Paper Citation Record · LEDGER

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$

As of 19 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2501.08993.

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

pith.paper-citation-record.v1
2501.08993 v2

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T20:23:13.221861Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

31 of 31 outbound references displayed

verified exact0
verified fuzzy28
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d4b47f7d-eb27-4c8a-9406-cd786ad31d68 · outbound

This paper cites Angeleri-H¨ ugel,Covers and envelopes via endoproperties of modules , Proc.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Angeleri-H¨ ugel,Covers and envelopes via endoproperties of modules , Proc

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.813917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2c73074e-ec3d-4d4d-b4c0-a5f586149cf0 · outbound

This paper cites Angeleri-H¨ ugel, Direct summands of products , Arch.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Angeleri-H¨ ugel, Direct summands of products , Arch

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.797085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0fb71bb7-b0db-4772-8126-33913c422cb0 · outbound

This paper cites Angeleri-H¨ ugel, On some precovers and preenvelopes , Habilitationsschrift, 2000.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Angeleri-H¨ ugel, On some precovers and preenvelopes , Habilitationsschrift, 2000

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.780958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 23e418d7-2bfd-4508-a151-d12239034bc4 · outbound

This paper cites Angeleri-H¨ ugel, J.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Angeleri-H¨ ugel, J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.764971Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c2d007dc-f18f-4df2-a0de-9b66bbf39f08 · outbound

This paper cites Bennett-Tennenhaus, Characterisations of Σ -pure-injectivity in triangulated categories and applications to endoperfect objects , Fund.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Bennett-Tennenhaus, Characterisations of Σ -pure-injectivity in triangulated categories and applications to endoperfect objects , Fund

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.748302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 603f71cc-f66e-4e5b-80ae-20587a683084 · outbound

This paper cites an unresolved cited work.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-10T20:23:13.088585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0650b918-a0d7-4269-afdc-04ec19e5acbf · outbound

This paper cites Breaz, Σ -pure injectivity and Brown Representability , Proc.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Breaz, Σ -pure injectivity and Brown Representability , Proc

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.729054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation de926006-daf2-4abc-a018-e6ed54375cb8 · outbound

This paper cites Breaz, and J.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Breaz, and J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.710806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 892c1c40-3b62-41c7-9f39-26fa6dbf6f66 · outbound

This paper cites Chase, On direct sums and products of modules , Paciﬁc J.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Chase, On direct sums and products of modules , Paciﬁc J

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.693947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ba8cca16-0c01-4121-b681-9e890313af66 · outbound

This paper cites The cotorsion pair generated by the Gorenstein projective modules and $\lambda$-pure-injective modules.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ The cotorsion pair generated by the Gorenstein projective modules and $\lambda$-pure-injective modules

Reference 10

Resolution: metadata mismatch; local_arxiv, observed 2026-08-10T20:23:13.283406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 41e419d2-ae7d-4846-82c1-cec5f22c3b9b · outbound

This paper cites Dugas, B.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Dugas, B

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.677579Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b2122eb2-a366-4017-8087-c94ebaf82d7b · outbound

This paper cites an unresolved cited work.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:23:13.660290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fd89a8dc-89a9-4dd1-8872-89b73d28dc53 · outbound

This paper cites Garkusha, M.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Garkusha, M

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.641301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fb517c6a-3452-4afb-a931-4781c9ced7c2 · outbound

This paper cites G¨ obel, J.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ G¨ obel, J

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.621667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 53ee1afe-7650-48a0-9c5a-6642c7422692 · outbound

This paper cites Holm and P.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Holm and P

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.602040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d189c636-f498-459a-a705-289b33a8129f · outbound

This paper cites Hrbek, L.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Hrbek, L

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.581817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f89702a3-ba17-4a64-ab30-349b8b5e2803 · outbound

This paper cites Huisgen-Zimmermann, Purity, algebraic compactness, direct sum decompositions , and representation type, in: Inﬁnite Length Modules (Bielefeld, 1998), Trends.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Huisgen-Zimmermann, Purity, algebraic compactness, direct sum decompositions , and representation type, in: Inﬁnite Length Modules (Bielefeld, 1998), Trends

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.564381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6b258136-0aaf-48cd-abc2-5269b4c53dc8 · outbound

This paper cites Krause, Chase’s lemma and its context , Expo.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Krause, Chase’s lemma and its context , Expo

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.546406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 661e4db6-abbf-44f4-9444-25116a3b5016 · outbound

This paper cites Krause, Homological Theory of Representations , Cambridge University Press, 2022.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Krause, Homological Theory of Representations , Cambridge University Press, 2022

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.529217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 221a38cf-dded-4c97-837c-ca08085cfa14 · outbound

This paper cites Krause, Coherent functors in stable homotopy theory , Fundamenta Math.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Krause, Coherent functors in stable homotopy theory , Fundamenta Math

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.512420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 57b42afb-12fc-4b03-aace-b3ceb53872b8 · outbound

This paper cites Krause, Smashing subcategories and the telescope and the telescope conjecture - an alge- braic approach, Invent.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Krause, Smashing subcategories and the telescope and the telescope conjecture - an alge- braic approach, Invent

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.495410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a365b49f-eccd-4ade-a109-e8be68ad4767 · outbound

This paper cites Krause, M.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Krause, M

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.476629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0c7c478d-955d-4862-b15a-710dfa066a13 · outbound

This paper cites Laking, Purity in compactly generated derivators and t-structures with Grothendieck hearts, Math.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Laking, Purity in compactly generated derivators and t-structures with Grothendieck hearts, Math

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.460308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 798e55b6-ed93-444a-a529-01bcc478cd01 · outbound

This paper cites Laking and J.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Laking and J

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.442836Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2165ad6c-90ce-4339-9547-4aaf0ae45e91 · outbound

This paper cites Prest, R.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Prest, R

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.419377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation eceb87a1-4d0b-49e3-b06d-f88bd382777f · outbound

This paper cites ˇSaroch, Enochs’ conjecture for small precovering classes of module s, Israel J.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ ˇSaroch, Enochs’ conjecture for small precovering classes of module s, Israel J

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.400606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 161fe94a-19c3-4568-a38a-452cb14b5380 · outbound

This paper cites ˇSaroch, Σ -algebraically compact modules and Lω 1ω -compact cardinals, Math.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ ˇSaroch, Σ -algebraically compact modules and Lω 1ω -compact cardinals, Math

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.379891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d124013c-3feb-40a7-9c35-2aadb9a109ff · outbound

This paper cites ˇSaroch, J.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ ˇSaroch, J

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.360376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2239d4d1-18cb-4a52-bb6c-a82d8dfe05b8 · outbound

This paper cites Simson, On pure semi-simple Grothendieck categories I , Fund.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Simson, On pure semi-simple Grothendieck categories I , Fund

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.341347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c845eda6-1675-45d5-a77c-d6eb5fb260d5 · outbound

This paper cites W alker, R.B.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ W alker, R.B

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.320975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d78e1039-49b9-49b5-bd05-c29619901940 · outbound

This paper cites Zimmermann-Huisgen, Rings whose right modules are direct sums of indecomposable mod- ules, Proc.

Comparing $\mathrm{Add}(M)$ with $\mathrm{Prod}(M)$ Zimmermann-Huisgen, Rings whose right modules are direct sums of indecomposable mod- ules, Proc

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:23:13.302322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

No inbound Pith citation observations are available.