{"as_of":"2026-08-13T15:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:da0e869f73bb96412dac28d9441887b686c1b2fda9bcc9a8a5309bf4f277325e","coverage":[{"denominator":56,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":56,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-28T11:54:35.118566Z","state":"measured"},{"denominator":56,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":56,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2606.02026/citation-record","integrity":"/paper/2606.02026/integrity","json":"/paper/2606.02026/citation-record.json","paper":"/paper/2606.02026"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T11:54:35.118566Z","title":"Altafi, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:9cae1d479528b8e2a2cd1a98228ec07bacaa30045c7a4db160397b74f265de79","observation_id":"681d1f2a-4e3b-458d-b5e1-53678f31c544","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:d631438186b1a7751c07cf0aa05357a8c8f17ab342ac0e22635e5cee1aef618f","observation_id":"afdc49af-9114-4926-85e0-374c4ff17477","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:2056b437d574ab16d859a559fa9d896568890121fc29f38f0c5f1cdf7019fcf0","observation_id":"4f4491b7-6608-4414-bb9b-0c35bb3b94be","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:b19402d3186bccc073dd697cce38538289ad41e9a7db3a04879944d63f56405f","observation_id":"6bd5a84c-8877-4cb0-8a22-4924ab277d35","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:7f395b111618738ca4d512acc6a2d8fc1be3321278ec31acded392047e4a7358","observation_id":"06de37bb-1a62-4934-a2b3-9ad715e28dab","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Baranovsky,The variety of pairs of commuting nilpotent matrices is irreducible,Trans- form","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:075a10571041f99b4c4c8f19f7ffbe3542b8b6902b92540a523d7ec7bff3ad39","observation_id":"e10c1309-7fa6-4686-9681-e53df7fafd09","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Basili.On the irreducibility of varieties of commuting matrices.J","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:2441af77a7e51c3946773ac7507804d0482e390c31cf3cde2c363a05d6cd10cb","observation_id":"4c40610d-d4e9-4be2-979e-3b9c318066c2","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Basili.On the irreducibility of commuting varieties of nilpotent matrices.J","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:e1d5552cb2933a5e08b94fe94d35f75ca149d5226ca92a424845ba42bb0eac6a","observation_id":"a102ad7d-41ad-4928-9273-c9921901e4d6","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Basili.On the maximal nilpotent orbit that intersects the centralizer of a matrix.Trans- form","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:a69bc0a461bc67c3989911c0be59a7485fb7e8eda0ef533544a3e9f12f9254f9","observation_id":"c64e81f1-7456-4998-bbc3-e16de2d1c83d","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Basili, A","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:f5c249e3f326dd026158994209fa0c0dd9ec72dbaaceaa646621bbd449ca8a7d","observation_id":"6af6fb26-f78d-420c-8d7e-1d1ca05a4e5d","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Basili, A","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:9033de0e2bcd3eea96d0dc0d0e9bac2dbc93fe291ff10346927717dcef5c200d","observation_id":"6539c75c-5508-4965-aa81-5a06e4ca1c7b","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Bogdani´ c, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:621ac99b76b2820e2db9b36b55931fb34d03cfe9701e7fc510ef6017d730d37c","observation_id":"21bd74c4-e3d5-40ed-8e8b-11a54483c1d4","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:d0e9710759e1bc461aec98641e17550c416f01e371d5766d9a5bbd19ef317130","observation_id":"d15ee2bb-d5dd-4910-8610-ec5feb247273","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:c6ae56b7296754891a2e131b30700d217d4b102f91adf81242c1b126d4167adb","observation_id":"9c9bfe28-3038-4691-a3eb-d3ceeedd39c3","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:b32d6fec091fe873954d29d53517a91bf7d94bfcaa608a65133fa046889a04d4","observation_id":"8557b671-77df-4051-a0d6-5b4ee69e0e0b","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:9a8217cb8f2530905b1ea462e4999f3ac74798f5c956608bab6950e9665f2946","observation_id":"8a7d6cec-fe03-4868-8d22-4a717bbc9bfe","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:37bf6549a0381df2bb47d52de5a219ae7b17151d75d5bde25e70c806482d83f6","observation_id":"818d1f3e-d58a-4e88-89bc-8891b7e7ddb2","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:fbb2dbe34e25a455a66152844b48af0332b54b75334ca41c522688e221349211","observation_id":"666c653b-174f-4317-acf7-bf9f1f34b901","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Frobenius","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:d1f27bd71f1fd00ebb541b16de10facdf0d65b1a8363bdec9f27e413d33bc323","observation_id":"dc4491b4-9ce3-42ef-938b-a26b564b412f","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Frobenius","venue":null,"work_id":null,"year":1910},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:d0e0277255320e6d44c97b6d0338022fe27bbb1ce032d1157ef7e392b573672a","observation_id":"0757e2c9-df3f-4ca2-99c8-4d6bb6e92aba","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Ganyushkin, V","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:67dcde5fac1ec950f3faf766a350eaf8f4f6b0dde82fd0b70b4d4228a4d77abc","observation_id":"9f544b9a-3eea-4a34-becb-23628a2ecf4f","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Gerstenhaber.On dominance and varieties of commuting matrices.Ann","venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:a2f8129093b1e8905a6b30be1e9bc252d33935b19855e9c41d6f4a61d6670e77","observation_id":"010430d0-810b-4595-9c91-5e4dcd3976e8","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Goddard.Commuting varieties and nilpotent orbits.Ph.D","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:cf7ce27266bca8a09ebedf0046bd58e90dcd0d76d8a1a996b3be4b51ea09e2f7","observation_id":"2efca767-afe4-4cb7-b0a9-5eeed1d78ee7","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Gohberg, P","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:04c9297d3aa222ba472d060567450b2a9cc5de8af348df48211f9248f2224387","observation_id":"b53aa37f-8f4c-4d56-8468-447d4a42cf03","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:5bd8e328c81909a4a6904fdd0c31c7765d0b6b824a627ea8b698c6b42d1ebf6e","observation_id":"6e7cf667-3280-4f13-b0ff-22b22b57a9ca","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Iarrobino, L","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:70e936b46480975a50d5f80d4aa28ab4f1995314a977a43457a4c33ee1ac689a","observation_id":"75febb0b-7223-4d31-9108-0ffbc621701f","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Iarrobino, L","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:da82b91ed504bc99e1260cb32adbde974f41eaf1c02c033c0bcdea1053b91ca8","observation_id":"0f365975-d40f-4fb3-be9b-e946463cee7d","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.16910","last_updated":"2024-08-29T21:19:12Z","snapshot_observed_at":"2026-08-12T22:54:51.247565Z","submitted_at":"2024-08-29T21:19:12Z","title":"A Generalized Burge Correspondence and $k$-measure of Partitions","version":1},"cited_work":{"arxiv_id":"2408.16910","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2408.16910","snapshot_observed_at":"2026-07-02T01:26:25.052212Z","title":"Irving.A generalized Burge correspondence andk-measure of partitions.Preprint on arXiv:2408.16910","venue":null,"work_id":"57691d18-1864-4609-b03b-de37b047f402","year":null},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"cited_paper":"/paper/2408.16910","citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:98fbc8858b4a94525e84df2aeb2f6c5c06c3610559f199c3266443fae87b63b6","observation_id":"59ec683d-7706-402c-b0dd-fb56220a40ef","resolution":{"observed_at":"2026-07-02T01:26:25.053710Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2403.18574","last_updated":"2024-04-02T21:30:09Z","snapshot_observed_at":"2026-08-13T00:43:50.599085Z","submitted_at":"2024-03-27T13:55:04Z","title":"A Proof of the Box Conjecture for Commuting Pairs of Matrices","version":2},"cited_work":{"arxiv_id":"2403.18574","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2403.18574","snapshot_observed_at":"2026-07-02T01:26:25.049589Z","title":"Irving, T","venue":null,"work_id":"f9301a9e-2866-441b-8830-3b4eb558b8b1","year":null},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"cited_paper":"/paper/2403.18574","citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:ccae91bbd7f0f983d82ae8a5ff8aaed23eb1e96a797c418e6c598dc2c23d349e","observation_id":"5824c398-d70c-4c6d-b5c5-bb70fea545ba","resolution":{"observed_at":"2026-07-02T01:26:25.050993Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T11:54:35.118566Z","title":"Khatami.The poset of the nilpotent commutator of a nilpotent matrix.Linear Algebra Appl.439(2013), no","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:c163dc371146de229bf5b88682d787e3c43e5629b54006fa66919a06693a853e","observation_id":"506ee8f3-8406-44b9-ab36-9e8b53e3a285","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Khatami.The smallest part of the generic partition of the nilpotent commutator of a nilpotent matrix.J","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:d7a714e495f5ecbd44acd4c609a817e498b2f66c0a608ce191629d166ed3156d","observation_id":"b612c96b-1275-4739-bf66-b1fa5ea386f2","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Khatami.Commuting Jordan types: a survey.Contemp","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:c2933cea673f972d1ded15d3f1ea347c6e822814c394577dc222d88c9e94ad17","observation_id":"ee6f86bd-1b23-48de-a1eb-5cfad445765d","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2605.27692","last_updated":"2026-05-26T21:13:23Z","snapshot_observed_at":"2026-08-08T21:15:02.918296Z","submitted_at":"2026-05-26T21:13:23Z","title":"Jordan types commuting with a hook partition","version":1},"cited_work":{"arxiv_id":"2605.27692","doi":null,"metadata_source":"pith","pith_arxiv_id":"2605.27692","snapshot_observed_at":"2026-07-02T01:26:25.054864Z","title":"Jordan types commuting with a hook partition","venue":"math.AC","work_id":"665806eb-023d-4b4e-bc16-97dfd356e79d","year":2026},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"cited_paper":"/paper/2605.27692","citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:46ee5bed1df1c45dc9bb60de6089bbdffa2662f09aeafc6eab8927b748633e39","observation_id":"a6c436a0-b3d2-4c68-a3bd-ed4b18260f15","resolution":{"observed_at":"2026-07-02T01:26:25.056110Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T11:54:35.118566Z","title":"Konieczny.Semigroups of Transformations Commuting with Injective Nilpotents.Com- munications in Algebra32(2004), No","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:b17a119a068b25544d542d2289dbb2988cfd327f2e26767a79d66167bcf37279","observation_id":"f1fcf1f4-6746-4f7a-8c74-a2dd3d577cde","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Konieczny.The structure of centralizers in the finite symmetric inverse semigroup.Com- munications in Algebra,48(2020), No.12, 5181-5194","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:852caeb6a5c6b137ce812b862a9d282632eba06b8d5277c1fdb111362d1e0861","observation_id":"60c91b00-d7eb-4769-aacc-15edf73a1b92","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:5f19624769eedc0633201b5c7813794d24ca404502ba0a3fe372913b29e96a46","observation_id":"31a261ac-3b2a-44e3-b682-ac01cc2220ea","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Koˇ sir, P","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:faa5df9b3f074b7cf8d0e66026f600d92f323d0438d24df088e2e8924aeddad7","observation_id":"ab24908c-23e0-4103-836c-eb9a39503ed0","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:931cc7a6809bfe6e503f024085359468a8913b2135d88d325391e8792d68f017","observation_id":"cf37fb01-ce2b-433f-9bb9-e693f4483bc1","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Lipscomb.Symmetric Inverse Semigroups.Math","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:0b7888dab4a7ea8ae2fdcb2863c196af1d3cd1fe876fea57bc6661902b6a4fff","observation_id":"13ecaba3-fc98-4971-b094-b4df1f5aa6a9","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":1933},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:8e2dfc02498219da220de68c148e6dabced0cd4fbf6f8902f887e6ffaa7ac1db","observation_id":"02ff748b-ec17-4ea9-a42a-2b85cf6764e2","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":1955},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:0d01fd9826265563f6237e15c826f92e72bf0bd89bb626c28417da1d15bddae3","observation_id":"e73c9ca0-9fca-4934-b1c0-9ba78d43b35a","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:493c0303ffebc1e1e3bb8458e069dbb99ae18b3cd23ae44e469eff9310d5eda6","observation_id":"acaf087a-cc37-418c-8924-46b1f5b9c2d6","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Oblak.The upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrix.Lin","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:80057006ce03b878663aee85c6ce7557e562ed9e098677991f26114ba96a6878","observation_id":"ec886a9b-96bc-4e31-a201-2268882d9970","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Oblak.Jordan forms for mutually annihilating nilpotent pairs.Lin","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:65f759a2d3627e6852f1a5af582b33144984dd5e5bf89ac3228f03576288c97c","observation_id":"86d0ff83-0dfd-4c40-994c-d02e5166ae02","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Oblak.On the nilpotent commutator of a nilpotent matrix.Lin","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:6506d5a085fdccfa57dce79efb64532ac6d020b8a7009b676a7203fec8a5a2c3","observation_id":"3dd4a0cd-669c-45e4-9a14-f33836ecb190","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:957fa70932548c79d62e5d25021ad685ca1e7736ef8dde678af0c4cbbbf7e19a","observation_id":"30254838-e26f-49b4-a980-7f5f715408d8","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Plemelj.Ein Satz ¨Uber vertauschbare Matrizen und seine Anwendung in der Theorie linearer Differentialgleichnungen.Monatshefte Math","venue":null,"work_id":null,"year":1901},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:f0d2f56710103cd70096577d3422142ebc65f002a6effd7b92856568e26c8776","observation_id":"3099f9cb-e9a7-4a7a-9e28-b22fd46b4985","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Premet.Nilpotent commuting varieties of reductive Lie algebras.Invent","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:c6519992743e1d4c5fc0c8f385f92ca782db46dac7ce821bd41055291ed28636","observation_id":"dcdf469b-21ab-4a9f-91d5-2c6a110f45f5","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Schur.Zur Theorie der vertauschbaren Matrizen.J","venue":null,"work_id":null,"year":1905},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:90ca81b1bb3ebbbd88e61652ce31d72ce62373991767dd7c29f98181ae34f713","observation_id":"c2e1486d-7891-4eca-a4fe-1a1fc5276009","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:5438fc9d1605f945e676f673968fbecafcb44edf5f2ca1791435af64af48746e","observation_id":"0158c401-ee70-4254-9db4-e677f489cd50","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:3ad637dbf14a76152f17375d8528af064910637e4a360d6a0b7fa700663626b3","observation_id":"e7a5de55-66d6-4ca2-8403-5ee17b329951","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Solomon.Representations of the rook monoid.J","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:a1b028f91e082b00c7bbe92213f6aa8c1e0470978c4b9b215937c713195444a0","observation_id":"f1d17ace-0c13-4039-a4a9-127fa7b0dc31","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":null,"venue":null,"work_id":null,"year":1968},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:ba105dda4ab2fd0cdd94957ba1b7847496b54fe79d1b41b55c48e3a032c7d587","observation_id":"9bf14c0e-4fc6-476c-b812-329e12affe13","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Sylvester.Sur les quantit´ es formant un groupe de nonions analogues aux quaternions de Hamilton.Acad","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:dd2ac8d8613ededccbea3b3f08bdaeb87e83936df44c35fc0525c2c4af5247ad","observation_id":"0b7f0ab9-f1a7-4b7d-8d2b-a0efb06ed5bd","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Taber.On the Matrical EquationΦΩ = ΩΦ.Proc","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:3c033e6e0ea1a33fca685c9f5438cf7a703b5f6a4ed75e61aeacb7a7dc2597cc","observation_id":"c093417b-0566-405d-8d48-ffc41ed97825","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","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":"2026-06-28T11:54:35.118566Z","title":"Taber.On a Theorem of Sylvester’s Relating to Non-degenerate Matrices.Proc","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-06-28T11:54:35.118566Z"},"links":{"citing_paper":"/paper/2606.02026"},"observation_digest":"sha256:0c870aacaf36174078d172c4405959dca851e12ba6e9ec48bca4ec5a2568144d","observation_id":"54518e2c-5198-46d9-b23e-086cbfcdac7d","resolution":{"observed_at":"2026-06-28T11:54:35.118566Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.02026","last_updated":"2026-06-01T10:15:27Z","latest_version":1,"primary_category":"math.AC","snapshot_observed_at":"2026-08-08T10:36:35.456242Z","submitted_at":"2026-06-01T10:15:27Z","title":"Jordan types for pairs of commuting nilpotent matrices: A survey"},"reference_resolution":{"displayed":56,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":53,"verified_exact":3,"verified_fuzzy":0},"total_outbound_references":56},"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 56 of 56 outbound references and 0 inbound Pith citation observations for arXiv:2606.02026."}