Paper Citation Record · LEDGER

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4

As of 19 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2504.13454.

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

pith.paper-citation-record.v1
2504.13454 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T12:14:06.566011Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

28 of 28 outbound references displayed

verified exact2
verified fuzzy18
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e210d94b-970c-4d7c-8fc3-9d857248332f · outbound

This paper cites Abe, Strong semimodular lattices and Frankl’s conjec ture, Algebra Universalis.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Abe, Strong semimodular lattices and Frankl’s conjec ture, Algebra Universalis

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.904614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 49884886-a2e2-4a19-a6e8-c64ce069a4bc · outbound

This paper cites Improved Lower Bound for Frankl's Union-Closed Sets Conjecture.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Improved Lower Bound for Frankl's Union-Closed Sets Conjecture

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-16T12:14:06.468314Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 89567db4-65e2-418b-b68f-d6e07fafa698 · outbound

This paper cites Boˇ snjak and P.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Boˇ snjak and P

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.892169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f25899fa-d740-4d9d-8733-9794e0784391 · outbound

This paper cites Bruhn and O.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Bruhn and O

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.881045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation af1ddc52-044a-439a-8241-fc51c2e3f4b8 · outbound

This paper cites Better bounds for the union-closed sets conjecture using the entropy approach.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Better bounds for the union-closed sets conjecture using the entropy approach

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-16T12:14:06.480791Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95dfe79f-62e8-40d8-8cb6-4ea5cf65d8e4 · outbound

This paper cites Approximate union closed conjecture.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Approximate union closed conjecture

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-16T12:14:06.485125Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 49eb1e8c-436d-40bd-acb2-c46444a5924c · outbound

This paper cites Cz´ edli, M.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Cz´ edli, M

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.868829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d5618e60-119c-420c-b2c2-26b8b9113e7c · outbound

This paper cites Frankl, On the Union-Closed Sets Conjecture, Unpubli shed manuscript, 1979.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Frankl, On the Union-Closed Sets Conjecture, Unpubli shed manuscript, 1979

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.858255Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7899b308-d289-47be-a756-1eb95e25bcf6 · outbound

This paper cites Finite groups admitting a coprime automorphism satisfying an additional polynomial identity.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Finite groups admitting a coprime automorphism satisfying an additional polynomial identity

Reference 9

Resolution: metadata mismatch; local_arxiv, observed 2026-08-16T12:14:06.663865Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b374fddf-0b14-468a-a14c-2b87e5e7adc6 · outbound

This paper cites https://github.com/features/copilot.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 https://github.com/features/copilot

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.847552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2fa72bc7-56c8-4f7f-baec-540d3357bc23 · outbound

This paper cites Gusakov, Formalizing the excluded minor characteri zation of binary ma- troids in the Lean theorem prover, Master Thesis, Universit y of Waterloo, 2024.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Gusakov, Formalizing the excluded minor characteri zation of binary ma- troids in the Lean theorem prover, Master Thesis, Universit y of Waterloo, 2024

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.837490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 09346e27-cfb0-46b9-8d35-775738f2f610 · outbound

This paper cites Hachimori and K.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Hachimori and K

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.827526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c507f94c-da0f-452a-aef2-e09470238247 · outbound

This paper cites Kashiwabara, Formal proof of a problem of ideal famil ies by Lean 4, GitHub.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Kashiwabara, Formal proof of a problem of ideal famil ies by Lean 4, GitHub

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.817134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fd85a6ff-3230-4a17-9099-ef651d68bd5e · outbound

This paper cites Lean Copilot: Assisting formal pro of development in Lean,.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Lean Copilot: Assisting formal pro of development in Lean,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.806728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3f3a26e2-1de4-469e-b83d-fdcfa541aed5 · outbound

This paper cites an unresolved cited work.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:14:06.796184Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 794a08ef-792b-4449-8bd0-9586644e0136 · outbound

This paper cites Liu, Improving the lower bound for the union-closed s ets conjecture via conditionally IID coupling, 58th Annual Conference on Information Scienc es and Systems (CISS), IEEE, 2024.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Liu, Improving the lower bound for the union-closed s ets conjecture via conditionally IID coupling, 58th Annual Conference on Information Scienc es and Systems (CISS), IEEE, 2024

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.785214Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fbe974af-2bff-46d0-9ee9-c48f790177b7 · outbound

This paper cites Formalizing Frankl's Conjecture: FC-families.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Formalizing Frankl's Conjecture: FC-families

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-16T12:14:06.648226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 80d2fa7d-3fde-4a11-9e02-b23b58b48eb7 · outbound

This paper cites A Note on the Union-closed Sets Conjecture.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 A Note on the Union-closed Sets Conjecture

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-16T12:14:06.632127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e5ca7b8f-0795-4f1b-b136-dcfb8e14ae57 · outbound

This paper cites Morris, FC-families and improved bounds for Frankl’ s conjecture, European Journal of Combinatorics 27 (2006), 269–282.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Morris, FC-families and improved bounds for Frankl’ s conjecture, European Journal of Combinatorics 27 (2006), 269–282

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.773262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 73bb5a95-e7b8-4007-87db-1bfb159f581c · outbound

This paper cites de Moura et al., The Lean 4 theorem prover and programm ing language, Proceedings of the 13th International Conference on Interactive Theore m Proving (ITP 2022), 2021.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 de Moura et al., The Lean 4 theorem prover and programm ing language, Proceedings of the 13th International Conference on Interactive Theore m Proving (ITP 2022), 2021

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.761609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b6dd28ab-f458-40e3-bdce-00c311bce93c · outbound

This paper cites Notes on the Union Closed Sets Conjecture.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Notes on the Union Closed Sets Conjecture

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-16T12:14:06.540855Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6b1ca10f-5551-4284-8192-028e6eb1c7d5 · outbound

This paper cites ChatGPT, https://openai.com.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 ChatGPT, https://openai.com

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.749475Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d4e9d2a1-4a1e-4f63-8649-c991ad68cc0e · outbound

This paper cites Extension of a Method of Gilmer.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Extension of a Method of Gilmer

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-16T12:14:06.548564Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ea996ed0-a583-4d27-b1fa-776f2663046c · outbound

This paper cites Poonen, Union-closed families, Journal of Combinat orial Theory, Series A 59 (1992), 253–268.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Poonen, Union-closed families, Journal of Combinat orial Theory, Series A 59 (1992), 253–268

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.738124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b3ae7706-0240-4f7d-aa01-f0d007aa8b5d · outbound

This paper cites Reinhold, Frankl’s conjecture is true for lower semi modular lattices, Graphs and Com- binatorics, 16 (2000), 115–116.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Reinhold, Frankl’s conjecture is true for lower semi modular lattices, Graphs and Com- binatorics, 16 (2000), 115–116

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.727267Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 48c5db4b-9359-4328-bb8c-1437aaa0c8b6 · outbound

This paper cites Roberts and J.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Roberts and J

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.715855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0169e471-40e3-4a95-a464-57af04bafa08 · outbound

This paper cites An improved lower bound for the union-closed set conjecture.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 An improved lower bound for the union-closed set conjecture

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-16T12:14:06.562430Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 775e441c-d057-4a45-989e-aa578b586e1a · outbound

This paper cites Yu, Dimension-free bounds for the union-closed sets conjecture.

On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4 Yu, Dimension-free bounds for the union-closed sets conjecture

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:14:06.704240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

No inbound Pith citation observations are available.