Paper Citation Record · LEDGER

Critical points of random polynomials and finite free cumulants

As of 12 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2506.08910.

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

pith.paper-citation-record.v1
2506.08910 v2

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:14:33.916895Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T21:04:04.480947Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T20:26:13.384124Z

Reference resolution

30 of 30 outbound references displayed

verified exact2
verified fuzzy12
unresolved16
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a1cf8e50-513f-4426-8bc4-58069dccae91 · outbound

This paper cites $S$-transform in Finite Free Probability.

Critical points of random polynomials and finite free cumulants $S$-transform in Finite Free Probability

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T05:14:33.823668Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b7ce41ae-bb1d-4066-a03c-7c06145eb19d · outbound

This paper cites Arizmendi, J.

Critical points of random polynomials and finite free cumulants Arizmendi, J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:14:34.304917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6b9b36fd-dcb8-4b12-b250-3cd4dfe3c00d · outbound

This paper cites Arizmendi and D.

Critical points of random polynomials and finite free cumulants Arizmendi and D

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T05:14:33.831055Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 24084e2c-d7b2-413c-bbd2-eb6d57f6b8ba · outbound

This paper cites Assiotis and J.

Critical points of random polynomials and finite free cumulants Assiotis and J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:14:34.287982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b3c1eede-41ce-4af5-8299-5c4c3315fb79 · outbound

This paper cites Bercovici and V.

Critical points of random polynomials and finite free cumulants Bercovici and V

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:14:34.276396Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f3503f1b-78fa-42b5-89b5-e62f734d6c6c · outbound

This paper cites Campbell.

Critical points of random polynomials and finite free cumulants Campbell

Reference 6

Resolution: verified exact; raw_fallback, observed 2026-08-07T05:14:34.053469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c0a92bb9-d4ec-4e45-afc2-5b20af964e95 · outbound

This paper cites Universality for roots of derivatives of entire functions via finite free probability.

Critical points of random polynomials and finite free cumulants Universality for roots of derivatives of entire functions via finite free probability

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T05:14:33.843626Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0d5369e3-6c46-4249-9cbe-3adec495a083 · outbound

This paper cites an unresolved cited work.

Critical points of random polynomials and finite free cumulants Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:14:34.265536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 926b9bf4-4a5c-4356-8282-9b5d165fd969 · outbound

This paper cites Gorin and V.

Critical points of random polynomials and finite free cumulants Gorin and V

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:14:34.253808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1ede3c87-5839-4c26-9697-7bf6949f39d2 · outbound

This paper cites Gorin and A.

Critical points of random polynomials and finite free cumulants Gorin and A

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T05:14:33.853038Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a38afa09-e017-4148-a877-b3db0312970c · outbound

This paper cites Roots of polynomials under repeated differentiation and repeated applications of fractional differential operators.

Critical points of random polynomials and finite free cumulants Roots of polynomials under repeated differentiation and repeated applications of fractional differential operators

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:14:33.964009Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 00abd10e-5722-438a-9ef9-041e8ab344e8 · outbound

This paper cites an unresolved cited work.

Critical points of random polynomials and finite free cumulants Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:14:34.237759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 57db2e76-d949-4314-9d8a-85238dae70d4 · outbound

This paper cites an unresolved cited work.

Critical points of random polynomials and finite free cumulants Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:14:34.225864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d3364672-b72c-479c-b300-0bfaaab83046 · outbound

This paper cites Hoskins and Z.

Critical points of random polynomials and finite free cumulants Hoskins and Z

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T05:14:33.864593Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f99fadda-fbe8-433d-a0e0-bd0b8be89c40 · outbound

This paper cites an unresolved cited work.

Critical points of random polynomials and finite free cumulants Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T05:14:33.867513Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4c62bbc4-f150-41d2-b4c3-3f7576a92723 · outbound

This paper cites Kabluchko and H.

Critical points of random polynomials and finite free cumulants Kabluchko and H

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:14:34.202123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 016643ca-c012-4419-82b6-5f8be539c7b4 · outbound

This paper cites Kallenberg.

Critical points of random polynomials and finite free cumulants Kallenberg

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T05:14:33.873152Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23e99a69-45ef-430c-b0ad-b16a9277db54 · outbound

This paper cites Polynomial convolutions and (finite) free probability.

Critical points of random polynomials and finite free cumulants Polynomial convolutions and (finite) free probability

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T05:14:33.876321Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5d4a2b39-40f8-434c-85ea-410399c558b2 · outbound

This paper cites an unresolved cited work.

Critical points of random polynomials and finite free cumulants Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T05:14:33.879711Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 392bda1d-7302-417f-bec4-a16f2de1bd5e · outbound

This paper cites an unresolved cited work.

Critical points of random polynomials and finite free cumulants Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T05:14:33.882284Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d8c1939-4292-40cc-9135-9811c089512a · outbound

This paper cites an unresolved cited work.

Critical points of random polynomials and finite free cumulants Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T05:14:33.885094Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9edff86e-037d-4404-8b86-0cddf5610787 · outbound

This paper cites Michelen and X.-T.

Critical points of random polynomials and finite free cumulants Michelen and X.-T

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:14:34.166164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 25b57f4c-1999-4de1-af9f-edf17f3480c6 · outbound

This paper cites Michelen and X.-T.

Critical points of random polynomials and finite free cumulants Michelen and X.-T

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:14:34.154493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 05936c95-27da-4810-a7e7-0927e1fd5e40 · outbound

This paper cites an unresolved cited work.

Critical points of random polynomials and finite free cumulants Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:14:34.143178Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 9679c6b7-ca2e-4851-ada8-4d613f6aec31 · outbound

This paper cites O’Rourke and N.

Critical points of random polynomials and finite free cumulants O’Rourke and N

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:14:34.130920Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e2b26d33-406c-484e-a23a-2127a75cfb6f · outbound

This paper cites O’Rourke and N.

Critical points of random polynomials and finite free cumulants O’Rourke and N

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:14:34.118595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0a219400-e82d-43ab-b4d5-dd31f55ee06b · outbound

This paper cites Pemantle and I.

Critical points of random polynomials and finite free cumulants Pemantle and I

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:14:34.108137Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a8d43ba7-369c-4c16-a15a-c97848324df6 · outbound

This paper cites Pemantle and S.

Critical points of random polynomials and finite free cumulants Pemantle and S

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:14:34.097015Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 42ee0303-fbbc-483f-bae2-0fa3a92b23ce · outbound

This paper cites an unresolved cited work.

Critical points of random polynomials and finite free cumulants Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:14:34.085736Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a8ee355d-a5e1-46fb-9ffa-46a528af585f · outbound

This paper cites Shlyakhtenko and T.

Critical points of random polynomials and finite free cumulants Shlyakhtenko and T

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:14:34.074752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

Observation 567f8dce-5150-4729-85e2-1ca0285c0ccc · inbound

P\'olya--Schur problems and free probability cites this paper.

P\'olya--Schur problems and free probability Critical points of random polynomials and finite free cumulants

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-07-01T20:26:13.386048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.