{"as_of":"2026-08-10T03:53:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fcbef0ddb2b7b26e8f81ce753ea41f404657a8c43fe51f5059c7f7f3cc971390","coverage":[{"denominator":18,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":18,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T12:35:37.276811Z","state":"measured"},{"denominator":20,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":20,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T10:36:03.958808Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-06T22:57:16.707264Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.24752","snapshot_observed_at":"2026-08-07T10:36:03.958808Z","title":"On N oether's degree bound for finite group schemes","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.05650","last_updated":"2026-07-07T17:35:30Z","snapshot_observed_at":"2026-08-07T10:11:20.865843Z","submitted_at":"2025-06-06T00:41:56Z","title":"Generic orbits, normal bases, and generation degree for fields of rational invariants","version":4},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-07T10:36:03.958808Z"},"links":{"cited_paper":"/paper/2505.24752","citing_paper":"/paper/2506.05650"},"observation_digest":"sha256:136b745a2479d2fe88bdde041152763e14072615e90f89bfa68e6d385cea7f2c","observation_id":"5ec11228-8889-44f2-bd13-f6f67372a499","resolution":{"observed_at":"2026-08-07T10:36:03.958808Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"cited_work":{"arxiv_id":"2505.24752","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.24752","snapshot_observed_at":"2026-08-06T22:57:16.707264Z","title":"On Noether's Degree Bound for Finite Group Schemes","venue":"math.AC","work_id":"2e90178c-4f54-4fc8-98ad-a01ab3337c00","year":2025},"citing_paper":{"arxiv_id":"2506.21210","last_updated":"2025-06-26T13:03:13Z","snapshot_observed_at":"2026-08-06T22:28:00.011480Z","submitted_at":"2025-06-26T13:03:13Z","title":"An arithmetic analog of Klein's classification of finite subgroups of $\\mathrm{SL}_2(\\mathbb{C})$","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T22:57:16.347902Z"},"links":{"cited_paper":"/paper/2505.24752","citing_paper":"/paper/2506.21210"},"observation_digest":"sha256:4489ef27d0bb7801f1597998a8612f6c0ee8139d0e2382a8c6c6124681c3edf6","observation_id":"3d6d94d8-4fb4-47f0-be18-dc8d9fbb8f9a","resolution":{"observed_at":"2026-08-06T22:57:16.804667Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.24752/citation-record","integrity":"/paper/2505.24752/integrity","json":"/paper/2505.24752/citation-record.json","paper":"/paper/2505.24752"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:35:35.016288Z","title":"Abramovich, M","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:35.016288Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:e515797084ad16aa3ee86e7cda80b546b75681daf48d6e7fff7644c11c4de89b","observation_id":"e225557d-f669-45fa-948c-4b75a1d15cd9","resolution":{"observed_at":"2026-08-07T12:35:35.016288Z","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":"2026-08-07T12:35:39.255042Z","title":"Brion, Finite Group Schemes, Groups St Andrews 2022 in Newcastle, London Mathematical Society Lecture Note Series 496 (2025), 1-53","venue":null,"work_id":"cced4620-3d2a-480c-8e0e-9b731ce1fb0b","year":2025},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:35.169904Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:60e371f69c17872cbe0a17fb03586a472b066ba906164182929e178da14357f7","observation_id":"285db62b-b6db-44a4-80a2-ff1ca37a1cea","resolution":{"observed_at":"2026-08-07T12:35:39.320210Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:35:35.343972Z","title":"Chin, Crossed products of semisimple cocommutative Hopf algebras, Proc","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:35.343972Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:5c0eb19eb32b87229a761952f0bd994984ab131d6f376a5ccb266bae9dde9047","observation_id":"e7b02d0b-c022-4d6b-b6b1-7678d10e27ec","resolution":{"observed_at":"2026-08-07T12:35:35.343972Z","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":"2026-08-07T12:35:39.091767Z","title":"Derksen, G","venue":null,"work_id":"bf23b4ee-592a-4b19-918c-1d3e8fcbb581","year":2015},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:35.502417Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:c486e876db1297f49151de801fb527b011a28eec743495c2b47e312e2d8c9ea7","observation_id":"be0b1f82-e2dd-422f-a86d-35fe87892870","resolution":{"observed_at":"2026-08-07T12:35:39.164579Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:35:38.946352Z","title":"Fleischmann, The Noether bound in invariant theory of finite groups, Adv","venue":null,"work_id":"9d81024d-eb91-4c92-814c-63b08e2be33d","year":2000},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:35.747539Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:0d2eed2fec4f3f68c08ee16fa33b74250b6f407829e389d622b98a263768974b","observation_id":"df60b6e1-ec71-44a3-8edf-01cfd17863c0","resolution":{"observed_at":"2026-08-07T12:35:39.013100Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:35:38.764397Z","title":"Fogarty, On Noether's bound for polynomial invariants of a finite group, Electron","venue":null,"work_id":"653c9985-e70f-4006-a1a1-22ffaf46c88f","year":2001},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:35.926684Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:15a00287ba49400a292fc8f965ff1732368fbfb8d5679c9e02a3d63efb4c0e76","observation_id":"5db969ef-518e-4bc6-8a88-470d07d4ee04","resolution":{"observed_at":"2026-08-07T12:35:38.841941Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2008.09862","last_updated":"2022-09-15T13:18:32Z","snapshot_observed_at":"2026-08-08T16:16:38.608704Z","submitted_at":"2020-08-22T16:06:22Z","title":"Notes on the combinatorial fundamentals of algebra","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2008.09862","snapshot_observed_at":"2026-08-07T12:35:36.116366Z","title":"Grinberg, Notes on the combinatorial fundamentals of algebra, arXiv:2008.09862v3 (2022)","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:36.116366Z"},"links":{"cited_paper":"/paper/2008.09862","citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:e932333e82dd62c3845b66b3bea366570d9f4621c88dafa6040939e475fec1d1","observation_id":"372b5559-3ca2-4cb3-a05b-0caa9142d1c4","resolution":{"observed_at":"2026-08-07T12:35:36.116366Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:35:36.310225Z","title":"Hashimoto, Classification of the linearly reductive finite subgroup schemes of SL_2 , Acta Math","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:36.310225Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:c053ce959be6a67861562d35027ba1a9d7a8d4150dc115b97d9c3720227fcfa3","observation_id":"f149d920-6e5b-418a-8fec-4ca5b7a30ad9","resolution":{"observed_at":"2026-08-07T12:35:36.310225Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:35:36.375395Z","title":"Liedtke, G","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:36.375395Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:1614ced0c8c3a51e75374813219ae34dc7bf8491a195132c9df73f01eb1a4b2f","observation_id":"3b54cf64-61d4-45cf-99d6-2172eeac8116","resolution":{"observed_at":"2026-08-07T12:35:36.375395Z","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":"2026-08-07T12:35:38.572192Z","title":"Mumford, F","venue":null,"work_id":"1346a533-6330-4d35-928f-e06ab5f687e8","year":1968},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:36.485425Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:748171d3096e5bfbef2519228c6b0c0e5cf03cea09269cc6c587a87d1d1259d9","observation_id":"fede6282-03ed-4c26-97c2-bbee51a74e3b","resolution":{"observed_at":"2026-08-07T12:35:38.674732Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:35:38.382694Z","title":"Uber die Invarianten der linearen Substitutionsgruppen, Sitzungber. K\\","venue":null,"work_id":"07380750-89dc-4c52-86e4-24f27f265f88","year":null},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:36.597580Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:ef4b111f01a7c0d100041aaf147893288ebadca488c3e37b9b11418d81985c71","observation_id":"fbd44150-97ef-487b-8f6b-db3be7aae0d7","resolution":{"observed_at":"2026-08-07T12:35:38.435605Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:35:36.670518Z","title":"Nagata, Complete reducibility of rational representations of a matric group, J","venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:36.670518Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:21cc942148eaa53ee4c229c4a20cdefab2bbd4b95bf3a5563799761f734bd80f","observation_id":"ffeefed9-42c6-4742-a99f-283b964f3343","resolution":{"observed_at":"2026-08-07T12:35:36.670518Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:35:36.823822Z","title":"Noether, Der Endlichkeitssatz der Invarianten endlicher Gruppen, Math","venue":null,"work_id":null,"year":1916},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:36.823822Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:988c597855028860cc26a86c42d27fd6bb9f68d8f1d1e17f1e63dd8ea28b90a6","observation_id":"25391b20-2c31-4723-9a57-66a3af1602f5","resolution":{"observed_at":"2026-08-07T12:35:36.823822Z","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":"2026-08-07T12:35:38.176432Z","title":"Oort, Finite group schemes, local moduli for abelian varieties, and lifting problems, Compositio Math","venue":null,"work_id":"58bd5f93-a6ba-42a3-96d3-46878d0d647f","year":1971},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:36.913027Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:3fd2755cfcdd62046acf3a55e62566319aeab33f0922c89cd7c25df42baa2703","observation_id":"3608366e-35e1-4f95-9c03-02007dcdc741","resolution":{"observed_at":"2026-08-07T12:35:38.271632Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:35:37.979277Z","title":"Richman, On vector invariants over finite fields, Adv","venue":null,"work_id":"ee33f91b-1909-4122-8dbb-aad7d8527f0c","year":1990},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:37.010654Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:41d91409afa880f8e2fd5da1cf30f7162098256a52f8b4d52e8e58c966f05790","observation_id":"01d2735d-d74d-4a7c-9245-845e495275ea","resolution":{"observed_at":"2026-08-07T12:35:38.087686Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:35:37.759874Z","title":"Richman, Invariants of finite groups over fields of characteristic p ,","venue":null,"work_id":"1656bbf0-0a29-436c-a81c-a92a727be214","year":null},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:37.111834Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:749dce74bd923b5b71b39499fb0bdf942b04bf3b287aa033876cfc0e9bdb55ab","observation_id":"d4a0b970-c931-4706-b38e-ebefde9dd7e4","resolution":{"observed_at":"2026-08-07T12:35:37.872304Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:35:37.602019Z","title":"Schmid, Finite groups and invariant theory, Topics in invariant theory (Paris, 1989/1990), 35--66, Lecture Notes in Math.1478, Springer-Verlag (1991)","venue":null,"work_id":"eca3096e-53af-4ff4-895e-67b18a851282","year":1991},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:37.206727Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:fde674fd1545116f859e0fabb6622892daeeaf0965cd44430bca8e7dbecfeacd","observation_id":"e18f08e0-db25-4e87-9343-6462a2b296a0","resolution":{"observed_at":"2026-08-07T12:35:37.669124Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:35:37.450330Z","title":"Waterhouse, Introduction to Affine Group Schemes, Springer (1979)","venue":null,"work_id":"3bf23821-d560-4979-adc7-b30f92a50789","year":1979},"citing_paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-07T12:35:37.276811Z"},"links":{"citing_paper":"/paper/2505.24752"},"observation_digest":"sha256:8a1e155e5d82a788439289dd1115b9d77d13947003360a4f448dfb6f4db0710b","observation_id":"50f627a0-0350-4c33-bf38-bd45785aaf02","resolution":{"observed_at":"2026-08-07T12:35:37.502768Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.24752","last_updated":"2025-05-30T16:13:20Z","latest_version":1,"primary_category":"math.AC","snapshot_observed_at":"2026-08-07T12:11:49.215111Z","submitted_at":"2025-05-30T16:13:20Z","title":"On Noether's Degree Bound for Finite Group Schemes"},"reference_resolution":{"displayed":18,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":0,"verified_fuzzy":11},"total_outbound_references":18},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 2 inbound Pith citation observations for arXiv:2505.24752."}