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Paper Citation Record · LEDGER

A sharp fixed-size spectral bound for $kK_3$-free graphs

As of 9 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2608.05869.

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

pith.paper-citation-record.v1
2608.05869 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T22:11:50.866869Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

21 of 21 outbound references displayed

  • verified exact0
  • verified fuzzy6
  • unresolved15
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5dbfd1b9-2741-4b32-a0f3-b3f18e66f6f9 · outbound

This paper cites Chen, A.-M.

A sharp fixed-size spectral bound for $kK_3$-free graphs Chen, A.-M

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T22:12:00.852696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.795281Z digest=sha256:8d1f80dff809ca4fadcfada31eda59a82ee1978b7856d5734df47d4c29a73209

Observation 21a25d4b-c8bc-4ac8-8df7-2f31fd7fca28 · outbound

This paper cites Chen, A.-M.

A sharp fixed-size spectral bound for $kK_3$-free graphs Chen, A.-M

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T22:12:00.841317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.799870Z digest=sha256:ea0212226965eb08a1dbdbc8d6c419e3f3b7c6126c8f24af554d1cbc359512bd

Observation 909414a2-00b0-49d8-bbd4-ef42f1fc78ae · outbound

This paper cites Erd˝ os, T.

A sharp fixed-size spectral bound for $kK_3$-free graphs Erd˝ os, T

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T22:12:00.830234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.803705Z digest=sha256:9c77ef0d8621582f349c4eccdde23520ab093bf10c482c32794a4557fa3bab33

Observation 1f220311-8fce-4adc-9506-f879cb29cc33 · outbound

This paper cites an unresolved cited work.

A sharp fixed-size spectral bound for $kK_3$-free graphs Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-07T22:12:00.818861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.808266Z digest=sha256:9b1f02c512961af5001a1fe78d7b92752d535d414d915fe5602e0fef5157215e

Observation 0891e8b4-95e0-47e0-ad43-32fe535ac925 · outbound

This paper cites an unresolved cited work.

A sharp fixed-size spectral bound for $kK_3$-free graphs Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-07T22:12:00.807632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.812774Z digest=sha256:188ae355e310cb4ba157f673231491db7e0bd81b2bb865cfad84cbd19a56f1d9

Observation c71d9961-9199-4a3f-8d6c-b8c802be042f · outbound

This paper cites an unresolved cited work.

A sharp fixed-size spectral bound for $kK_3$-free graphs Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-07T22:12:00.795851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.816658Z digest=sha256:6f782782f7ef7299705186b0464a94894f60808ed3efe5448b3c59929a42a660

Observation de894484-f61f-44cf-b548-3d98985967e1 · outbound

This paper cites an unresolved cited work.

A sharp fixed-size spectral bound for $kK_3$-free graphs Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-07T22:12:00.783820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.821543Z digest=sha256:c22e5097dc4e1ff8d11f4f21f6e853f723f05b651b3ab53d1fefb0a4fe9385aa

Observation 1fb16ef0-1cd6-4441-b26d-d9ff1cd43918 · outbound

This paper cites an unresolved cited work.

A sharp fixed-size spectral bound for $kK_3$-free graphs Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-07T22:12:00.770705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.825371Z digest=sha256:04053b2c2777e2b2f8e744b815dcdf30d279930136f6bab8c468d254c95418b3

Observation 617db3a0-023d-4400-aa87-1cb08f0e163b · outbound

This paper cites an unresolved cited work.

A sharp fixed-size spectral bound for $kK_3$-free graphs Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-07T22:12:00.760296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.828778Z digest=sha256:92c4bdd9ddbeb17629fa3b54388d64c67e29151e1c6c56bb2f2e899f2a2851cf

Observation cdb3def1-2899-4903-b7d9-8e7a5b539616 · outbound

This paper cites an unresolved cited work.

A sharp fixed-size spectral bound for $kK_3$-free graphs Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-07T22:12:00.746510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.832051Z digest=sha256:817c8fc493d08473e62baab8fe5ddfdbe07b51b4f0e66a9f22daaeff3b1771cc

Observation 25d590a4-f5b0-4923-8ea5-fa05da2d8e30 · outbound

This paper cites An edge-spectral Erd\H{o}s-Stone-Simonovits theorem and its stability.

A sharp fixed-size spectral bound for $kK_3$-free graphs An edge-spectral Erd\H{o}s-Stone-Simonovits theorem and its stability

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-07T22:11:50.835317Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T22:11:50.835317Z digest=sha256:ffd5154ccce761a69ca56285830e6bea128bf952089b9b968edb7cfe650ff8e9

Observation f0c71983-f519-48e3-a873-8cc69d9599fa · outbound

This paper cites an unresolved cited work.

A sharp fixed-size spectral bound for $kK_3$-free graphs Unresolved cited work

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-07T22:11:50.839189Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T22:11:50.839189Z digest=sha256:f492f63dd2f6c657afe4b294e9ee190efe62f138bc27ec645ee5339db34af61f

Observation 2519e70e-2958-413b-ae60-8751b8cc7a07 · outbound

This paper cites an unresolved cited work.

A sharp fixed-size spectral bound for $kK_3$-free graphs Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-07T22:12:00.733421Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.842359Z digest=sha256:d7702859f0a6271a013754c09e866b227dd72c4ec10c1216877220629d4dcdee

Observation 16285279-55ac-474d-a421-bf0bd04ac391 · outbound

This paper cites an unresolved cited work.

A sharp fixed-size spectral bound for $kK_3$-free graphs Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-07T22:12:00.722036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.845375Z digest=sha256:aaf35bc6120f35dc415a25873325bfbb96b59a5510333aec865210eaebac8314

Observation 12ea8c1e-084f-4471-9784-17f7ed4791e3 · outbound

This paper cites Nikiforov,Bounds on graph eigenvalues II, Linear Algebra Appl.

A sharp fixed-size spectral bound for $kK_3$-free graphs Nikiforov,Bounds on graph eigenvalues II, Linear Algebra Appl

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T22:12:00.710263Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.848528Z digest=sha256:f4be4c80b12777b8963fee84c1630842cf5ce58ec4e68cbb6dd7d18b31749301

Observation 0638b758-02ea-4d65-abb3-69a028e49273 · outbound

This paper cites Nikiforov,The spectral radius of graphs without paths and cycles of specified length, Linear Algebra Appl.

A sharp fixed-size spectral bound for $kK_3$-free graphs Nikiforov,The spectral radius of graphs without paths and cycles of specified length, Linear Algebra Appl

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T22:12:00.696985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.851434Z digest=sha256:1959eac5a7e2a1ab0b438d5518a0da2ee6d67935457b55710ba676c269386b9b

Observation abf6b40b-029a-48b9-9bee-0f638a2055c2 · outbound

This paper cites an unresolved cited work.

A sharp fixed-size spectral bound for $kK_3$-free graphs Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-07T22:12:00.682916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.854330Z digest=sha256:6e3c9991de96aaed849855d08913fdcbb65d8da3b4c0493d2918142071b5250f

Observation 2de189a2-2d45-42f7-a572-b54ac778de4b · outbound

This paper cites an unresolved cited work.

A sharp fixed-size spectral bound for $kK_3$-free graphs Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-07T22:12:00.670054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.857447Z digest=sha256:55cbf66dbe6d958cc9612b934bccade7ed640c0a8d45ead3782ecce4b2da9321

Observation 74c39508-45a4-4712-8e6f-d58a9da0b07a · outbound

This paper cites an unresolved cited work.

A sharp fixed-size spectral bound for $kK_3$-free graphs Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-07T22:12:00.658878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.860383Z digest=sha256:ba75bf2281055fecf5dec4da56065cddab4d646986dc7522607ebb7a95487719

Observation 2c3d25ab-bd70-4a42-80b8-ea2bafeb93ca · outbound

This paper cites an unresolved cited work.

A sharp fixed-size spectral bound for $kK_3$-free graphs Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-07T22:12:00.647918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.863274Z digest=sha256:d62eada05a11fbba531a49b7e96b2dc5690d66e76b0d3b2eebc7caada29fc7d2

Observation 2f768c2e-7381-4d51-ae26-c905e06c3776 · outbound

This paper cites Zhang, L.

A sharp fixed-size spectral bound for $kK_3$-free graphs Zhang, L

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T22:12:00.636333Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T22:11:50.866869Z digest=sha256:49f0aba16217bb98c3a808b7de404bd9f700bbce7c37539c86af340efbe0f190

Pith citing papers

No inbound Pith citation observations are available.