Paper Citation Record · LEDGER

A positive square-energy strengthening of Tur\'an's theorem

As of 16 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2607.18044.

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

pith.paper-citation-record.v1
2607.18044 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T16:25:45.653858Z

measured 38 of 38 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.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

38 of 38 outbound references displayed

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External citation measurements

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Outbound references

Observation 5960e7d2-a124-4139-860a-59752e6f3438 · outbound

This paper cites Abiad, L.

A positive square-energy strengthening of Tur\'an's theorem Abiad, L

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.557539Z

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Observation 8872b68a-14f5-4210-963f-4995c320f265 · outbound

This paper cites Ailon, M.

A positive square-energy strengthening of Tur\'an's theorem Ailon, M

Reference 2

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Observation a2a3c06f-ec37-43d4-9a6e-cf389f8b2ce6 · outbound

This paper cites Akbari, H.

A positive square-energy strengthening of Tur\'an's theorem Akbari, H

Reference 3

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Observation b59c02cc-60dd-4aa2-b2db-7f0c1699c102 · outbound

This paper cites Akbari, H.

A positive square-energy strengthening of Tur\'an's theorem Akbari, H

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.566316Z

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Observation 2ee0ab2a-82e5-44c1-8f51-29c7910f263d · outbound

This paper cites Refinement of a conjecture on positive square energy of graphs.

A positive square-energy strengthening of Tur\'an's theorem Refinement of a conjecture on positive square energy of graphs

Reference 5

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Observation 99bfe3aa-4a0c-4752-a0d1-3610e528d6ce · outbound

This paper cites Alon and J.

A positive square-energy strengthening of Tur\'an's theorem Alon and J

Reference 6

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Observation 55f2f0a3-e90e-4415-b751-83009dea4fa6 · outbound

This paper cites Ando and M.

A positive square-energy strengthening of Tur\'an's theorem Ando and M

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.575278Z

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Observation 60df9994-8be9-4532-b048-72926a662b60 · outbound

This paper cites Balogh, F.

A positive square-energy strengthening of Tur\'an's theorem Balogh, F

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.578040Z

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Observation b49eeeeb-f147-4706-9351-924ebab885c3 · outbound

This paper cites Greedy Sequential Maximal Independent Set and Matching are Parallel on Average.

A positive square-energy strengthening of Tur\'an's theorem Greedy Sequential Maximal Independent Set and Matching are Parallel on Average

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.580453Z

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Observation 46a1dca2-e4be-4fa7-955f-e26355b2517c · outbound

This paper cites Bollobás and V.

A positive square-energy strengthening of Tur\'an's theorem Bollobás and V

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.583110Z

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Observation 6e2f4714-62d3-46ca-b5f2-9006678e9137 · outbound

This paper cites Caro, New results on the independence number, Technical Report, Tel-Aviv University, 1979.

A positive square-energy strengthening of Tur\'an's theorem Caro, New results on the independence number, Technical Report, Tel-Aviv University, 1979

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.585647Z

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Observation b4a9495c-c586-44a9-9af4-45e69076336e · outbound

This paper cites Conic programming to understand sums of squares of eigenvalues of graphs.

A positive square-energy strengthening of Tur\'an's theorem Conic programming to understand sums of squares of eigenvalues of graphs

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.588243Z

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Observation 7518e18b-4cf3-425c-8eb3-f593a436c54e · outbound

This paper cites an unresolved cited work.

A positive square-energy strengthening of Tur\'an's theorem Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.590969Z

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Observation 6fdacd74-c9d5-4c08-9d33-8090801a6bd4 · outbound

This paper cites Elphick, M.

A positive square-energy strengthening of Tur\'an's theorem Elphick, M

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.593291Z

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Observation d1726ba8-1190-4959-9565-a483656072e2 · outbound

This paper cites Elphick and W.

A positive square-energy strengthening of Tur\'an's theorem Elphick and W

Reference 15

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Observation 6d1db9e8-ff78-4d3f-b739-699b9466462b · outbound

This paper cites Elphick, W.

A positive square-energy strengthening of Tur\'an's theorem Elphick, W

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.598057Z

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Observation c36dd69d-6276-4179-b168-930b9a566fab · outbound

This paper cites Elphick, Q.

A positive square-energy strengthening of Tur\'an's theorem Elphick, Q

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.600358Z

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Observation b7fe3c61-bcf0-4bcf-95d5-8cf9af941cb1 · outbound

This paper cites Conjectured lower bound for the clique number of a graph.

A positive square-energy strengthening of Tur\'an's theorem Conjectured lower bound for the clique number of a graph

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.602743Z

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Observation 8ff93515-07b3-4138-af90-c9ae08d761fe · outbound

This paper cites Fischer and A.

A positive square-energy strengthening of Tur\'an's theorem Fischer and A

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.605929Z

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Observation 1ad9534e-852f-4c41-b9f9-982a932e9c86 · outbound

This paper cites Füredi, A proof of the stability of extremal graphs, Simonovits’ stability from Szemerédi’s regularity,J.

A positive square-energy strengthening of Tur\'an's theorem Füredi, A proof of the stability of extremal graphs, Simonovits’ stability from Szemerédi’s regularity,J

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.608855Z

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Observation 1d37b1f7-6751-4326-99a6-28445f44c0f0 · outbound

This paper cites an unresolved cited work.

A positive square-energy strengthening of Tur\'an's theorem Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.611209Z

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Observation 5833b59f-a9aa-453b-86d0-a78f01d5aa2f · outbound

This paper cites an unresolved cited work.

A positive square-energy strengthening of Tur\'an's theorem Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.613632Z

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Observation afba4ea7-08c7-49bb-a28e-3dc41568252f · outbound

This paper cites an unresolved cited work.

A positive square-energy strengthening of Tur\'an's theorem Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.616259Z

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Observation 54d5ea7e-ce55-40c4-a5a7-258773178ccb · outbound

This paper cites Strengthening Wilf's lower bound on clique number.

A positive square-energy strengthening of Tur\'an's theorem Strengthening Wilf's lower bound on clique number

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.618935Z

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Observation 9181ee15-50f1-4f3d-a4f3-ae5826c580ed · outbound

This paper cites Kelly and L.

A positive square-energy strengthening of Tur\'an's theorem Kelly and L

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.621538Z

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Observation b517201a-138f-4963-baa8-c452eab567b5 · outbound

This paper cites Krivelevich, T.

A positive square-energy strengthening of Tur\'an's theorem Krivelevich, T

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.624031Z

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Observation acdfa6d4-1530-41b1-a940-83cfbcf78d02 · outbound

This paper cites Liu and B.

A positive square-energy strengthening of Tur\'an's theorem Liu and B

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.626187Z

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Observation b2eafad7-263d-4657-bddf-3223c8174729 · outbound

This paper cites an unresolved cited work.

A positive square-energy strengthening of Tur\'an's theorem Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.628728Z

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Observation 769a40eb-4b90-4f4b-8ed2-9a327e12ef1d · outbound

This paper cites Mantel, Vraagstuk XXVIII,Wiskundige Opgaven met de Oplossingen10(1907), 60–61.

A positive square-energy strengthening of Tur\'an's theorem Mantel, Vraagstuk XXVIII,Wiskundige Opgaven met de Oplossingen10(1907), 60–61

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.630917Z

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Observation 8a5bfb7a-fca4-46db-92d2-997841ccfb51 · outbound

This paper cites an unresolved cited work.

A positive square-energy strengthening of Tur\'an's theorem Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.633464Z

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Observation 5d7b9294-4f99-4757-b319-f53627aa5643 · outbound

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

A positive square-energy strengthening of Tur\'an's theorem Nikiforov, Some inequalities for the largest eigenvalue of a graph,Combin

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.635971Z

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Observation 20296c63-d987-4abe-a625-1d24c0733412 · outbound

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

A positive square-energy strengthening of Tur\'an's theorem Simonovits, A method for solving extremal problems in graph theory, stability problems, inTheory of Graphs (Proc

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.638693Z

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Observation df4e0f81-5856-4e66-bebf-7c2ca09f3aeb · outbound

This paper cites an unresolved cited work.

A positive square-energy strengthening of Tur\'an's theorem Unresolved cited work

Reference 33

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Observation 64a18427-1eb0-4187-821f-ddeb11cd9e35 · outbound

This paper cites Turán, On an extremal problem in graph theory,Mat.

A positive square-energy strengthening of Tur\'an's theorem Turán, On an extremal problem in graph theory,Mat

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.643606Z

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Observation ec5a6a4c-8981-4c24-8d44-c8ecf952959d · outbound

This paper cites an unresolved cited work.

A positive square-energy strengthening of Tur\'an's theorem Unresolved cited work

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.646160Z

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Observation a9f8b11a-298f-40aa-8cac-c7c2ab6ae1f9 · outbound

This paper cites an unresolved cited work.

A positive square-energy strengthening of Tur\'an's theorem Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.648868Z

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Observation 284b2d53-b481-4de1-ad90-8f4446213782 · outbound

This paper cites Wocjan and C.

A positive square-energy strengthening of Tur\'an's theorem Wocjan and C

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.651394Z

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Observation d1ab1d7e-e7a2-4ed2-8094-57455cdc22e3 · outbound

This paper cites Extremal values for the square energies of graphs.

A positive square-energy strengthening of Tur\'an's theorem Extremal values for the square energies of graphs

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:45.653858Z

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