{"as_of":"2026-08-19T16:06:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:092ff76dbb308c0f70c0753fe7d8d9433725bc868c57e62d7d953a3dab84e120","coverage":[{"denominator":15,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":15,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-26T19:01:05.634416Z","state":"measured"},{"denominator":15,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":15,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2606.19028/citation-record","integrity":"/paper/2606.19028/integrity","json":"/paper/2606.19028/citation-record.json","paper":"/paper/2606.19028"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T19:01:05.634416Z","title":"Classification of the irreducible representations of sl (2, C )","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:d88917419f85e0c402e4c1b0eacc4855e9379619434697b381f3fcf6df21dac6","observation_id":"a733a5a5-02a8-4fa0-9254-3368bd82a1c9","resolution":{"observed_at":"2026-06-26T19:01:05.634416Z","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":"2026-06-26T19:01:05.634416Z","title":"The irreducible representations of the Lie algebra sl (2) and of the Weyl algebra","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:671065d3f64a3a1630e3e9339a10c04d3b855829e9bbc6ec5955d9e3bfc030cb","observation_id":"ef6e7c90-78d7-4e71-bbcb-d4a72c9d88c7","resolution":{"observed_at":"2026-06-26T19:01:05.634416Z","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":"2026-06-26T19:01:05.634416Z","title":"Irreducible skew polynomials over domains","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:eaf18e479364ea463da0981a12fe607c4a605f332089c46e9f6511774015bb45","observation_id":"db6b8374-e941-4372-8edb-b8fbe0edc638","resolution":{"observed_at":"2026-06-26T19:01:05.634416Z","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":"2026-06-26T19:01:05.634416Z","title":"How a nonassociative algebra reflects the properties of a skew polynomial","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:44d429a3517950c77023f8583b43ef46fe48938d4a21182bf395ef70fccd521b","observation_id":"0555e6ef-a39e-4a37-bf10-7acc1d524a02","resolution":{"observed_at":"2026-06-26T19:01:05.634416Z","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":"2026-06-26T19:01:05.634416Z","title":"Enveloping algebras","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:2eff1be12c2ecde11223b6d874b0dceaaff42a10f683c07d5484e9f264d0f2f4","observation_id":"ef664918-1017-45af-8d86-31bd6cc271d8","resolution":{"observed_at":"2026-06-26T19:01:05.634416Z","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":"2603.04303","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T02:49:25.082510Z","title":"Simple sl _2 -modules that are torsion free U(h) -mo\\-du\\-les of rank 1","venue":null,"work_id":"07185180-4f96-4cfb-9f11-4e93d3ce0e14","year":null},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:2ac969ea4f672d2a45dda1355a1822e129fa7b183f6d5ce86237c2c96d5686bc","observation_id":"876673e9-53e8-4d99-af57-6357986e53dd","resolution":{"observed_at":"2026-07-04T02:49:25.084072Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2601.21197","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T02:49:25.085163Z","title":"A family of simple U( h ) -free modules of rank 2 over sl _2","venue":null,"work_id":"462c4721-6ea3-48e5-81ab-b3bded314444","year":null},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:806dc726a76f47da04621d0a4ccb1b1ad2d455be91ceaed0882d4a114e529c80","observation_id":"58ac8473-666a-482f-887a-3200d533fe34","resolution":{"observed_at":"2026-07-04T02:49:25.086898Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-06-26T19:01:05.634416Z","title":"Representations of semisimple Lie algebras in the BGG category O","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:9fe2b72567622fc958c795cd9b5d4c32ce34c378e64e80216cad5d62b9c6205b","observation_id":"ba5b6277-72b9-4ebb-ba03-69737d238b4d","resolution":{"observed_at":"2026-06-26T19:01:05.634416Z","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":"2026-06-26T19:01:05.634416Z","title":"On category O for affine Grassmannian slices and categorified tensor products","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:a6db5dbeac7a7bde7642946bf33858f44447f4967a43a5413b0ff97ad1f2a761","observation_id":"79f21b9a-4512-4c97-b564-286d00e771e2","resolution":{"observed_at":"2026-06-26T19:01:05.634416Z","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":"2512.01520","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T02:49:25.081308Z","title":"Lifting free modules to generalized Weyl algebras","venue":null,"work_id":"a490bb57-7fe8-41a0-a3d4-323893e132ae","year":null},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:f64f5dd61c768641d9054b3ce68bb67217c7e96e68d1b617d460a62325bbe975","observation_id":"ab3a4c55-c140-44b5-92f7-9b495d0457e8","resolution":{"observed_at":"2026-07-04T02:49:25.082756Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-06-26T19:01:05.634416Z","title":"Classification of irreducible weight modules","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:69d32570d0284d5b475129a3a9ab4bc29d018c670becc6fdbf9bd9ebd6e3b6ad","observation_id":"bb8f363f-5eb3-4b83-b6d2-8bf685813041","resolution":{"observed_at":"2026-06-26T19:01:05.634416Z","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":"2026-06-26T19:01:05.634416Z","title":"Lectures on sl _2( C ) -modules","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:cc65d1aa87698b737f0611b538ceec4b8e9d17808e003fc835e1f036177cb32d","observation_id":"aacdf0db-a83d-46d8-8fd8-3130100f7af4","resolution":{"observed_at":"2026-06-26T19:01:05.634416Z","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":"2026-06-26T19:01:05.634416Z","title":"Simple sl _ n+1 -module structures on U(h)","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:fcbfcffc24b4315cfe7549bdac480984989de71d4756cdbc6a7ad29519f43722","observation_id":"05b8f9df-eaa1-44f8-bb6d-ca44a745dfca","resolution":{"observed_at":"2026-06-26T19:01:05.634416Z","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":"2026-06-26T19:01:05.634416Z","title":"Simple sl (V) -modules which are free over an abelian subalgebra","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:18349cd4fd0433d34c0f059302c13553630b9c94cd0c9f285d151704a4aea53b","observation_id":"a2f1eef0-885d-4c6c-a69a-0e9c51fba679","resolution":{"observed_at":"2026-06-26T19:01:05.634416Z","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":"2026-06-26T19:01:05.634416Z","title":"Galois theory of difference equations","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-06-26T19:01:05.634416Z"},"links":{"citing_paper":"/paper/2606.19028"},"observation_digest":"sha256:9bea5445ff21bd86122add027799b901466f17be05645e3a8a1bb2d2ecef96bc","observation_id":"72df740e-cb84-4521-991d-6b30e44a4dfb","resolution":{"observed_at":"2026-06-26T19:01:05.634416Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.19028","last_updated":"2026-06-17T12:56:40Z","latest_version":1,"primary_category":"math.RT","snapshot_observed_at":"2026-08-09T15:28:58.780157Z","submitted_at":"2026-06-17T12:56:40Z","title":"Simple gradable $\\mathbb{C}\\lbrack\\mathtt{h}\\rbrack$-torsion free $\\mathfrak{sl}_2$-modules"},"reference_resolution":{"displayed":15,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":3,"verified_fuzzy":0},"total_outbound_references":15},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:2606.19028."}