Paper Citation Record · LEDGER

Proof of a conjecture by Starr and log-concavity for random commuting permutations

As of 8 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:2506.06894.

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

pith.paper-citation-record.v1
2506.06894 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T06:00:12.481984Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-27T04:06:38.156334Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-03T17:28:44.664752Z

Reference resolution

33 of 33 outbound references displayed

verified exact4
verified fuzzy20
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation cd1f030a-a7fc-4599-bd97-a8be083dcd40 · outbound

This paper cites Abdesselam, A physicist’s proof of the Lagrange-Good multivariable inversion formula.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Abdesselam, A physicist’s proof of the Lagrange-Good multivariable inversion formula

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:19.219388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation bcc98544-c403-4f5b-96c6-02bcdd9aa55c · outbound

This paper cites Abdesselam, Feynman diagrams in algebraic combinatorics.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Abdesselam, Feynman diagrams in algebraic combinatorics

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:19.087477Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f65325b8-0d9a-4779-9c00-4071f11f75b8 · outbound

This paper cites Non-Abelian correlation inequalities and stable determinantal polynomials.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Non-Abelian correlation inequalities and stable determinantal polynomials

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-07T06:00:13.757921Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 31cd4a40-61cf-492c-bb12-e5159318c018 · outbound

This paper cites Abdesselam, Log-concavity with respect to the number of orbits for infinite tuples of commuting permutations.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Abdesselam, Log-concavity with respect to the number of orbits for infinite tuples of commuting permutations

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:18.753651Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 23565f11-27d5-4c92-b83c-3366969fd207 · outbound

This paper cites Abdesselam, P.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Abdesselam, P

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:18.427347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation eb22bc22-0735-44ee-92bf-08b7ace333cc · outbound

This paper cites Abdesselam, and S.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Abdesselam, and S

Reference 6

Resolution: verified exact; raw_fallback, observed 2026-08-07T06:00:13.523955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7955bf42-610e-4596-8c5c-94626c54b887 · outbound

This paper cites an unresolved cited work.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:00:18.158165Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9ce5581f-83ba-4b95-b032-1e8290570043 · outbound

This paper cites an unresolved cited work.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:00:17.919016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1ba3ee86-2a35-4d47-89b8-f8a06f694123 · outbound

This paper cites an unresolved cited work.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:00:17.790835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 172792ec-29bb-4af5-a1c5-2707b347f312 · outbound

This paper cites Bringmann, J.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Bringmann, J

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:17.625887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 39337a1a-c0d3-47bb-aeec-4301b3b9ef3d · outbound

This paper cites an unresolved cited work.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:00:17.448085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b140125b-deb3-40aa-bdbc-bf3fa8cbd1e5 · outbound

This paper cites Bryan, and J.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Bryan, and J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:17.256344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 976ad257-3ae2-4811-a54a-8695046f8743 · outbound

This paper cites Debruyne, and G.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Debruyne, and G

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:17.078795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 86ce2fe3-d0b2-4527-b6b6-f7639726ca8a · outbound

This paper cites an unresolved cited work.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:00:16.896323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 295fd581-86f7-48ca-af8d-373415190c6b · outbound

This paper cites Flajolet, X.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Flajolet, X

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:16.754785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e078be6e-ac90-44a4-9436-24fa1b0dfb6b · outbound

This paper cites Heim, and M.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Heim, and M

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:16.572225Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0e562ec1-cac8-4852-80b7-e470abd234f4 · outbound

This paper cites Hwang, Limit theorems for the number of summands in integer partitions.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Hwang, Limit theorems for the number of summands in integer partitions

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:16.394790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 12c0d6e7-3f77-47dc-97be-55906154759a · outbound

This paper cites Kowalski, Un Cours de Th´ eorie Analytique des Nombres.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Kowalski, Un Cours de Th´ eorie Analytique des Nombres

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:16.214922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6cd9bc51-9210-408b-8b67-45f998fedb25 · outbound

This paper cites an unresolved cited work.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:00:16.034524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 453707c3-af5f-4131-b9f3-c9019df39cdf · outbound

This paper cites an unresolved cited work.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:00:15.852336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 107d42c0-68a3-469d-8a42-f7ec39276301 · outbound

This paper cites A Local Limit Theorem for Integer Partitions into Small Powers.

Proof of a conjecture by Starr and log-concavity for random commuting permutations A Local Limit Theorem for Integer Partitions into Small Powers

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-07T06:00:13.192192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d32e8845-f869-4153-a312-f86fb07c3ac1 · outbound

This paper cites Madritsch, and S.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Madritsch, and S

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:15.684622Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 29e41169-38bd-4af5-aac8-0e59553569e0 · outbound

This paper cites Moser, M.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Moser, M

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:15.543239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a1675276-5017-4f73-88fb-e2561bbf5816 · outbound

This paper cites an unresolved cited work.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:00:15.384589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9dc8ba3a-a778-438a-8fe9-397e56c2ae5f · outbound

This paper cites Pemantle, and M.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Pemantle, and M

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:15.207187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2a144ca2-002e-42a2-b7ce-b4747f4481a7 · outbound

This paper cites Riemann, ¨Uber die Anzahl der Primzahlen unter einer gegebenen Gr¨ osse.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Riemann, ¨Uber die Anzahl der Primzahlen unter einer gegebenen Gr¨ osse

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:15.013643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a4a5984d-3f93-4f7d-a171-2d4ef63f9e48 · outbound

This paper cites Some Observations about the "Generalized Abundancy Index".

Proof of a conjecture by Starr and log-concavity for random commuting permutations Some Observations about the "Generalized Abundancy Index"

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-07T06:00:12.855215Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e72ddc37-c3bc-4c3c-b1ac-040850796505 · outbound

This paper cites Tao, Compactness and Contradiction.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Tao, Compactness and Contradiction

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:14.862504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3ae817ff-2f0d-4efb-be4e-da71b8d7fae9 · outbound

This paper cites Tenenbaum, Introduction to Analytic and Probabilistic Number Theory.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Tenenbaum, Introduction to Analytic and Probabilistic Number Theory

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:14.718793Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3a467c1c-193f-4ac0-9d31-92555086a113 · outbound

This paper cites Tenenbaum, J.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Tenenbaum, J

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:14.572814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 40897ef4-b5ec-4ade-88b5-8ed739590ff6 · outbound

This paper cites an unresolved cited work.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:00:14.357379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b27fb6f2-f833-4313-92c7-e3d671ec7c64 · outbound

This paper cites Wigert, Sur la s´ erie de Lambert et son application ` a la th´ eorie des nombres.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Wigert, Sur la s´ erie de Lambert et son application ` a la th´ eorie des nombres

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:14.141961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c5eb4bfb-2da0-46cf-910a-d67a04628179 · outbound

This paper cites Zagier, The Mellin transfom and related analytic techniques.

Proof of a conjecture by Starr and log-concavity for random commuting permutations Zagier, The Mellin transfom and related analytic techniques

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:00:13.936123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

Observation 83d568a1-e862-4b64-8c3c-4356da1403b6 · inbound

Dominant Zeros of Nekrasov--Okounkov Polynomials cites this paper.

Dominant Zeros of Nekrasov--Okounkov Polynomials Proof of a conjecture by Starr and log-concavity for random commuting permutations

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-07-03T17:28:44.666367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.