Paper Citation Record · LEDGER

Brick-splitting Torsion Pairs and Left Modularity

As of 22 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 1 inbound Pith citation observation for arXiv:2506.13602.

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

pith.paper-citation-record.v1
2506.13602 v2

Coverage vector

measured 42 of 42 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:11:27.360592Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-09T22:28:47.763916Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-09T22:29:06.509982Z

Reference resolution

42 of 42 outbound references displayed

verified exact0
verified fuzzy20
unresolved22
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 786d26ac-a172-4b4c-b45a-d10c2776aff3 · outbound

This paper cites Adachi, O.

Brick-splitting Torsion Pairs and Left Modularity Adachi, O

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.165899Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c3e1ff08-b38c-4d4e-8da4-5b8605baa85a · outbound

This paper cites Fans and polytopes in tilting theory I: Foundations.

Brick-splitting Torsion Pairs and Left Modularity Fans and polytopes in tilting theory I: Foundations

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.171467Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83fbdd3e-a3a7-46fc-b4b2-e02a4a3e71fc · outbound

This paper cites Asai, Semibricks, Int.

Brick-splitting Torsion Pairs and Left Modularity Asai, Semibricks, Int

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.991046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5eb86be4-d663-4900-b5c8-5b650f00bab8 · outbound

This paper cites Asai, The wall-chamber structures of the real Grothendieck groups, Adv.

Brick-splitting Torsion Pairs and Left Modularity Asai, The wall-chamber structures of the real Grothendieck groups, Adv

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.181334Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c8fb355-52da-4717-8ea6-132dc0f0d672 · outbound

This paper cites Asai, Mutations of simple-minded collections and -tilting reduction (in preparation).

Brick-splitting Torsion Pairs and Left Modularity Asai, Mutations of simple-minded collections and -tilting reduction (in preparation)

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.964516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b0ba0297-f7d3-42a1-b4f1-c6150350253a · outbound

This paper cites an unresolved cited work.

Brick-splitting Torsion Pairs and Left Modularity Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:11:27.948474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f188cad8-b1e7-40c7-9d3d-1cf19562aed4 · outbound

This paper cites Assem, D.

Brick-splitting Torsion Pairs and Left Modularity Assem, D

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.932753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 30b029db-0139-4b41-9244-f09ce58be9da · outbound

This paper cites Auslander, I.

Brick-splitting Torsion Pairs and Left Modularity Auslander, I

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.916206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 766fbb99-c6d5-4db5-9ae5-1c553a26f7ef · outbound

This paper cites Barnard, A.

Brick-splitting Torsion Pairs and Left Modularity Barnard, A

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.205318Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 03c728e4-d3ba-468b-a77d-ed82a44fc3e6 · outbound

This paper cites Baumann, J.

Brick-splitting Torsion Pairs and Left Modularity Baumann, J

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.891232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 228331d1-ec36-4020-bd0b-31c32faf3f81 · outbound

This paper cites Blass, B.

Brick-splitting Torsion Pairs and Left Modularity Blass, B

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.214686Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d5cbe374-9e80-41f4-9bd2-5d7bafdcc60f · outbound

This paper cites Br\" u stle, D.

Brick-splitting Torsion Pairs and Left Modularity Br\" u stle, D

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.867151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 24fc00c3-6aad-4c55-b4a1-84209df2e0c7 · outbound

This paper cites Bobiński, G.

Brick-splitting Torsion Pairs and Left Modularity Bobiński, G

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.852014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 964a2c19-2d1a-484d-95a5-18b75dcaa8bd · outbound

This paper cites Davey, H.

Brick-splitting Torsion Pairs and Left Modularity Davey, H

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.228669Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47e95232-762c-43b5-997e-d4329514ba86 · outbound

This paper cites Demonet, O.

Brick-splitting Torsion Pairs and Left Modularity Demonet, O

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.233181Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c0ca392-03db-48bd-98e6-7dc9d1a93165 · outbound

This paper cites Demonet, O.

Brick-splitting Torsion Pairs and Left Modularity Demonet, O

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.238062Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ad036e7b-a3e1-4c2f-80cb-e4e7d753f55e · outbound

This paper cites Dräxler, Auslander-Reiten Quivers of Algebras whose Indecomposable Modules are Bricks, Bulletin of the London Mathematical Society, Volume 23 (1991), 141-145.

Brick-splitting Torsion Pairs and Left Modularity Dräxler, Auslander-Reiten Quivers of Algebras whose Indecomposable Modules are Bricks, Bulletin of the London Mathematical Society, Volume 23 (1991), 141-145

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.807841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation fb992538-8dc0-49f4-b7b2-23415004ee7c · outbound

This paper cites Fei, Combinatorics of F -polynomials, Int.

Brick-splitting Torsion Pairs and Left Modularity Fei, Combinatorics of F -polynomials, Int

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.791857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a831515f-fd50-4bda-a6f2-211b44059577 · outbound

This paper cites Fei, Tropical F-polynomials and general presentations, J.

Brick-splitting Torsion Pairs and Left Modularity Fei, Tropical F-polynomials and general presentations, J

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.777162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 059e737d-5f3d-481f-9ccd-4399f81852a6 · outbound

This paper cites Garver, T.

Brick-splitting Torsion Pairs and Left Modularity Garver, T

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.257755Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fbeda06d-3ef8-4b2c-9b5a-496956c8d323 · outbound

This paper cites Grätzer, General Lattice Theory, 2nd edition.

Brick-splitting Torsion Pairs and Left Modularity Grätzer, General Lattice Theory, 2nd edition

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.262723Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0a2bf541-25fc-48f8-9e7c-b0ba8b199da9 · outbound

This paper cites Happel, Triangulate categories in the representation theory of finite dimensional algebras, London Math.

Brick-splitting Torsion Pairs and Left Modularity Happel, Triangulate categories in the representation theory of finite dimensional algebras, London Math

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.742436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation cab11309-1ec3-4e93-9db6-92bae32a7af2 · outbound

This paper cites Jasso, Reduction of -tilting modules and torsion pairs, Int.

Brick-splitting Torsion Pairs and Left Modularity Jasso, Reduction of -tilting modules and torsion pairs, Int

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.726968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 13ed4940-1363-43b9-af98-09cfeb1b2e71 · outbound

This paper cites Keller, L.

Brick-splitting Torsion Pairs and Left Modularity Keller, L

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.712031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6b3125f7-986f-441b-a316-b8db959453a3 · outbound

This paper cites King, Moduli of representations of finite dimensional algebras, Quart.

Brick-splitting Torsion Pairs and Left Modularity King, Moduli of representations of finite dimensional algebras, Quart

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.696188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b2e03f55-7da8-4eaa-82f4-1db17b134534 · outbound

This paper cites an unresolved cited work.

Brick-splitting Torsion Pairs and Left Modularity Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:11:27.680071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation aa1a19f7-088a-4d81-a68e-0297db8695e8 · outbound

This paper cites Markowsky, Primes, irreducibles and extremal lattices, Order 9 (1992), no.

Brick-splitting Torsion Pairs and Left Modularity Markowsky, Primes, irreducibles and extremal lattices, Order 9 (1992), no

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.289661Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f63ae51b-f50b-43b3-9caa-a95f0aa7a015 · outbound

This paper cites Marks, J.

Brick-splitting Torsion Pairs and Left Modularity Marks, J

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.656354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8e7d2a6c-3e1f-48cb-ae17-8f852323f7e5 · outbound

This paper cites Mousavand, -tilting finiteness of biserial algebras, Algebr.

Brick-splitting Torsion Pairs and Left Modularity Mousavand, -tilting finiteness of biserial algebras, Algebr

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.298419Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd5b75bc-5569-4331-8e67-6ce2c76b20c3 · outbound

This paper cites Mousavand, -tilting finiteness of minimal representation-infinite algebras, PhD thesis presented at the University of Montréal (2020).

Brick-splitting Torsion Pairs and Left Modularity Mousavand, -tilting finiteness of minimal representation-infinite algebras, PhD thesis presented at the University of Montréal (2020)

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.631612Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8378c0d3-ea39-4167-97a2-eff80c30145f · outbound

This paper cites Mousavand, -tilting finiteness of non-distributive algebras and their module varieties, Journal of Algebra 608 (2022), 673-690.

Brick-splitting Torsion Pairs and Left Modularity Mousavand, -tilting finiteness of non-distributive algebras and their module varieties, Journal of Algebra 608 (2022), 673-690

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.615193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e1a36a33-c58b-4996-abd6-05ac0f89cce8 · outbound

This paper cites Mousavand, C.

Brick-splitting Torsion Pairs and Left Modularity Mousavand, C

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.311959Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ef13b13a-292e-4325-b490-9dea864671f6 · outbound

This paper cites Hom-orthogonal modules and brick-Brauer-Thrall conjectures.

Brick-splitting Torsion Pairs and Left Modularity Hom-orthogonal modules and brick-Brauer-Thrall conjectures

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.316370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0991072c-67c1-42f1-9571-375d23084ad6 · outbound

This paper cites Mousavand and C.

Brick-splitting Torsion Pairs and Left Modularity Mousavand and C

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.599053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b72be122-2aa8-4649-adc3-f769d56ffa55 · outbound

This paper cites Mühle, Extremality, Left-Modularity and Semidistributivity, Algebra Universalis 84, 16 (2023).

Brick-splitting Torsion Pairs and Left Modularity Mühle, Extremality, Left-Modularity and Semidistributivity, Algebra Universalis 84, 16 (2023)

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.582827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 531c3fab-68a8-43fb-8688-10168ec969f3 · outbound

This paper cites Reading, D.

Brick-splitting Torsion Pairs and Left Modularity Reading, D

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.332155Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation da424021-7f80-4c48-8ad6-f0f76c816b9c · outbound

This paper cites Brick chain filtrations.

Brick-splitting Torsion Pairs and Left Modularity Brick chain filtrations

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.337496Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 61abb88c-e925-4468-b93c-2a35348350fa · outbound

This paper cites an unresolved cited work.

Brick-splitting Torsion Pairs and Left Modularity Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:11:27.557873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 82a45975-0469-4ce7-a872-930d8a0e5d52 · outbound

This paper cites Simson, A.

Brick-splitting Torsion Pairs and Left Modularity Simson, A

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:11:27.542467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c5f8b57f-e679-409f-8d00-4d9a53692d10 · outbound

This paper cites Thomas, An analogue of distributivity for ungraded lattices, Order 23 (2006), no.

Brick-splitting Torsion Pairs and Left Modularity Thomas, An analogue of distributivity for ungraded lattices, Order 23 (2006), no

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.352176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 834e7dc1-5ad6-45f2-9143-f2e2fe11724b · outbound

This paper cites Thomas, N.

Brick-splitting Torsion Pairs and Left Modularity Thomas, N

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.356420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1dfe241a-2654-4df9-8b57-6288cf351fd4 · outbound

This paper cites Yurikusa, Wide subcategories are semistable, Doc.

Brick-splitting Torsion Pairs and Left Modularity Yurikusa, Wide subcategories are semistable, Doc

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-15T20:11:27.360592Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 1ac7b1cb-e665-44a0-b609-c29cdbf3751d · inbound

Left modularity and extremality for (some) infinite lattices cites this paper.

Left modularity and extremality for (some) infinite lattices Brick-splitting Torsion Pairs and Left Modularity

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-09T22:29:06.511176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.