Paper Citation Record · LEDGER

Sum-Essential Graphs of Modules

As of 22 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:1908.05921.

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

pith.paper-citation-record.v1
1908.05921 v1

Coverage vector

measured 10 of 10 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T13:14:45.073436Z

measured 10 of 10 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 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

10 of 10 outbound references displayed

verified exact7
verified fuzzy2
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 17e08917-99a0-4579-a940-8072c3a1ba28 · outbound

This paper cites Akbari, M.

Sum-Essential Graphs of Modules Akbari, M

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-14T13:14:45.019591Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d12674a8-91fa-4b6e-9ea2-a55e49429af6 · outbound

This paper cites Akbari, R.

Sum-Essential Graphs of Modules Akbari, R

Reference 2

Resolution: verified exact; doi, observed 2026-08-14T13:14:45.218310Z

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 95a6ddf6-0f18-4100-a16d-0ff4fe6e5808 · outbound

This paper cites Akbari, H.

Sum-Essential Graphs of Modules Akbari, H

Reference 3

Resolution: verified exact; doi, observed 2026-08-14T13:14:45.201631Z

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 12ad03d3-3ab2-4339-b7aa-b62d2a767203 · outbound

This paper cites Amini, B.

Sum-Essential Graphs of Modules Amini, B

Reference 4

Resolution: verified exact; doi, observed 2026-08-14T13:14:45.184325Z

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 6099a159-217e-4503-895a-3ef4e8ae2d6f · outbound

This paper cites Amjadi, The essential ideal graph of a commutative rin g, Asian-Eur.

Sum-Essential Graphs of Modules Amjadi, The essential ideal graph of a commutative rin g, Asian-Eur

Reference 5

Resolution: verified exact; doi, observed 2026-08-14T13:14:45.167309Z

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 3be8a0d5-24c8-4fcf-9b2f-756ce2c62401 · outbound

This paper cites Lam, A First Course in Noncommutative Rings, Spring er-Verlag, New York, 2001.

Sum-Essential Graphs of Modules Lam, A First Course in Noncommutative Rings, Spring er-Verlag, New York, 2001

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:14:45.402508Z

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 69870891-0e6c-4d44-853e-cf96f9b4b67f · outbound

This paper cites Lam, Lectures on Modules and Rings, Springer-Verla g, New York 1999.

Sum-Essential Graphs of Modules Lam, Lectures on Modules and Rings, Springer-Verla g, New York 1999

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:14:45.387374Z

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 67df2537-04d5-4d77-be45-614071e864de · outbound

This paper cites Matczuk, M.

Sum-Essential Graphs of Modules Matczuk, M

Reference 8

Resolution: verified exact; doi, observed 2026-08-14T13:14:45.150230Z

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 9f7607b0-49ac-4f2a-8554-0704c3d8d668 · outbound

This paper cites an unresolved cited work.

Sum-Essential Graphs of Modules Unresolved cited work

Reference 9

Resolution: verified exact; doi, observed 2026-08-14T13:14:45.134160Z

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 fbce9641-b65b-40e6-b64d-41da530999a4 · outbound

This paper cites an unresolved cited work.

Sum-Essential Graphs of Modules Unresolved cited work

Reference 10

Resolution: verified exact; doi, observed 2026-08-14T13:14:45.112205Z

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.

Pith citing papers

No inbound Pith citation observations are available.