Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T18:14:55.992588Z
Paper Citation Record · LEDGER
$\omega$-left approximation dimensions under Stable equivalence
As of 14 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2507.09286.
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 2026-08-14T06:32:32.682623+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
25 of 25 outbound references displayed
- verified exact1
- verified fuzzy19
- unresolved5
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 78cd0b02-0a75-4fc6-90ec-1230e8b22a67 · outbound
This paper cites Bridger, , Stable module theory, Memoirs Amer.
$\omega$-left approximation dimensions under Stable equivalence Bridger, , Stable module theory, Memoirs Amer
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:15:00.118319Z
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 b9351744-7e7d-4125-b24a-75a16e4c8bbc · outbound
This paper cites Auslander, I.
$\omega$-left approximation dimensions under Stable equivalence Auslander, I
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:59.931946Z
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 c3a36a97-504f-4a84-a3ea-f6c053c5e2fd · outbound
This paper cites Auslander, I.
$\omega$-left approximation dimensions under Stable equivalence Auslander, I
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:59.716738Z
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 e34adda6-53f2-430c-9b1e-95dae7e18498 · outbound
This paper cites Auslander, I.
$\omega$-left approximation dimensions under Stable equivalence Auslander, I
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:59.553570Z
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 4fa6ac67-541c-4485-9dd0-d2a0adde3f8b · outbound
This paper cites Algebra, 1980, 66: 61-22.
$\omega$-left approximation dimensions under Stable equivalence Algebra, 1980, 66: 61-22
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:59.432937Z
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 7b237f6b-d9cd-421c-810f-b727ba89814a · outbound
This paper cites Auslander and I.
$\omega$-left approximation dimensions under Stable equivalence Auslander and I
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:59.225898Z
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 fd07737d-85a9-44cc-9bb2-22261f1e89eb · outbound
This paper cites Brenner and M.
$\omega$-left approximation dimensions under Stable equivalence Brenner and M
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:59.054577Z
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 dfd3a7c8-70df-4ee6-b571-434a6ebeb826 · outbound
This paper cites Beligiannis, I.
$\omega$-left approximation dimensions under Stable equivalence Beligiannis, I
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:58.885657Z
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 91eb8f6b-39f4-47da-85a8-7fc7cbb34dc4 · outbound
This paper cites an unresolved cited work.
$\omega$-left approximation dimensions under Stable equivalence Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T18:14:58.709798Z
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 7c549a02-df9f-4879-9404-da048a59f45b · outbound
This paper cites Relative torsionfreeness and Frobenius extensions.
$\omega$-left approximation dimensions under Stable equivalence Relative torsionfreeness and Frobenius extensions
Reference 10
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T18:14:56.305010Z
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 db2944ab-083f-4d8b-bdbc-58d7a04558db · outbound
This paper cites an unresolved cited work.
$\omega$-left approximation dimensions under Stable equivalence Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T18:14:58.580793Z
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 aa5d8a85-defc-49da-925f-813fc56fcc13 · outbound
This paper cites Guo, Representation dimension: an invariant under stable equivalence, Trans.
$\omega$-left approximation dimensions under Stable equivalence Guo, Representation dimension: an invariant under stable equivalence, Trans
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:58.432673Z
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 148adee6-818c-40c0-bb5b-76dfc52e088f · outbound
This paper cites Enochs, O.M.G.
$\omega$-left approximation dimensions under Stable equivalence Enochs, O.M.G
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:58.235231Z
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 c4aa590e-27f6-49bb-a4fd-2c64b88e613a · outbound
This paper cites an unresolved cited work.
$\omega$-left approximation dimensions under Stable equivalence Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T18:14:58.078675Z
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 74a61157-97a6-4896-879a-b0ac18601d96 · outbound
This paper cites Huang, ω-k-torsionfree modules and ω-n-left approximation dimension, Science in China (Series A)(2000), 44(2): 184-192.
$\omega$-left approximation dimensions under Stable equivalence Huang, ω-k-torsionfree modules and ω-n-left approximation dimension, Science in China (Series A)(2000), 44(2): 184-192
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:57.921759Z
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 2948b793-034e-4216-b081-897d223ddff7 · outbound
This paper cites Huang, Extension closure of k-torsionfree modules, Comm.
$\omega$-left approximation dimensions under Stable equivalence Huang, Extension closure of k-torsionfree modules, Comm
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:57.735387Z
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 35874a22-4b08-4db1-9595-0dd0ca37e6ac · outbound
This paper cites an unresolved cited work.
$\omega$-left approximation dimensions under Stable equivalence Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T18:14:57.596751Z
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 4fab534e-a810-44c8-ad7c-b2fc58195346 · outbound
This paper cites Maximal self-orthogonal modules and a new generalization of tilting modules.
$\omega$-left approximation dimensions under Stable equivalence Maximal self-orthogonal modules and a new generalization of tilting modules
Reference 20
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T18:14:54.948873Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 244765c3-0260-4952-ba36-4f866c8dbf62 · outbound
This paper cites Miyashita, Tilting modules of finite projective dimension, Math.
$\omega$-left approximation dimensions under Stable equivalence Miyashita, Tilting modules of finite projective dimension, Math
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:57.440470Z
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 2be45c32-c992-47b1-bb46-ab163bccbc0d · outbound
This paper cites Martinez-Villa, Properties that are left invariant under stable equivalence.
$\omega$-left approximation dimensions under Stable equivalence Martinez-Villa, Properties that are left invariant under stable equivalence
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:57.300927Z
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 8a89b67c-1c14-4695-957f-40a793b96ef1 · outbound
This paper cites Mantese and I.
$\omega$-left approximation dimensions under Stable equivalence Mantese and I
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:57.151474Z
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 c21eb461-a645-49aa-9648-5c6f2106802f · outbound
This paper cites Sun, J.L.
$\omega$-left approximation dimensions under Stable equivalence Sun, J.L
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:57.003607Z
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 23b4a3c0-6b72-47cb-bd25-e2a303024ffc · outbound
This paper cites Wakamatsu, On modules with trivial self-extensions, J.
$\omega$-left approximation dimensions under Stable equivalence Wakamatsu, On modules with trivial self-extensions, J
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:56.882140Z
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 2ed3b204-acfc-4354-8b9b-479f00225b6d · outbound
This paper cites Wei, Auslander generators and homological conjectures, Glasg.
$\omega$-left approximation dimensions under Stable equivalence Wei, Auslander generators and homological conjectures, Glasg
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:56.722818Z
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 f3a1c1c2-8ce4-4af9-b37a-223c37473176 · outbound
This paper cites Wei, Auslander bounds and homological conjectures, Rev.
$\omega$-left approximation dimensions under Stable equivalence Wei, Auslander bounds and homological conjectures, Rev
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:14:56.551111Z
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
No inbound Pith citation observations are available.