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Paper Citation Record · LEDGER

Edge-spectral supersaturation for tripartite color-critical graphs

As of 16 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2608.04485.

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

pith.paper-citation-record.v1
2608.04485 v2

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T14:49:07.804045Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

26 of 26 outbound references displayed

  • verified exact0
  • verified fuzzy9
  • unresolved17
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3a904ae4-48ae-417a-bca1-d5c2163f6533 · outbound

This paper cites Bollob´ as, V.

Edge-spectral supersaturation for tripartite color-critical graphs Bollob´ as, V

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T14:49:08.232926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.709480Z digest=sha256:dccbee1e6f67132adcf26d00a7360426042632c83d280f1efa770aaa1ecd0c99

Observation 92918b8a-3a04-4c48-906d-aa92e72be3a6 · outbound

This paper cites Supersaturation in Nosal graphs: Triangles and books.

Edge-spectral supersaturation for tripartite color-critical graphs Supersaturation in Nosal graphs: Triangles and books

Reference 2

Resolution
unresolved
no resolver link, observed 2026-08-15T14:49:07.713997Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T14:49:07.713997Z digest=sha256:5336461cd82463273d2fdb5edfb323611781f57fc130e71e8e65f19a45b20ec4

Observation 98dbde75-1001-4bb1-ba90-f7553b96ea44 · outbound

This paper cites an unresolved cited work.

Edge-spectral supersaturation for tripartite color-critical graphs Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-15T14:49:08.220723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.718230Z digest=sha256:c089f788c0b5ee2da38ef8bb03f35c04995bd5d01b261a4f0f125bc129f146cb

Observation 09e4407a-b8e4-4303-b85f-b32e26cb87ef · outbound

This paper cites an unresolved cited work.

Edge-spectral supersaturation for tripartite color-critical graphs Unresolved cited work

Reference 4

Resolution
unresolved
no resolver link, observed 2026-08-15T14:49:07.722152Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T14:49:07.722152Z digest=sha256:e772e56b6c9222816b71c1c0d6da4d7f0d69113c13b34de7820b027962c6ff55

Observation ebfe8876-da76-46a2-b064-b3d3a7830371 · outbound

This paper cites an unresolved cited work.

Edge-spectral supersaturation for tripartite color-critical graphs Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-15T14:49:08.208182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.726114Z digest=sha256:1e5583f1cd9721f829b4258e0ae29dcba9aa38150146a9124b024b564e932c70

Observation 9d2e1ab0-8111-4256-8c85-1de54881aae8 · outbound

This paper cites an unresolved cited work.

Edge-spectral supersaturation for tripartite color-critical graphs Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-15T14:49:08.196182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.729692Z digest=sha256:9baae6f0c1c89357f8e187216476ee126d310be783c303e350531b44b1ada00f

Observation fa0a06a4-50de-45cb-9da7-e505156bec7c · outbound

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

Edge-spectral supersaturation for tripartite color-critical graphs An edge-spectral Erd\H{o}s-Stone-Simonovits theorem and its stability

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-15T14:49:07.733422Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T14:49:07.733422Z digest=sha256:ab30b3b3da7fb3acc29f2bebf37cf0b709c2569d6ed0a7df9834dcb9616ca46e

Observation e572f7d1-350f-49df-afd3-d004e472d829 · outbound

This paper cites an unresolved cited work.

Edge-spectral supersaturation for tripartite color-critical graphs Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-15T14:49:08.184476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.737329Z digest=sha256:22898e4a87a62ad697671c057ec7a42cf25d36691c56dc96ae76b309a3c35341

Observation b2e9fd5b-2ab0-4ba7-b3a6-a188857a2fc0 · outbound

This paper cites an unresolved cited work.

Edge-spectral supersaturation for tripartite color-critical graphs Unresolved cited work

Reference 9

Resolution
unresolved
no resolver link, observed 2026-08-15T14:49:07.741212Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T14:49:07.741212Z digest=sha256:92b72abc2a4bc4cfad5009c0ffec6cb0a206ca2f5739b8033ce7ca3c9c93da42

Observation 166b7da6-50de-454e-a716-68fb4eac881d · outbound

This paper cites Spectral Sidorenko inequalities and edge-spectral supersaturation.

Edge-spectral supersaturation for tripartite color-critical graphs Spectral Sidorenko inequalities and edge-spectral supersaturation

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-15T14:49:07.744756Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T14:49:07.744756Z digest=sha256:42a9819515fa38206951511bac839334393899d89d1a16fc8a3c4b8d22e7a593

Observation 40ff8111-eb32-4355-b32a-cb5c06e11702 · outbound

This paper cites an unresolved cited work.

Edge-spectral supersaturation for tripartite color-critical graphs Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-15T14:49:08.172909Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.748972Z digest=sha256:2d2a2bb4704138576ece605d538708de44bc340bd3de3dc6451e455601acb753

Observation b084d945-0654-4c52-8bf8-1c4498010151 · outbound

This paper cites Lov´ asz, M.

Edge-spectral supersaturation for tripartite color-critical graphs Lov´ asz, M

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T14:49:08.161294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.752816Z digest=sha256:67434a6189ab49dbcab22fa76509455c9122b767001e0f9e921c80b30a9cbc09

Observation 2b68f572-2ad5-4dc7-8fd1-7c13208be395 · outbound

This paper cites an unresolved cited work.

Edge-spectral supersaturation for tripartite color-critical graphs Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-15T14:49:08.150292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.756387Z digest=sha256:5821baa7670feab37172bd7e2404c81d28c0f4c49e8c85ac6959f5780249d53a

Observation 7429b909-2c88-4d1b-a37d-251d90ff3782 · outbound

This paper cites Mubayi, Counting substructures I: Color critical graphs,Adv.

Edge-spectral supersaturation for tripartite color-critical graphs Mubayi, Counting substructures I: Color critical graphs,Adv

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-15T14:49:07.759882Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T14:49:07.759882Z digest=sha256:afcc8b33799c4f595ed973894cc222672f427fe9e9950eae8c1f5a09e572e755

Observation 1bdcc8b8-b0da-4228-82bf-422dcab55cca · outbound

This paper cites Nikiforov, The number of cliques in graphs of given order and size,Trans.

Edge-spectral supersaturation for tripartite color-critical graphs Nikiforov, The number of cliques in graphs of given order and size,Trans

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T14:49:08.130838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.763514Z digest=sha256:80efdbdde8d7755912cef8633e393b62bb94c09a66d22698cc07b0aa64d32d7a

Observation 21320a79-4463-494f-8a62-29aa1c327679 · outbound

This paper cites Nikiforov, Some inequalities for the largest eigenvalue of a graph,Combin.

Edge-spectral supersaturation for tripartite color-critical graphs Nikiforov, Some inequalities for the largest eigenvalue of a graph,Combin

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T14:49:08.118812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.766897Z digest=sha256:9065013c9aaaeb9233629de1173cea06158a539ee9f9e3b44f8dc99f75d42106

Observation 819e5ac4-f5a5-4a75-805e-9bd611871686 · outbound

This paper cites Nikiforov, Walks and the spectral radius of graphs,Linear Algebra Appl.418(2006), no.

Edge-spectral supersaturation for tripartite color-critical graphs Nikiforov, Walks and the spectral radius of graphs,Linear Algebra Appl.418(2006), no

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T14:49:08.105855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.770626Z digest=sha256:8a32a615c033dd4e9bada67135e38fff41b30060660b433022606b83b18579c3

Observation 813df0e6-f37e-47d9-bbb3-696ebad7b21c · outbound

This paper cites Nikiforov, More spectral bounds on the clique and independence numbers,J.

Edge-spectral supersaturation for tripartite color-critical graphs Nikiforov, More spectral bounds on the clique and independence numbers,J

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T14:49:08.094377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.774102Z digest=sha256:f13c169046d4c6d4bd005bae89a551895bfa089b4df883e234f14396a62d6085

Observation 67e5896f-3026-457f-bc83-3dffa6d4d283 · outbound

This paper cites an unresolved cited work.

Edge-spectral supersaturation for tripartite color-critical graphs Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-15T14:49:08.082323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.777590Z digest=sha256:7a2f673de4db2d4a01184a8517b8bbaeb197f312fdd123f5abb728249d00c432

Observation 6a759ad5-6703-429f-8631-14a9bdb553fc · outbound

This paper cites Nosal, Eigenvalues of graphs, Master’s thesis, University of Calgary, 1970.

Edge-spectral supersaturation for tripartite color-critical graphs Nosal, Eigenvalues of graphs, Master’s thesis, University of Calgary, 1970

Reference 20

Resolution
unresolved
no resolver link, observed 2026-08-15T14:49:07.781105Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T14:49:07.781105Z digest=sha256:c0c1a6cd9039b50272361185bc9bbc58a73ce7b575dd9822b8ded720efad9659

Observation 7cdc06a9-327f-4b22-9289-52ec9292bd0a · outbound

This paper cites Pikhurko, Z.

Edge-spectral supersaturation for tripartite color-critical graphs Pikhurko, Z

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T14:49:08.062270Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.784765Z digest=sha256:c968cd360f33ff1b93566a7d56f19625448d3f7287fe4efdf6418805dd3c4c69

Observation e1623892-fa44-412a-941c-77b1fd2142e9 · outbound

This paper cites Sauer, On the existence of regularn-graphs with given girth,J.

Edge-spectral supersaturation for tripartite color-critical graphs Sauer, On the existence of regularn-graphs with given girth,J

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T14:49:08.050181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.788565Z digest=sha256:2342351034f3e1f84e38e9845d0478e5b9c9ef3a5a67e5bf50586917dde1bf24

Observation bda52d39-7443-44c1-91e1-5e6db9be0dcf · outbound

This paper cites Simonovits, A method for solving extremal problems in graph theory, stability problems, Theory of Graphs (Proc.

Edge-spectral supersaturation for tripartite color-critical graphs Simonovits, A method for solving extremal problems in graph theory, stability problems, Theory of Graphs (Proc

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T14:49:08.036283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.792499Z digest=sha256:07e29d6497f0def4a09832ae7fcc9ec867d3db534d2d2e3c7697548d9ae4e138

Observation 18ecc438-9481-47c1-8369-1ef553229366 · outbound

This paper cites an unresolved cited work.

Edge-spectral supersaturation for tripartite color-critical graphs Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-15T14:49:08.022032Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.796804Z digest=sha256:ee9b9b849f3222b845002e51eaf3c30179638a75939308f2dc97268189c06965

Observation 5770fc7e-98b7-4ed2-9d64-4eb2a106b42a · outbound

This paper cites an unresolved cited work.

Edge-spectral supersaturation for tripartite color-critical graphs Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-15T14:49:08.008690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-15T14:49:07.800557Z digest=sha256:2c4d5abfadc16c4fd479489a7f35852f4dbaa19e710b6edb80008ab6503b6404

Observation 30673640-98eb-4885-9357-6fdf1568fa97 · outbound

This paper cites Two problems on booksize and triangular edges in Nosal graphs.

Edge-spectral supersaturation for tripartite color-critical graphs Two problems on booksize and triangular edges in Nosal graphs

Reference 26

Resolution
unresolved
no resolver link, observed 2026-08-15T14:49:07.804045Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T14:49:07.804045Z digest=sha256:61c987974ea8f995d3cb417c618e284fe34df456232800eb4a5242426c675f82

Pith citing papers

No inbound Pith citation observations are available.