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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:a7d46a7bbaf6f7cfb03b14bf41e022788d91f211a719cb07e0e2e0c46f24b6df

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=sha256:6f5053a3128c4a03a3205bba22d41e8a42fa6923d9e15b0089e411f1edb25c18

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=sha256:473c4b3400ba2419b332f61d89792612b5aab653bb4bb801d3cff2913e7b52d8

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=sha256:24d218138654a8fa8f2c0a34a560fc79a28d5c88bfa7dce3c8ce6c8b22a89865

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=sha256:3dbf2f338b88ec53aeeaa64ab9975effbda9846da63336c2deeda385637de13f

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=sha256:3b3a27b3023b15a3900921bac4560c9b29ebc5f7a9dcf5c256da932c2b3b7551

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=sha256:4e3b3014b92d282fce68a188178fe7e717455618f32b67a85c13cb3b693159e5

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=sha256:72c786841bdf3a4527dcef0e7a87c4fa255c3ed1d04bacca7b71ef5cf13d7127

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=sha256:0b5423a87124dfd13f2960cc2ebb3e963f90dda2f8bed6472e9062594ae38272

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:bd807c368e1684c10bdcbe96812380d8e1605b283b9604c3b6b8a42be9980272

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=sha256:4861b431adb4049e12000f26878c5816d3e9c893c1532612e5cc506734d487de

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=sha256:2164beef3e5d865b089b8f02ea9f29efb9f7fd656d3895e12deb7f84b3bd7869

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=sha256:24dc687bd4c67abc4248fee5ef0fb44dacd8ce5b108d4eccf8eccd7ea63a8ed6

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=sha256:05e4adf18e41945d622110cb634ac0208ae22cf74004bedd748793d632ed7080

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=sha256:09438c25359caf125c152c7f9c51c65bf544a742b619c9dfe61eb0c3b2d44291

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:e6eb48e9eedea88629b3f9691b6590e30ad2b618a1f73fc3d6f369082122d508

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=sha256:2990ed535308d0587d4c5487b18c592e28416d5d9cecd25b48b7ba435da7cf87

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=sha256:9cd1220a8abaefe8bb652cff045897a7eb4d33a377c130657263aeb09a5c6f87

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:d1fb4b25570883ec01e5b4e822db76a2423b75f97b11c5e31378b2a0d5cbc29e

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=sha256:7537f4a6b2145383519e51f5ddbf25268e03a672e41c877433fcc680a43714cd

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=sha256:1edaa7d03ca6203f731bb3dd37a8370e85688472af5657344d7dad4b3f9e2208

Pith citing papers

No inbound Pith citation observations are available.