Paper Citation Record · LEDGER

Full-Trace Modules

As of 14 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 1 inbound Pith citation observation for arXiv:2505.14961.

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

pith.paper-citation-record.v1
2505.14961 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:38:54.006570Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-09T16:48:00.150652Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-09T16:48:00.634750Z

Reference resolution

24 of 24 outbound references displayed

verified exact0
verified fuzzy22
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 79e410ee-1d27-4251-a250-310b04b43eb9 · outbound

This paper cites Stable module theory.

Full-Trace Modules Stable module theory

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:39:00.697684Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3b8e8e18-9452-411e-9640-ce28545d5cef · outbound

This paper cites Brennan, Jürgen Herzog, and Bernd Ulrich.

Full-Trace Modules Brennan, Jürgen Herzog, and Bernd Ulrich

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:39:00.423940Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation dac066c4-6016-4af6-9da9-398f18ee9328 · outbound

This paper cites Cohen-Macaulay rings, volume 39 of Cambridge Studies in Advanced Mathematics.

Full-Trace Modules Cohen-Macaulay rings, volume 39 of Cambridge Studies in Advanced Mathematics

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:39:00.092603Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b5f1a2b0-7433-4f3a-9157-389b5d3036fe · outbound

This paper cites Generalized Gorenstein Arf rings.

Full-Trace Modules Generalized Gorenstein Arf rings

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:59.932335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 09d2c2ca-d2df-4ff9-b976-5d44eb08075e · outbound

This paper cites Vanishing of Tor, and why we care about it.

Full-Trace Modules Vanishing of Tor, and why we care about it

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:59.619400Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0aeb6db3-214a-49ab-be32-53f849a0b300 · outbound

This paper cites Stable trace ideals and applications.

Full-Trace Modules Stable trace ideals and applications

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:59.337451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 94431874-cf79-496e-ba67-d46cab9a583e · outbound

This paper cites A note on the index of Cohen-Macaulay local rings.

Full-Trace Modules A note on the index of Cohen-Macaulay local rings

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:59.079113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4d5ef398-486b-492f-a186-22a4a96b4c20 · outbound

This paper cites On modules of finite projective dimension.

Full-Trace Modules On modules of finite projective dimension

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:58.773341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 865b1eaf-c4b1-4f22-9a7a-96cbdd82ec29 · outbound

This paper cites Gulliksen.

Full-Trace Modules Gulliksen

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:58.452674Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3b7677c8-b5a4-4e10-ad40-37ef07aff52b · outbound

This paper cites an unresolved cited work.

Full-Trace Modules Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:38:58.129107Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e4f7e435-d7f3-4395-9d54-c5139966d05d · outbound

This paper cites Integral closure of ideals, rings, and modules , volume 336 of London Mathematical Society Lecture Note Series.

Full-Trace Modules Integral closure of ideals, rings, and modules , volume 336 of London Mathematical Society Lecture Note Series

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:57.830840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 50dc1463-307e-4693-ac44-567ccb33778b · outbound

This paper cites Rings whose ideals are isomorphic to trace ideals.

Full-Trace Modules Rings whose ideals are isomorphic to trace ideals

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:57.566595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2784cefc-fbd5-4f9b-8044-5fe9f77db733 · outbound

This paper cites Leuschke and Roger Wiegand.

Full-Trace Modules Leuschke and Roger Wiegand

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:57.370917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation bc9f4510-d1cf-4f77-b21b-43c00669031d · outbound

This paper cites Trace ideals and centers of endomorphism rings of modules over commutative rings.

Full-Trace Modules Trace ideals and centers of endomorphism rings of modules over commutative rings

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:56.978640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3b9e1ff6-b868-43fa-800e-4431630eba5e · outbound

This paper cites Trace ideals and the Gorenstein property.

Full-Trace Modules Trace ideals and the Gorenstein property

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:56.653631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 37ac25b4-2298-4656-8e7b-6f0b61994a7c · outbound

This paper cites Stable ideals and Arf rings.

Full-Trace Modules Stable ideals and Arf rings

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:56.323810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9b2edfd8-421d-4c6a-ac85-cd4ca32c5da4 · outbound

This paper cites Partial trace ideals, torsion and canonical module.

Full-Trace Modules Partial trace ideals, torsion and canonical module

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:56.039104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b7c5901b-175c-4426-a130-53411e021af6 · outbound

This paper cites Commutative ring theory, volume 8 of Cambridge Studies in Advanced Mathematics.

Full-Trace Modules Commutative ring theory, volume 8 of Cambridge Studies in Advanced Mathematics

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:55.753195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5bfccce5-94ff-455c-89a5-dc28d8b1c5eb · outbound

This paper cites Syzygy modules with semidualizing or G-projective summands.

Full-Trace Modules Syzygy modules with semidualizing or G-projective summands

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:55.569829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 714bead8-9599-4613-a866-31ae7c76f7eb · outbound

This paper cites Homology of Noetherian rings and local rings.

Full-Trace Modules Homology of Noetherian rings and local rings

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:55.361011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9a66e192-9d31-4951-bd21-3262a49be187 · outbound

This paper cites Gorenstein rings and modules with high numbers of generators.

Full-Trace Modules Gorenstein rings and modules with high numbers of generators

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:55.196115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 995defdc-e4e2-4843-be7a-1b4487bd2db0 · outbound

This paper cites Vasconcelos.

Full-Trace Modules Vasconcelos

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:54.913788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3c80a3ff-14f3-4b2f-b8cd-148ae4736cf0 · outbound

This paper cites Vasconcelos.

Full-Trace Modules Vasconcelos

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:38:54.622769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8ec3771d-04c9-42ac-838c-52747d3d70fa · outbound

This paper cites an unresolved cited work.

Full-Trace Modules Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:38:54.293385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

Observation f803a0e7-26fc-4b64-b442-37347445f459 · inbound

When do pseudo-Gorenstein rings become Gorenstein? cites this paper.

When do pseudo-Gorenstein rings become Gorenstein? Full-Trace Modules

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-09T16:48:00.639516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.