot_observed_at":"2026-08-12T17:53:43.105002Z","submitted_at":"2024-11-18T21:44:56Z","title":"On nearly Gorenstein affine semigroups","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.12081","snapshot_observed_at":"2026-08-09T16:48:00.216960Z","title":"Jafari, F","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.216960Z"},"links":{"cited_paper":"/paper/2411.12081","citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:9418946df6c6f3204b5bb86a34df0d640c7174dd62e7fc437b252006b5e76bd9","observation_id":"82d5d3cb-e85f-443c-867f-087ac1fd5d58","resolution":{"observed_at":"2026-08-09T16:48:00.216960Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.03442","last_updated":"2025-01-28T17:13:29Z","snapshot_observed_at":"2026-08-13T18:20:49.708265Z","submitted_at":"2025-01-07T00:07:21Z","title":"Trace ideals, conductors, and ideals of finite (phantom) projective dimension","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.03442","snapshot_observed_at":"2026-08-09T16:48:00.220998Z","title":"Kimura,Trace ideals, conductors, and ideals of finite (phantom) projective dimension, arXiv preprint arXiv:2501.03442 (2025).↑2","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.220998Z"},"links":{"cited_paper":"/paper/2501.03442","citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:f97d16d1da21b8ea7d96f933cd815feb267484450da31a892e7165c9940a1364","observation_id":"8d06ed4a-1293-4ee9-a170-1d0958de7ef7","resolution":{"observed_at":"2026-08-09T16:48:00.220998Z","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":"2026-08-09T16:48:00.775635Z","title":"Kumashiro, N","venue":null,"work_id":"fd45000e-99d3-480b-b5c4-07729538f9c6","year":2025},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.224961Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:3f375924ce8dc0fb2ea412e2bb0e58ae6d28cf95389287f54f564ff6adb5dbb0","observation_id":"a8c5d164-21ce-48a7-b7ef-252c20d398f3","resolution":{"observed_at":"2026-08-09T16:48:00.779888Z","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":"2506.04899","last_updated":"2026-04-28T06:04:55Z","snapshot_observed_at":"2026-08-02T05:35:23.763525Z","submitted_at":"2025-06-05T11:30:52Z","title":"Canonical traces of graded fiber products: applications to disconnected Stanley--Reisner rings","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.04899","snapshot_observed_at":"2026-08-09T16:48:00.228668Z","title":"Kumashiro and S","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.228668Z"},"links":{"cited_paper":"/paper/2506.04899","citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:ffdcb0b418e4a63d8fe0d33a1a45d583d7a22f9183c67784acb3aa2bef256acd","observation_id":"656affb6-7e4b-4082-86f5-d76bb0b499a7","resolution":{"observed_at":"2026-08-09T16:48:00.228668Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.05024","last_updated":"2025-05-19T22:14:43Z","snapshot_observed_at":"2026-08-12T22:29:10.671689Z","submitted_at":"2024-10-07T13:25:34Z","title":"The chain algebra of a pure poset","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.05024","snapshot_observed_at":"2026-08-09T16:48:00.233163Z","title":"Lu,The chain algebra of a pure poset, arXiv preprint arXiv:2410.05024 (2024).↑2","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.233163Z"},"links":{"cited_paper":"/paper/2410.05024","citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:af615c6c351fd615f20197cd881b54ea8070fe502dd459a0b1f33c75b3aade7e","observation_id":"00bc6a9a-7937-403c-86ca-9cb409c7c5ff","resolution":{"observed_at":"2026-08-09T16:48:00.233163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.04686","last_updated":"2024-09-07T02:48:18Z","snapshot_observed_at":"2026-08-12T22:49:36.541492Z","submitted_at":"2024-09-07T02:48:18Z","title":"Annihilators of (co)homology and their influence on the trace Ideal","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.04686","snapshot_observed_at":"2026-08-09T16:48:00.237826Z","title":"Lyle and S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.237826Z"},"links":{"cited_paper":"/paper/2409.04686","citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:f4cea8d925293848c43315e73a2ff699999bd86e1781b936a32f9f5466b1dc5b","observation_id":"20cc4739-9cbf-4ad7-81e9-f03bd5bee9fb","resolution":{"observed_at":"2026-08-09T16:48:00.237826Z","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":"2026-08-09T16:48:00.761854Z","title":"Miyashita,Comparing generalized Gorenstein properties in semi-standard graded rings, Journal of Algebra647(2024), 823–843.↑2, 7, 10","venue":null,"work_id":"786ab8bb-c3ce-47eb-b65c-bf64ed17ad01","year":2024},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.242444Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:70f5cf70f6314659d0b7a760f8b4a1bd273edc98ed76323bf2621ffa467ccbeb","observation_id":"e55e5205-edbf-4f05-9ca8-166a65716768","resolution":{"observed_at":"2026-08-09T16:48:00.766373Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T16:48:00.246715Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.246715Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:58f629f0b826a87fb6b7f08f1b66b07fbba024ce0b95af44d7483d049ab6e5aa","observation_id":"e21d20f4-d714-4a23-8271-1231e0cbde11","resolution":{"observed_at":"2026-08-09T16:48:00.246715Z","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":"2026-08-09T16:48:00.748850Z","title":"Miyashita and M","venue":null,"work_id":"404293f2-36be-4b7e-9433-0fa811daa8a2","year":2025},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.251296Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:94acdf96103e5bb43626199ee28725a0eda6a2a72e144cf0b608aa85776d4e6b","observation_id":"90b94ff5-945e-4503-9c0b-142e71b8bed4","resolution":{"observed_at":"2026-08-09T16:48:00.753142Z","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":"2026-08-09T16:48:00.735407Z","title":"Miyazaki and J","venue":null,"work_id":"fdadb6f0-fb89-4f80-9901-cf05ac975d9b","year":2024},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.255472Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:f95667ac71c76c3b47db941676535c202017ad0bb9fb40b543d41785a89dcc02","observation_id":"7c81d83e-eed7-49ca-b91c-0219b31fe091","resolution":{"observed_at":"2026-08-09T16:48:00.739890Z","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":"2026-08-09T16:48:00.722008Z","title":"Moscariello and F","venue":null,"work_id":"bb7fb778-f378-4a3d-8264-f80a4458bbb7","year":2021},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.259684Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:72eebb79b97aa5b8179e0eaa6c3aec915b9d8bb1c37d260917b5c97b3a9ee3a7","observation_id":"15062469-16f4-4699-a0c0-577dc93be7c2","resolution":{"observed_at":"2026-08-09T16:48:00.726451Z","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":"2026-08-09T16:48:00.706126Z","title":"Rinaldo, F","venue":null,"work_id":"474b4b50-20b8-42d6-bcc6-9dc078b3ef1f","year":2024},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.264044Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:c8866396404c75f42a35d5280aee7efb4bef22c3341234447417f655cc283543","observation_id":"efbe87ec-e0d9-4f4d-b449-af20c7ab73ca","resolution":{"observed_at":"2026-08-09T16:48:00.711520Z","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":"2026-08-09T16:48:00.691828Z","title":"Rinaldo and R","venue":null,"work_id":"ff718e82-8e44-4b9f-b801-512203d6b6fd","year":2023},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.268253Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:1e335f298820f280736fbfb5356206122a3f9687406913e5da2a8c1ff2a0c64d","observation_id":"e4c7a066-692b-48a7-a086-7adf0f75cb70","resolution":{"observed_at":"2026-08-09T16:48:00.695929Z","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":"2026-08-09T16:48:00.677935Z","title":"P Stanley,Hilbert functions of graded algebras, Advances in Mathematics28(1978), no","venue":null,"work_id":"c43bd016-fc01-4174-923c-fdbe3ea23573","year":1978},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.272714Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:1e19bda79b392f3adf6652bf37d99fd48f56cad46df6845ed09d754c7e3107c6","observation_id":"b02841f3-3757-454e-9916-232eaaf72a2c","resolution":{"observed_at":"2026-08-09T16:48:00.682191Z","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":"2026-08-09T16:48:00.663752Z","title":"2-3, 319–331.↑4","venue":null,"work_id":"b872a382-78b1-4666-9a64-3317db251873","year":1991},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.277037Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:3a31b3aeb7b2404a5f3f52658cf83e6a115fe2a2e38fb3cfac9238976fe75b93","observation_id":"f115e2f6-9aff-406e-8c96-2919452ba4eb","resolution":{"observed_at":"2026-08-09T16:48:00.667745Z","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":"2026-08-09T16:48:00.649231Z","title":"41, Springer Science & Business Media, 2007.↑1, 3, 4, 10, 11 (S","venue":null,"work_id":"4e683d3a-a165-4b82-bda4-f28e9aa8d0e4","year":2007},"citing_paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?","version":6},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-09T16:48:00.281318Z"},"links":{"citing_paper":"/paper/2502.01133"},"observation_digest":"sha256:51042362692ca33468a7f3a10cf56dde80ea3fa18ce0af20e5cb66899cecd581","observation_id":"4cf5effd-37cc-4706-95c0-5bbd5acca45b","resolution":{"observed_at":"2026-08-09T16:48:00.653770Z","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"}}],"paper":{"arxiv_id":"2502.01133","last_updated":"2025-06-24T16:42:26Z","latest_version":6,"primary_category":"math.AC","snapshot_observed_at":"2026-08-13T16:35:10.565752Z","submitted_at":"2025-02-03T07:59:21Z","title":"When do pseudo-Gorenstein rings become Gorenstein?"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":13,"verified_exact":2,"verified_fuzzy":23},"total_outbound_references":38},"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 38 of 38 outbound references and 1 inbound Pith citation observation for arXiv:2502.01133."}