{"as_of":"2026-08-12T21:36:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:66b6db0f55b9cabf894fb91298fcc6c6d92f1d95f6e27ae880278c7bffa7a507","coverage":[{"denominator":34,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":34,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T14:52:42.818549Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2509.22625/citation-record","integrity":"/paper/2509.22625/integrity","json":"/paper/2509.22625/citation-record.json","paper":"/paper/2509.22625"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:39.066750Z","title":"On the structure of triangulated categories with finitely many indecomposables","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:39.066750Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:1a8f88a4b37681a7788fbb440c2d5babe7a26f88e1dbaefddc5b58726d37d610","observation_id":"ad07de03-d131-41e5-9ff7-05651cf2077a","resolution":{"observed_at":"2026-08-04T14:52:39.066750Z","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":"2026-08-04T14:52:42.504009Z","title":"Skew Calabi-Yau triangu- lated categories and Frobenius Ext-algebras","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:42.504009Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:4ed69263c5b530db6da76d080c73f2f39538e57a062a720321cc3e8855dfc222","observation_id":"e93a8a30-fcea-4d5c-9d63-47d06dbb1b3d","resolution":{"observed_at":"2026-08-04T14:52:42.504009Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0612139","last_updated":"2007-01-09T21:08:48Z","snapshot_observed_at":"2026-07-07T06:02:41.538848Z","submitted_at":"2006-12-06T05:07:21Z","title":"Calabi-Yau algebras","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0612139","snapshot_observed_at":"2026-08-04T14:52:40.267376Z","title":"Calabi–Yau algebras","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:40.267376Z"},"links":{"cited_paper":"/paper/math/0612139","citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:977a421f1860c001fa3198cc1f31c535946b5502e92878f5e516186b85dd2ece","observation_id":"906dcc21-0999-4bf0-8e17-5d2d8cc318ba","resolution":{"observed_at":"2026-08-04T14:52:40.267376Z","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":"2026-08-04T14:52:40.442615Z","title":"Cluster tilting objects in generalized higher cluster cate- gories","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:40.442615Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:644d142e4df2b40bc151c6df925733564697b298e282c669a5f5b4c1ce771749","observation_id":"f4bbd7cb-5098-440c-99e7-036f6cc79355","resolution":{"observed_at":"2026-08-04T14:52:40.442615Z","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":"2026-08-04T14:52:40.738513Z","title":"Higher Nakayama algebras III: Spherical objects in higher Auslander–Reiten theory and triangulations of the cyclic apeirotope","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:40.738513Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:167139fae73566b035321d5a8f7f1f53c5ca71823dc380b05c62083582c90e8e","observation_id":"0e8d9aee-ee4d-487b-b776-fefbc1f2c696","resolution":{"observed_at":"2026-08-04T14:52:40.738513Z","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":"2026-08-04T14:52:40.862576Z","title":"Springer, Cham, 2024, pp","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:40.862576Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:a09c5e1c72f7255a3abd5adae4a7bbf1bef9b55b37eb3de3bf65943d4a33ec65","observation_id":"e2f85626-8812-4b38-8a9b-af8ffe0bd1bf","resolution":{"observed_at":"2026-08-04T14:52:40.862576Z","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":"2026-08-04T14:52:39.281094Z","title":"Preprojective modules over Artin algebras","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:39.281094Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:020bd8f761f29f26c2d26dd9722e6ed4b7f8997428361efa93fd16e350167ccc","observation_id":"837584cf-5fe7-4c9c-93d5-45cbe94108d1","resolution":{"observed_at":"2026-08-04T14:52:39.281094Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.00093","last_updated":"2025-02-26T10:28:45Z","snapshot_observed_at":"2026-08-02T10:04:21.301234Z","submitted_at":"2024-04-30T18:00:01Z","title":"Dg enhanced orbit categories and applications","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.00093","snapshot_observed_at":"2026-08-04T14:52:40.153465Z","title":"Notes on Kontsevich-Soibelman’s theorem about cyclicA ∞-algebras","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:40.153465Z"},"links":{"cited_paper":"/paper/2405.00093","citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:13213c1acc17157bf9566758cbcd76141029d76cea0d5812f74147668470ebf1","observation_id":"eeae4e1b-ff3e-4724-8e70-7bd06ecf55fb","resolution":{"observed_at":"2026-08-04T14:52:40.153465Z","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":"2026-08-04T14:52:42.818549Z","title":"Calabi-Yau de- formations and negative cyclic homology","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:42.818549Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:bcf5606b14e5e95cc43083cd542fd671810dfe5b6fb9718a9aca310e65922589","observation_id":"d38b3f4b-746c-43ee-aca9-4cdfa20fff6c","resolution":{"observed_at":"2026-08-04T14:52:42.818549Z","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":"2026-08-04T14:52:40.734211Z","title":"Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:40.734211Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:73a69223d86a9d20f2d3c616b4014ed717a4043ab3b675a6c98427c2816fce33","observation_id":"c2abd616-8509-4e26-881d-af20bc9bef3f","resolution":{"observed_at":"2026-08-04T14:52:40.734211Z","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":"2026-08-04T14:52:42.249706Z","title":"Homotopy algebras are homotopy algebras","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":131,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:42.249706Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:0ee7b8b58105c8ec6a8ec0ff3cb2400ca07b85d84ae0950f7e16504a62d60146","observation_id":"ff2821fc-4625-4ff2-b0b6-7d0280a879cb","resolution":{"observed_at":"2026-08-04T14:52:42.249706Z","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":"2026-08-04T14:52:40.668183Z","title":"Quotients of triangulated categories and equivalences of Buchweitz, Orlov, and Amiot–Guo–Keller","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":168,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:40.668183Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:62bf31e39070f34ef2a0bca966f63c0194af9460d55381a4b9756988abcb7015","observation_id":"a83d3540-098b-4f24-bfb3-b6a40f9cb1a5","resolution":{"observed_at":"2026-08-04T14:52:40.668183Z","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":"2026-08-04T14:52:42.614779Z","title":"TheA ∞ deformation theory of a point and the derived categories of local Calabi-Yaus","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":172,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:42.614779Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:79a28d33272fbfe596c78c72473b2a99fb1097aefdaed454941abc8241159626","observation_id":"98b4f8f4-3516-43ef-bc6f-219f11a0e5f3","resolution":{"observed_at":"2026-08-04T14:52:42.614779Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0807.1960","last_updated":"2010-03-19T20:38:40Z","snapshot_observed_at":"2026-08-04T20:01:47.295899Z","submitted_at":"2008-07-12T09:44:14Z","title":"Cluster algebras, quiver representations and triangulated categories","version":11},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0807.1960","snapshot_observed_at":"2026-08-04T14:52:41.065375Z","title":"Calabi-Yau triangulated categories","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":190,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:41.065375Z"},"links":{"cited_paper":"/paper/0807.1960","citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:3b84b61dbfe1b4feb7dcebeed009c3766b61f7321e6cd0ff8664dbb45a460a6e","observation_id":"e79c36b0-8511-4368-a742-2877d5714871","resolution":{"observed_at":"2026-08-04T14:52:41.065375Z","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":"2026-08-04T14:52:41.928592Z","title":"The diagonal of the Stasheff polytope","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":265,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:41.928592Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:2c21d3ef987bd3e91148795068a35c6147f320e2612131a9569138afe0724fa6","observation_id":"ddc65359-45d0-41fc-a7a5-7cba335ed4d8","resolution":{"observed_at":"2026-08-04T14:52:41.928592Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.15915","last_updated":"2026-07-28T05:31:56Z","snapshot_observed_at":"2026-08-05T20:21:10.325554Z","submitted_at":"2024-06-22T18:38:39Z","title":"Rabinowitz Fukaya categories as cluster categories","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.15915","snapshot_observed_at":"2026-08-04T14:52:42.044910Z","title":"Homological mirror symmetry for Rabinowitz Fukaya categories of Milnor fibers of Brieskorn-Pham singularities","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":287,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:42.044910Z"},"links":{"cited_paper":"/paper/2406.15915","citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:d18a916a0445fb964fa34c2a56f22336c15699975e44e5e26526cb20ca7254cc","observation_id":"95af481d-f5ad-4850-bde8-34c29e5b0d08","resolution":{"observed_at":"2026-08-04T14:52:42.044910Z","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":"2026-08-04T14:52:39.516692Z","title":"Representable functors, Serre functors, and reconstructions","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":304,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:39.516692Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:cb75d3173a1bc497fdf336a0f144778a676f2d9b19cf38a61182e8a66de3071f","observation_id":"7e2d1698-7a4c-420b-8ea5-fd33d0b5fcbf","resolution":{"observed_at":"2026-08-04T14:52:39.516692Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2302.03681","last_updated":"2024-04-28T13:03:04Z","snapshot_observed_at":"2026-07-06T14:49:26.865897Z","submitted_at":"2023-02-07T18:56:49Z","title":"Calabi-Yau structures on Drinfeld quotients and Amiot's conjecture","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2302.03681","snapshot_observed_at":"2026-08-04T14:52:41.229240Z","title":"Deformed Calabi-Yau completions","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":375,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:41.229240Z"},"links":{"cited_paper":"/paper/2302.03681","citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:cdd00bf6a7b8bf31b8dd142f2ec44ccbd6dd0ebdb59633ad87050e46e6d2db8c","observation_id":"761d9406-6dd9-4912-b817-342ab3fe8b5b","resolution":{"observed_at":"2026-08-04T14:52:41.229240Z","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":"2026-08-04T14:52:39.167172Z","title":"Cluster categories for algebras of global dimension 2 and quivers with potential","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":474,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:39.167172Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:157ebee32b12e99385db241e8c9a30bebd930b7ae5db6ce51ac93f89867321ed","observation_id":"37918cfe-1b28-4be3-a03e-63f34b7159aa","resolution":{"observed_at":"2026-08-04T14:52:39.167172Z","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":"2026-08-04T14:52:39.398249Z","title":"Relative Calabi-Yau structures","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":614,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:39.398249Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:9619949ea6c84ccf6e11646130a4779f75246e3d0fce3261360c53d49a873125","observation_id":"1f6d940b-d190-4ddc-b885-8303d121e985","resolution":{"observed_at":"2026-08-04T14:52:39.398249Z","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":"2026-08-04T14:52:39.867468Z","title":"On the exceptional fibres of Kleinian singulari- ties","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":618,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:39.867468Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:55308b8710845f07f6cdc6a9b21dbce0bfe10b5ba3c826fd6e349e453aa6a643","observation_id":"c1ab7b88-e1b8-441b-9aca-4e975c6eea4f","resolution":{"observed_at":"2026-08-04T14:52:39.867468Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0811.2435","last_updated":"2008-11-16T21:00:44Z","snapshot_observed_at":"2026-07-06T01:50:53.296268Z","submitted_at":"2008-11-16T21:00:44Z","title":"Stability structures, motivic Donaldson-Thomas invariants and cluster transformations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0811.2435","snapshot_observed_at":"2026-08-04T14:52:41.672169Z","title":"Stability structures, motivic Donaldson- Thomas invariants and cluster transformations","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":757,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:41.672169Z"},"links":{"cited_paper":"/paper/0811.2435","citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:648d7f08a0f3811db49a1b6a92408304c7d631502a2c9f965feece14bde88727","observation_id":"29ca5de8-d0a1-4437-9c39-e5539616c2b7","resolution":{"observed_at":"2026-08-04T14:52:41.672169Z","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":"2026-08-04T14:52:39.629581Z","title":"Realizability of modules over Tate cohomology","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":1337,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:39.629581Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:3fdf88ba6968af33c6920965f7516728e3ce24117e06bbd539e130a27dd5ac1f","observation_id":"72b73627-687b-4864-a606-c35f1f418aa2","resolution":{"observed_at":"2026-08-04T14:52:39.629581Z","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":"2026-08-04T14:52:40.590239Z","title":"n-representation infinite algebras","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":1920,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:40.590239Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:b63616d7e73ff52e4daec728e0230c3e353fa14f108f2a3600d836a06d27f373","observation_id":"16a3fdc7-79cc-49d3-b295-403018af43f9","resolution":{"observed_at":"2026-08-04T14:52:40.590239Z","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":"2026-08-04T14:52:41.528574Z","title":"Cluster-tilted algebras are Gorenstein and stably Calabi-Yau","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":1998,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:41.528574Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:e5089c4614a7c1cd3ce9166a3b4bc94e95db95efd6dd10cdff92eca234273f7c","observation_id":"c2a4caf4-8c0f-4849-b6c7-43c02011511b","resolution":{"observed_at":"2026-08-04T14:52:41.528574Z","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":"2026-08-04T14:52:42.137650Z","title":"Homotopy unitalA ∞-algebras","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":2008,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:42.137650Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:364099eb025654cbd0f3d5e2e91c9122655a9590100300c2f7ede70995b4f3ee","observation_id":"c7466f12-3f52-4c31-9cae-9c564a5366e6","resolution":{"observed_at":"2026-08-04T14:52:42.137650Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2012.11927","last_updated":"2024-04-05T12:10:42Z","snapshot_observed_at":"2026-08-10T02:48:25.677827Z","submitted_at":"2020-12-22T11:00:07Z","title":"Periodic trivial extension algebras and fractionally Calabi-Yau algebras","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2012.11927","snapshot_observed_at":"2026-08-04T14:52:40.036438Z","title":"Poisson cohomol- ogy, Koszul duality, and Batalin-Vilkovisky algebras","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":2020,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:40.036438Z"},"links":{"cited_paper":"/paper/2012.11927","citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:d86a59ee728ac846b97e0532da31ed93769828df3ae87ecf900f1f711ada73bf","observation_id":"b3357bee-0fd6-4f50-9729-e6103b6670e6","resolution":{"observed_at":"2026-08-04T14:52:40.036438Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2111.10771","last_updated":"2023-08-31T13:58:44Z","snapshot_observed_at":"2026-08-05T13:29:45.681164Z","submitted_at":"2021-11-21T08:57:50Z","title":"An introduction to relative Calabi-Yau structures","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2111.10771","snapshot_observed_at":"2026-08-04T14:52:41.814514Z","title":"Dualit´ e de Van den Bergh et structure de Batalin-Vilkoviski ˘i sur les alg` ebres de Calabi-Yau","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:41.814514Z"},"links":{"cited_paper":"/paper/2111.10771","citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:4e84a37709c12515494ea7acc0c3b2b0eaa2ea4df8f985a7be7d82eb2a488a14","observation_id":"6ac8ccb3-c3a9-4bed-9fa5-515259c4d67c","resolution":{"observed_at":"2026-08-04T14:52:41.814514Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2208.14413","last_updated":"2026-05-12T10:02:12Z","snapshot_observed_at":"2026-08-06T20:04:45.021934Z","submitted_at":"2022-08-30T17:27:09Z","title":"The Derived Auslander-Iyama Correspondence","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2208.14413","snapshot_observed_at":"2026-08-04T14:52:40.768215Z","title":"The Donovan–Wemyss Conjecture via the Derived Auslander–Iyama Correspondence","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:40.768215Z"},"links":{"cited_paper":"/paper/2208.14413","citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:82a93fc8dcdd209171b25d87a846543e6f32aecc14e97e00933bea379f5f2e80","observation_id":"1fed08f5-8b85-49ff-882b-d0be2f8bda90","resolution":{"observed_at":"2026-08-04T14:52:40.768215Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.06538","last_updated":"2024-09-02T09:54:03Z","snapshot_observed_at":"2026-07-06T16:46:02.857589Z","submitted_at":"2023-11-11T11:22:02Z","title":"On Amiot's conjecture","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.06538","snapshot_observed_at":"2026-08-04T14:52:41.397415Z","title":"Trivial extension DG-algebras, unitally positiveA ∞-algebras, and applications","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:41.397415Z"},"links":{"cited_paper":"/paper/2311.06538","citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:ad80e75269fee4360153d040fcb17e74fa7dbc26f20748327d20a3494fde34d1","observation_id":"8713f405-0a2d-43b8-b1a1-81901317f162","resolution":{"observed_at":"2026-08-04T14:52:41.397415Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.17568","last_updated":"2025-07-23T14:58:33Z","snapshot_observed_at":"2026-08-09T10:16:01.706481Z","submitted_at":"2025-07-23T14:58:33Z","title":"Obstruction theory for $A$-infinity bimodules","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.17568","snapshot_observed_at":"2026-08-04T14:52:40.947848Z","title":"The algebraic structure in the homology of an A(∞)-algebra","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:40.947848Z"},"links":{"cited_paper":"/paper/2507.17568","citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:60a0bbba5507dd271c88a7e515ee0caae3210c4d90bcf5dd7dc8b8917dfe5a11","observation_id":"6411e56f-6633-475a-ac5c-f329b5636c8a","resolution":{"observed_at":"2026-08-04T14:52:40.947848Z","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":"2026-08-04T14:52:42.720701Z","title":"Homological mirror symmetry for the quartic surface","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":3268,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:42.720701Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:59ca18941e4fc75e09bec5f71512c5d61017faa609116eed11fa190429def5b8","observation_id":"7d292d8e-1009-4fbe-bc56-3c4240a0e306","resolution":{"observed_at":"2026-08-04T14:52:42.720701Z","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":"2026-08-04T14:52:42.375383Z","title":"EnhancedA ∞-obstruction theory","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":3281,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:42.375383Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:3d6a9f0e2e4eda7b589f8643fc0106212fb6388b2acc367296efa19891c4a6ab","observation_id":"d085c949-ba15-4f2b-b381-77da8b8f6c2a","resolution":{"observed_at":"2026-08-04T14:52:42.375383Z","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":"2026-08-04T14:52:39.746752Z","title":"On the derived category of an algebra over an operad","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures","version":4},"reference_index":3668,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:39.746752Z"},"links":{"citing_paper":"/paper/2509.22625"},"observation_digest":"sha256:2d119ab2ddca766a34b76a1b04059109f9816d83d63500a8cfbecc6ebcfd418e","observation_id":"9213298a-cfca-438b-ba34-7d587b339630","resolution":{"observed_at":"2026-08-04T14:52:39.746752Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2509.22625","last_updated":"2026-07-14T07:33:26Z","latest_version":4,"primary_category":"math.RT","snapshot_observed_at":"2026-08-09T04:32:12.313439Z","submitted_at":"2025-09-26T17:51:20Z","title":"The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures"},"reference_resolution":{"displayed":34,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":34,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":34},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2509.22625."}