{"as_of":"2026-08-08T09:14:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:13adb079442273da737bc0980759c2cddecf796e2590785bc7548a45a6a08a0d","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T11:32:09.067329Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2506.02307/citation-record","integrity":"/paper/2506.02307/integrity","json":"/paper/2506.02307/citation-record.json","paper":"/paper/2506.02307"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:32:13.316594Z","title":"Cambridge University Press, 2006","venue":null,"work_id":"4f455b61-c0cf-4fea-b368-d04ed3d7d58d","year":2006},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:07.046984Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:c3eb9d59872e4333702897bfb058c8a2aed7b2d75b48a280b13af97b35aab177","observation_id":"b7183d81-3a0d-4792-9296-ab1957879f86","resolution":{"observed_at":"2026-08-07T11:32:13.356327Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.16422","last_updated":"2024-10-21T18:43:47Z","snapshot_observed_at":"2026-07-06T19:37:24.895623Z","submitted_at":"2024-10-21T18:43:47Z","title":"Delooping levels","version":1},"cited_work":{"arxiv_id":"2410.16422","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.16422","snapshot_observed_at":"2026-08-07T11:32:09.591096Z","title":"Delooping levels","venue":"math.RT","work_id":"36f2b544-55d5-429a-a969-08cb3fa2a10e","year":2024},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:07.139328Z"},"links":{"cited_paper":"/paper/2410.16422","citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:e5c222ccf83512a1f9e79006aff77248e854476ec14867350277175f88546657","observation_id":"72ec0af9-ee75-4370-906c-d12e843bbb6e","resolution":{"observed_at":"2026-08-07T11:32:09.686793Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:13.078305Z","title":"Generalised igusa-todorov func- tions and lat-igusa-todorov algebras.Journal of Algebra, 580:63–83, 2021","venue":null,"work_id":"52b7f49d-a4ae-415b-9544-f6098bcd614d","year":2021},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:07.243211Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:c9acdcd77ace7b98aa46981bcab2a332a04faacf28121650a3a0494f3d6915f2","observation_id":"75f5d4bf-d145-47bf-b886-7a9f3881d7ec","resolution":{"observed_at":"2026-08-07T11:32:13.226797Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:12.903521Z","title":"The finitistic dimension of an artin algebra with radical square zero.Proceedings of the American Mathematical Society, 149(12):5001–5012, 2021","venue":null,"work_id":"20013acd-4cc9-47dd-a455-b0ed893e15ac","year":2021},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:07.342450Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:2d83d0c28a9539c76a2519774e2f576e6594102838f0f34408137356ef1336e4","observation_id":"afc1f965-1fdf-45ea-9097-f249068c0b00","resolution":{"observed_at":"2026-08-07T11:32:12.987315Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:12.693946Z","title":"The depth, the delooping level and the finitistic dimension.Advances in Mathematics, 394:108052, 2022","venue":null,"work_id":"1abbb674-e837-4015-a09f-1724c198ae13","year":2022},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:07.473649Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:556061320f336160d3ea766b91f174718f5bb4457f3919fbcfc3e890f5a4c860","observation_id":"dad09c9e-6427-499e-bd29-bbcfb2f32422","resolution":{"observed_at":"2026-08-07T11:32:12.799408Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:12.521254Z","title":"Projective resolutions over artin algebras with zero relations.Illinois Journal of Mathematics, 29(1):180–190, 1985","venue":null,"work_id":"fe751277-1a43-4c55-95d7-7214c56be7f8","year":1985},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:07.567591Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:cd8903f90ce9d750073c11124029539696e8020c3663b9c34f38c9b67ccdb4bf","observation_id":"a78f6e7f-b2da-47d2-9bd0-cbabdb192d72","resolution":{"observed_at":"2026-08-07T11:32:12.616988Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:12.284320Z","title":"Finitistic dimensions of finite dimensional monomial algebras.Journal of algebra, 136(1):37–50, 1991","venue":null,"work_id":"124a9707-cccf-4cfe-b1d1-dcfb709c9757","year":1991},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:07.655588Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:9371c74426811f68a9c7c8a4458c715bbbc8f66d4c46ff2e169c64ce6e6eddde","observation_id":"615c029d-4cfc-4d5d-887a-5372aa1d8b00","resolution":{"observed_at":"2026-08-07T11:32:12.356393Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.00253","last_updated":"2025-08-02T04:10:39Z","snapshot_observed_at":"2026-07-06T18:23:39.931536Z","submitted_at":"2024-06-01T01:18:29Z","title":"Symmetry of Derived Delooping Level","version":2},"cited_work":{"arxiv_id":"2406.00253","doi":null,"metadata_source":"pith","pith_arxiv_id":"2406.00253","snapshot_observed_at":"2026-08-07T11:32:09.382735Z","title":"Symmetry of Derived Delooping Level","venue":"math.RT","work_id":"648309a0-6033-4aaa-92c2-9ba5393e4f48","year":2024},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:07.745490Z"},"links":{"cited_paper":"/paper/2406.00253","citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:11528bd74c4797a573671ced19f496b39c08e7fda93c677d690eb0f12a0591bf","observation_id":"fc16619d-c531-436c-9be3-7611cccd94ab","resolution":{"observed_at":"2026-08-07T11:32:09.489575Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:12.117001Z","title":"Derived delooping levels and finitistic dimension.Advances in Mathe- matics, 464:110152, 2025","venue":null,"work_id":"8feab01b-1d0d-40f9-bc14-2fd49d8309ad","year":2025},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:07.860511Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:ef34208a88e2a6d54fe5a2f0eef79e7acd259a58428c83cc97d72dd3ddafccea","observation_id":"d5de14ff-5dee-468b-ac1b-d333481e49ce","resolution":{"observed_at":"2026-08-07T11:32:12.211247Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:11.934361Z","title":"Algebras of finite global dimension","venue":null,"work_id":"6a4714c9-35ec-46b0-9f3c-fc570d0078b6","year":2011},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:07.923974Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:6e2dd2cdfed2d5802233dd41974bf4b2f71b814eb57fe6139fd8757675ba62ee","observation_id":"049e2134-0f75-4a7e-bdc3-129e0889b84f","resolution":{"observed_at":"2026-08-07T11:32:12.013645Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:11.733122Z","title":"Syzygies and homological dimensions over left serial rings","venue":null,"work_id":"33354e33-fa97-4d92-99c1-912883f6a2fc","year":1992},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:08.022102Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:5a3901adfad97d5e6c586f0795f4193f3e177a10cca56310b6673385eebb708e","observation_id":"d1047306-851e-46b8-9eac-88883a783cb5","resolution":{"observed_at":"2026-08-07T11:32:11.853780Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:11.581906Z","title":"Predicting syzygies over monomial relations algebras.manuscripta math- ematica, 70:157–182, 1991","venue":null,"work_id":"4d8b6678-3c1e-4d07-9bdc-0d1bb0ad9f35","year":1991},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:08.099257Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:12b6ec8c6f6f93c495824d5ba11ecfd410511b211e9bf1871c150720c7c11e5f","observation_id":"4dd1c8cb-3314-4d30-8fc6-a1f4be065a54","resolution":{"observed_at":"2026-08-07T11:32:11.655167Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:11.385913Z","title":"Homological domino effects and the first finitistic dimension conjecture","venue":null,"work_id":"53783a2c-0e20-4351-9ff1-03942a2405c8","year":1992},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:08.175537Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:4305550490b351c1cd0d5fa40c9ac300f604cd4b981d94d1d04a8b3428e168e6","observation_id":"1879c20e-17de-450b-b99b-7fcc66a10f7e","resolution":{"observed_at":"2026-08-07T11:32:11.466837Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:11.130375Z","title":"On the finitistic global dimension conjecture for artin algebras","venue":null,"work_id":"0b17d957-b275-4706-8aff-42e091d8b3d7","year":2005},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:08.253861Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:31200cca9841d981f461ebeb094c1acfbe45f01a5acffd2086ee9a2999f01eae","observation_id":"c8b774c9-55dd-442d-9d5f-d66e59a0f386","resolution":{"observed_at":"2026-08-07T11:32:11.269639Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:10.947524Z","title":"Syzygy pairs in a monomial algebra.Proceedings of the American Mathematical Society, pages 601–604, 1990","venue":null,"work_id":"76294e51-71f8-4384-9f05-e43200571ba5","year":1990},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:08.336902Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:3cba8dac977762fac363a4d77386e3b8464cfd7c6fc22527365d63e7c9ba7412","observation_id":"061cb8c6-0db0-4ff1-b0d4-00a5bd35afe2","resolution":{"observed_at":"2026-08-07T11:32:11.053188Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:10.810798Z","title":"Homological dimension and representation type of algebras under base field extension.manuscripta mathematica, 39(1):1–13, 1982","venue":null,"work_id":"453cc335-a8e9-491c-8633-e5d8e5e74fa0","year":1982},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:08.454957Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:7633bfdf0eb5817b3669cc12fabeeddd86a079f88d384f5ab8df010740bb1580","observation_id":"8217f684-4352-4ac6-a6d1-ef4000d7dc24","resolution":{"observed_at":"2026-08-07T11:32:10.876814Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2305.09109","last_updated":"2023-05-16T02:23:03Z","snapshot_observed_at":"2026-08-01T22:37:17.496556Z","submitted_at":"2023-05-16T02:23:03Z","title":"A finite dimensional algebra with infinite delooping level","version":1},"cited_work":{"arxiv_id":"2305.09109","doi":null,"metadata_source":"pith","pith_arxiv_id":"2305.09109","snapshot_observed_at":"2026-08-07T11:32:09.190141Z","title":"A finite dimensional algebra with infinite delooping level","venue":"math.RT","work_id":"134bb715-2550-4350-900c-b505d79abe47","year":2023},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:08.552719Z"},"links":{"cited_paper":"/paper/2305.09109","citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:d0e7c88fb6ca806464ccd068030a9a56b73341e5610b48694e454471cc9b3332","observation_id":"ca217d32-7768-40cf-b05f-03e5fb610b1a","resolution":{"observed_at":"2026-08-07T11:32:09.260836Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:10.625731Z","title":"On the symmetry of the finitistic dimension.Comptes Rendus","venue":null,"work_id":"24e9a15d-5299-4319-a39e-cadd6bda6bf3","year":2023},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:08.627832Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:0fdfef70b0cb59fde920975a4bf70539437fba8a92ea75e73badd27fa77532db","observation_id":"a4d5e10f-4e7b-4ab0-a889-d1d498709136","resolution":{"observed_at":"2026-08-07T11:32:10.723980Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:10.442691Z","title":"The finitistic dimension of a nakayama algebra.Journal of Algebra, 576:95–145, 2021","venue":null,"work_id":"0028f0d9-cb58-419e-a4c9-85e5defe4621","year":2021},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:08.703344Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:07e426bbb4d1c8605e7408d7c22ef57d2e2f50d53ce5e326a53487bea57515de","observation_id":"c7845bc8-7c10-46cb-8ddb-4db8ef1b75ba","resolution":{"observed_at":"2026-08-07T11:32:10.522922Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:10.289560Z","title":"Springer, 2014","venue":null,"work_id":"f3c3751f-5afd-4044-a634-df671ab3d88f","year":2014},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:08.783287Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:afaabcc8a905df732116543cc11ba001a2392d83d9dc1e40aa5a9e94d2e309f3","observation_id":"9dd829f9-4a30-44c6-bd01-8110c3a30c61","resolution":{"observed_at":"2026-08-07T11:32:10.370869Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:10.153083Z","title":"Delooping level of nakayama algebras.Archiv der Mathematik, 117(2):141–146, 2021","venue":null,"work_id":"b7da3a2b-926c-4e74-90b7-c602f445c4d8","year":2021},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:08.858089Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:9aa70340672b11c31d1936509fa1ef19758b4a14174fc50547655bad5ea2f9b9","observation_id":"99188cf5-7b9e-418e-8959-d7744f85a5d4","resolution":{"observed_at":"2026-08-07T11:32:10.249990Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:10.012525Z","title":"Finitistic dimension of monomial algebras.Journal of Algebra, 264(2):397–407, 2003","venue":null,"work_id":"e34882c0-7a69-437d-9a17-ff490642862a","year":2003},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:08.962714Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:574f9e2d35de20436949a7163806504f1b3ae9f77ca0a922347d4f217f86ffc1","observation_id":"9b6a7488-9a1d-4ee1-985e-e5cf06aa22e2","resolution":{"observed_at":"2026-08-07T11:32:10.072296Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T11:32:09.844915Z","title":"Finitistic dimension and igusa–todorov algebras.Advances in Mathematics, 222(6):2215– 2226, 2009","venue":null,"work_id":"c84cfbff-f161-4d03-9cab-a132174390e8","year":2009},"citing_paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T11:32:09.067329Z"},"links":{"citing_paper":"/paper/2506.02307"},"observation_digest":"sha256:c471e566e86445761aefaee44b746ff4fa4fc966be48414bcdf8b1f663cd9f6e","observation_id":"110f127a-1c51-451f-af7d-5c163a78ead6","resolution":{"observed_at":"2026-08-07T11:32:09.922744Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.02307","last_updated":"2025-06-02T22:54:50Z","latest_version":1,"primary_category":"math.RT","snapshot_observed_at":"2026-08-07T11:24:17.824866Z","submitted_at":"2025-06-02T22:54:50Z","title":"Homological Invariants of Left and Right Serial Path Algebras"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":3,"verified_fuzzy":20},"total_outbound_references":23},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2506.02307."}