Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:19:30.285799Z
Paper Citation Record · LEDGER
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories
As of 13 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2506.08685.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
33 of 33 outbound references displayed
- verified exact10
- verified fuzzy9
- unresolved14
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation f2b2e39d-08c8-489b-a3ef-e6001e595208 · outbound
This paper cites an unresolved cited work.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:19:30.845295Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation bed40f3c-108f-4fc9-a139-e72cc4525d59 · outbound
This paper cites Artin, A.
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:19:30.832553Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation f3ff5489-c0b0-40de-9af1-3ea873a25a20 · outbound
This paper cites an unresolved cited work.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:19:30.819220Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4dcd68f6-28fa-4a98-b55a-19304f07c286 · outbound
This paper cites an unresolved cited work.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:19:30.807087Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c6404502-b027-451a-b116-23a7f29263d3 · outbound
This paper cites Enveloping Classes over Commutative Rings.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Enveloping Classes over Commutative Rings
Reference 5
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T05:19:30.614921Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 06af0caa-7712-464e-b156-f42d945c8e63 · outbound
This paper cites Churhch, J.
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:19:30.795541Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 65f1f881-4a21-4bf9-9cbc-e44cbf497dc3 · outbound
This paper cites FI-modules over Noetherian rings.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories FI-modules over Noetherian rings
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T05:19:30.172118Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 89cd688c-9a79-488e-ad56-8b871870a9e7 · outbound
This paper cites Sheaves of modules on atomic sites and discrete representations of topological groups.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Sheaves of modules on atomic sites and discrete representations of topological groups
Reference 8
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T05:19:30.588128Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 96ee9a14-bbdb-46fb-8f2e-ce58e90c6945 · outbound
This paper cites Representations over diagrams of abelian categories I: Global structure and homological objects.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Representations over diagrams of abelian categories I: Global structure and homological objects
Reference 9
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T05:19:30.571557Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 036219ea-2cd0-4bfb-a49c-7690cab605ff · outbound
This paper cites an unresolved cited work.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:19:30.783084Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 79a8262d-5e2c-4b0b-b8d7-6b6c9f398390 · outbound
This paper cites Gabriel and M.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Gabriel and M
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:19:30.772355Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 8668efd2-f5e5-4542-b393-4a2086ca1eaa · outbound
This paper cites an unresolved cited work.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:19:30.761304Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d0e5a809-9f5a-4c6e-abb2-b8ffa13100db · outbound
This paper cites an unresolved cited work.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:19:30.748882Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 9eabc54e-4b92-46e3-aea3-721f34c4bda9 · outbound
This paper cites an unresolved cited work.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:19:30.736810Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 8156835c-c59b-4f99-a5b9-9f8a60ec5fcb · outbound
This paper cites Geigle and H.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Geigle and H
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:19:30.724020Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation b13be9e3-c35b-4c42-995e-83c4f0ac1749 · outbound
This paper cites G¨ unt¨ urk¨ un and A.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories G¨ unt¨ urk¨ un and A
Reference 16
- Resolution
- verified exact
- raw_fallback, observed 2026-08-07T05:19:30.553821Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 32079e99-a9e3-470b-a261-a2825708c5da · outbound
This paper cites Johnstone.
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:19:30.713334Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation cb8e33d0-6ad5-4568-8e21-62bc743a540c · outbound
This paper cites Grothendieck topologies on posets.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Grothendieck topologies on posets
Reference 18
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T05:19:30.467179Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a672e947-9fc4-4366-86fc-9ed0fee633f6 · outbound
This paper cites Kashiwara and P.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Kashiwara and P
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:19:30.702234Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 5cd91e15-3690-41f9-8fac-55684b36b0f8 · outbound
This paper cites an unresolved cited work.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:19:30.689511Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 691a3d66-a6e8-4da8-8050-505f93af30e9 · outbound
This paper cites Li and E.
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:19:30.677242Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation feea3aa8-8e24-4773-88e5-6b4383d9171e · outbound
This paper cites Grothendieck topologies on a poset.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Grothendieck topologies on a poset
Reference 22
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T05:19:30.448903Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ba45ef44-48ef-43fb-8cf8-5b348077e6d2 · outbound
This paper cites Mac Lane and I.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Mac Lane and I
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:19:30.663783Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a3ffce8f-2771-4354-a61d-56fa67fdeeca · outbound
This paper cites an unresolved cited work.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:19:30.652009Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ffeaac5a-717c-41d5-9959-32a7d8a5a5f8 · outbound
This paper cites $\mathrm{VI}$ modules in non-describing characteristic, Part I.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories $\mathrm{VI}$ modules in non-describing characteristic, Part I
Reference 25
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T05:19:30.250392Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5e516fa5-7f50-4c78-b71e-25ec2abfcc13 · outbound
This paper cites VI modules in non-describing characteristic, Part II.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories VI modules in non-describing characteristic, Part II
Reference 26
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T05:19:30.410870Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 8d867546-6274-4919-bbf5-fdb7a62964b3 · outbound
This paper cites GL-equivariant modules over polynomial rings in infinitely many variables.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories GL-equivariant modules over polynomial rings in infinitely many variables
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T05:19:30.258925Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 946f93e1-54da-4723-8ec3-bcab2dfe7c32 · outbound
This paper cites Gr\"obner methods for representations of combinatorial categories.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Gr\"obner methods for representations of combinatorial categories
Reference 28
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T05:19:30.263180Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2bde1e60-7bf2-41ac-84cd-c0a1ee168c26 · outbound
This paper cites Available at stacks.math.columbia.edu.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Available at stacks.math.columbia.edu
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:19:30.639780Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 9f16aeca-c27f-40d8-aad2-c4dd44f82e1e · outbound
This paper cites an unresolved cited work.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:19:30.626685Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 7a583a67-be17-4472-8d4e-b388ca68c208 · outbound
This paper cites Skew category algebras and modules on ringed finite sites.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories Skew category algebras and modules on ringed finite sites
Reference 31
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T05:19:30.364096Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 0971709a-d439-449b-ad42-d292d0e6c4ab · outbound
This paper cites On sheaves in finite group representations.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories On sheaves in finite group representations
Reference 32
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T05:19:30.345520Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 541408a7-af9a-46c7-87c0-18fba9ede33e · outbound
This paper cites On cohomological characterizations of endotrivial modules.
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories On cohomological characterizations of endotrivial modules
Reference 33
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T05:19:30.329081Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Pith citing papers
No inbound Pith citation observations are available.