Paper Citation Record · LEDGER

The singularity category as a stable module category

As of 10 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2509.01056.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2509.01056 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T13:18:45.944432Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-14T00:24:30.334357Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-14T00:28:30.022520Z

Reference resolution

37 of 37 outbound references displayed

verified exact1
verified fuzzy35
unresolved1
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External citation measurements

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Outbound references

Observation 7dfb0759-0af8-4ca9-9f91-d854f28a1318 · outbound

This paper cites Abrams, and G.

The singularity category as a stable module category Abrams, and G

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:55.614383Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 39f656a8-a606-4411-8519-76a766623acc · outbound

This paper cites Ara, M.A.

The singularity category as a stable module category Ara, M.A

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:55.396593Z

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Observation e25d2d92-4744-4a74-a2c4-0defad44ac7f · outbound

This paper cites Ara, and E.

The singularity category as a stable module category Ara, and E

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:55.163970Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation dd0332c8-a890-4a69-8de1-4af57e80cbad · outbound

This paper cites Auslander , Representation Dimension of Artin Algebras, Math.

The singularity category as a stable module category Auslander , Representation Dimension of Artin Algebras, Math

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:54.932847Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f66f755b-54b6-4e48-af35-bd2b404f1d78 · outbound

This paper cites Auslander, I.

The singularity category as a stable module category Auslander, I

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:54.670067Z

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Observation e1afac93-2ab0-49ad-9694-e580f9f7df02 · outbound

This paper cites Beligiannis, The homological theory of contravariantly ﬁnite subcatego ries: Auslander- Buchweitz contexts, Gorenstein categories and (co-)stabi lization, Comm.

The singularity category as a stable module category Beligiannis, The homological theory of contravariantly ﬁnite subcatego ries: Auslander- Buchweitz contexts, Gorenstein categories and (co-)stabi lization, Comm

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:54.374519Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 8f0e07c8-b8ba-4867-9539-d5b726bc6537 · outbound

This paper cites Beligiannis, and M.

The singularity category as a stable module category Beligiannis, and M

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:54.073742Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a9ddf0fb-8ac3-46c6-a97d-2e728be58fc5 · outbound

This paper cites Bergh , Orbit algebras and periodicity , Colloq.

The singularity category as a stable module category Bergh , Orbit algebras and periodicity , Colloq

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:53.814637Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1d03653e-1868-4b8a-a555-52c8131a8a61 · outbound

This paper cites Buchweitz , Maximal Cohen-Macaulay Modules and Tate-cohomology over Goren- stein Rings, with appendices by L.L.

The singularity category as a stable module category Buchweitz , Maximal Cohen-Macaulay Modules and Tate-cohomology over Goren- stein Rings, with appendices by L.L

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:53.591945Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation da05e7e8-6983-4b26-9f35-55784ba79850 · outbound

This paper cites Carlsen, and E.

The singularity category as a stable module category Carlsen, and E

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:53.324882Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3ee63e54-dcd6-403c-a6a4-5c2d08996249 · outbound

This paper cites Canonaco, and P.

The singularity category as a stable module category Canonaco, and P

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:53.090611Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9c4d2c08-7f26-4045-b5ec-4f4749b414ff · outbound

This paper cites Chen , Relative singularity categories and Gorenstein-projecti ve modules , Math.

The singularity category as a stable module category Chen , Relative singularity categories and Gorenstein-projecti ve modules , Math

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:52.868906Z

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Observation 19368c8f-0037-49a4-90b0-6d5d2b1e65da · outbound

This paper cites Chen, and Z.

The singularity category as a stable module category Chen, and Z

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-05T13:18:43.120056Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b6477212-a1b3-48bb-8385-314a037038a0 · outbound

This paper cites Chen, and Z.

The singularity category as a stable module category Chen, and Z

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:52.597940Z

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Observation ddf5e03d-0468-4fec-a39c-c898f9703e24 · outbound

This paper cites Chen, and D.

The singularity category as a stable module category Chen, and D

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:52.327103Z

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Observation 121298ae-9d49-4283-a592-6c8fb3694827 · outbound

This paper cites Clark, J.

The singularity category as a stable module category Clark, J

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:52.073709Z

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Observation 6f2bd265-bd33-48e3-b120-94591834e611 · outbound

This paper cites Cuntz, and D.

The singularity category as a stable module category Cuntz, and D

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:51.742110Z

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Observation fbaacc04-967b-467b-b20c-3bc6251061df · outbound

This paper cites Dade , Group-graded rings and modules , Math.

The singularity category as a stable module category Dade , Group-graded rings and modules , Math

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:51.452008Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 43ad5359-8ab1-4ed3-9607-f240950cfb71 · outbound

This paper cites Damiano , Coﬂat rings and modules , Paciﬁc J.

The singularity category as a stable module category Damiano , Coﬂat rings and modules , Paciﬁc J

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:51.187939Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 720ced74-3a8f-4295-9dd2-9169b5733cc3 · outbound

This paper cites Drinfeld , DG quotients of DG categories , J.

The singularity category as a stable module category Drinfeld , DG quotients of DG categories , J

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:50.885257Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ff8934fc-147a-4b8b-a576-93d5d02869d1 · outbound

This paper cites Ebeling , Homological mirror symmetry for singularities , in: Representation Theory– Current Trends and Perspectives, EMS Series Congress Repor ts, 75–107, European Math.

The singularity category as a stable module category Ebeling , Homological mirror symmetry for singularities , in: Representation Theory– Current Trends and Perspectives, EMS Series Congress Repor ts, 75–107, European Math

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:50.595305Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e0ac14e9-2593-4d8c-97d7-60dc367578fe · outbound

This paper cites Happel , Triangulated Categories in the Representation Theory of F inite Dimensional Algebras, London Math.

The singularity category as a stable module category Happel , Triangulated Categories in the Representation Theory of F inite Dimensional Algebras, London Math

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:50.340123Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation de3f40b8-e648-44e8-a436-62e21c8d8d0c · outbound

This paper cites Hazrat , The dynamics of Leavitt path algebras , J.

The singularity category as a stable module category Hazrat , The dynamics of Leavitt path algebras , J

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:50.095233Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9cb9ac7e-7c26-4976-bed7-4f23a27c9eb0 · outbound

This paper cites Hazrat , Graded Rings and Graded Grothendieck Groups, London Math.

The singularity category as a stable module category Hazrat , Graded Rings and Graded Grothendieck Groups, London Math

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:49.697406Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6c595407-bdd8-4e5b-96f7-f65d44339844 · outbound

This paper cites Heller , The loop-space functor in homological algebra , Trans.

The singularity category as a stable module category Heller , The loop-space functor in homological algebra , Trans

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:49.481130Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a8dda0b6-4fc9-464e-b79b-4ad72891477b · outbound

This paper cites Heller , Stable homotopy categories , Bull.

The singularity category as a stable module category Heller , Stable homotopy categories , Bull

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:49.197498Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7bea6298-914e-4aa2-a3b9-5238f15cc377 · outbound

This paper cites Kalck, A new equivalence between singularity categories of commut ative algebras, Adv.

The singularity category as a stable module category Kalck, A new equivalence between singularity categories of commut ative algebras, Adv

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:48.964464Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 39a25e55-5519-4293-958d-b6a7701ae24a · outbound

This paper cites Noncommutative Kn\"orrer type equivalences via noncommutative resolutions of singularities.

The singularity category as a stable module category Noncommutative Kn\"orrer type equivalences via noncommutative resolutions of singularities

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-08-05T13:18:46.351227Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d3e402e5-1828-435a-81f9-81f39424a200 · outbound

This paper cites Keller , Derived categories and universal problems , Comm.

The singularity category as a stable module category Keller , Derived categories and universal problems , Comm

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:48.693900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a15bd916-2afc-46f0-a23c-2e52d0ca7e3e · outbound

This paper cites Keller , On the cyclic homology of exact categorues , J.

The singularity category as a stable module category Keller , On the cyclic homology of exact categorues , J

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:48.376175Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 34d13462-1460-454b-8bb3-a5112d7215ec · outbound

This paper cites Keller, and D.

The singularity category as a stable module category Keller, and D

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:48.157975Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b06d95b2-c3e0-43b5-a37f-a2b60d5e4bfd · outbound

This paper cites Leavitt, The module type of a ring , Trans.

The singularity category as a stable module category Leavitt, The module type of a ring , Trans

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:47.870018Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6a97287e-0dc9-4c21-b6c8-275aa2a7f5a0 · outbound

This paper cites Lenzing , Wild canonical algebras and rings of automorphic forms , in: Finite- Dimensional Algebras and Related Topics, NATO ASI Ser.

The singularity category as a stable module category Lenzing , Wild canonical algebras and rings of automorphic forms , in: Finite- Dimensional Algebras and Related Topics, NATO ASI Ser

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:47.623312Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e77ff0bb-1433-44c0-930d-05dd99284a7f · outbound

This paper cites Nastasescu, and F.

The singularity category as a stable module category Nastasescu, and F

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:47.351928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fc21dfe3-0532-4f64-9225-2c7751d3cea7 · outbound

This paper cites Orlov, Triangulated categories of singularities and D-branes in Landau-Ginzburg mod- els, Proc.

The singularity category as a stable module category Orlov, Triangulated categories of singularities and D-branes in Landau-Ginzburg mod- els, Proc

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:47.120299Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation caf85e4b-7d73-4856-b740-442ffe9d1a11 · outbound

This paper cites Smith , Category equivalences involving graded modules over path a lgebras of quivers , Adv.

The singularity category as a stable module category Smith , Category equivalences involving graded modules over path a lgebras of quivers , Adv

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:46.927198Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9bfbc2e9-6561-414f-98df-0a379e6beea4 · outbound

This paper cites Tierney , Categorical Constructions in Stable Homotopy Theory, Lec ture Notes in Math.

The singularity category as a stable module category Tierney , Categorical Constructions in Stable Homotopy Theory, Lec ture Notes in Math

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:18:46.656611Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

Observation 01379ae5-c59e-47b8-9cba-bcf058921cf1 · inbound

Lectures on singularity categories cites this paper.

Lectures on singularity categories The singularity category as a stable module category

Reference 39

Resolution: verified exact; arxiv_id, observed 2026-05-14T00:28:30.026889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.