Paper Citation Record · LEDGER

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials

As of 8 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 1 inbound Pith citation observation for arXiv:2606.09545.

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

pith.paper-citation-record.v1
2606.09545 v2

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T11:50:26.030339Z

measured 19 of 19 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 2026-08-02T00:45:44.506261Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

18 of 18 outbound references displayed

verified exact13
verified fuzzy0
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 606ac6ab-92c1-432e-84aa-a039c003ad48 · outbound

This paper cites Abdesselam.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Abdesselam

Reference 1

Resolution: verified exact; doi, observed 2026-06-27T15:00:59.625380Z

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 9d288344-d618-46c9-8537-62fde1012872 · outbound

This paper cites Deléglise.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Deléglise

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-07-03T03:47:35.220783Z

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 cb229bf4-e0d2-4f58-b979-6bddfe4cd64b · outbound

This paper cites D’Arcais.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials D’Arcais

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-27T14:53:49.781305Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58838f42-0b13-42c4-8eee-f88aec9e756a · outbound

This paper cites Halberstam.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Halberstam

Reference 4

Resolution: verified exact; doi, observed 2026-06-27T15:00:59.614255Z

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 13d89e35-2a82-4f2c-9e7b-a3fc11741ae8 · outbound

This paper cites The Nekrasov-Okounkov hook length formula: refinement, elementary proof, extension and applications.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials The Nekrasov-Okounkov hook length formula: refinement, elementary proof, extension and applications

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-06-27T15:00:59.610152Z

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 81ac5b09-2009-4fe5-988d-7c3397380e14 · outbound

This paper cites Heim and M.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Heim and M

Reference 6

Resolution: verified exact; doi, observed 2026-06-27T15:00:59.604342Z

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 f6a02f70-2167-433e-b87a-77af584afe15 · outbound

This paper cites an unresolved cited work.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-27T14:53:49.781305Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d5136e0f-d030-4a37-b470-cade7a4ba23a · outbound

This paper cites an unresolved cited work.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Unresolved cited work

Reference 8

Resolution: verified exact; doi, observed 2026-06-27T15:00:59.621830Z

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 5c7f4148-78f2-4c4e-9726-79a89430ef6f · outbound

This paper cites an unresolved cited work.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Unresolved cited work

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-07-03T03:47:35.223526Z

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 861fe033-5a10-48bd-af45-ec7788b9e94d · outbound

This paper cites an unresolved cited work.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Unresolved cited work

Reference 10

Resolution: verified exact; doi, observed 2026-06-27T15:00:59.618462Z

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 942afc98-d5d4-4ad7-9bb2-c5c288f191e1 · outbound

This paper cites Summer 2010 research group on Abundancy, Abundancy bounds, 2010.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Summer 2010 research group on Abundancy, Abundancy bounds, 2010

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-27T14:53:49.781305Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78913804-2c6c-4797-a525-1ef915fba697 · outbound

This paper cites an unresolved cited work.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-27T14:53:49.781305Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d93ff89e-9327-43ba-b724-f59fd358c359 · outbound

This paper cites an unresolved cited work.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Unresolved cited work

Reference 13

Resolution: verified exact; doi, observed 2026-06-27T15:00:59.639590Z

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 2877bdcb-304b-4692-a25d-3694d2ad3ca6 · outbound

This paper cites an unresolved cited work.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Unresolved cited work

Reference 14

Resolution: verified exact; doi, observed 2026-06-27T15:00:59.634684Z

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 01f5e7bb-fc99-4ac2-8ca0-524d260f58e9 · outbound

This paper cites Ramanujan.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Ramanujan

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-27T14:53:49.781305Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 519ff302-958d-41ee-9cfa-405dd57b5e44 · outbound

This paper cites Starr, Asymptotics of the D’Arcais numbers at smallk, arXiv:2601.18599.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Starr, Asymptotics of the D’Arcais numbers at smallk, arXiv:2601.18599

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-07-03T03:47:35.218766Z

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 7eec5992-2ba9-4152-bcab-e2d995b120f8 · outbound

This paper cites an unresolved cited work.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Unresolved cited work

Reference 17

Resolution: verified exact; doi, observed 2026-06-27T15:00:59.629870Z

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 4c394205-aa2c-42d4-becc-e7b128c554cd · outbound

This paper cites an unresolved cited work.

On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials Unresolved cited work

Reference 18

Resolution: verified exact; doi, observed 2026-06-27T15:00:59.632173Z

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 61823559-4601-49dd-9dda-a72a58d3f8d2 · inbound

On the Log-Concavity of the D'Arcais Polynomials for Normalised Functions cites this paper.

On the Log-Concavity of the D'Arcais Polynomials for Normalised Functions On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T00:45:44.506261Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.