Paper Citation Record · LEDGER

Dragging the roots of a polynomial to the unit circle

As of 16 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 1 inbound Pith citation observation for arXiv:1908.03208.

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

pith.paper-citation-record.v1
1908.03208 v3

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:40:10.036297Z

measured 48 of 48 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-14T15:38:57.337054Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-14T15:38:57.367934Z

Reference resolution

47 of 47 outbound references displayed

verified exact14
verified fuzzy16
unresolved10
parse uncertain0
malformed identifier7
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5b29e4bc-c46a-4431-8b3f-458dbfe38dc8 · outbound

This paper cites Basic hypergeometric polynomials with zeros on the unit circle.

Dragging the roots of a polynomial to the unit circle Basic hypergeometric polynomials with zeros on the unit circle

Reference 1

Resolution: verified exact; doi, observed 2026-08-14T14:40:10.392362Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a1e5582f-0382-4211-83a2-d4fcfc5819dc · outbound

This paper cites Combinatorics and complexity of partition func- tions.

Dragging the roots of a polynomial to the unit circle Combinatorics and complexity of partition func- tions

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-14T14:40:09.806982Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4dcfaa11-f0c8-4336-8974-041221750851 · outbound

This paper cites Algorithms in real algebraic geometry.

Dragging the roots of a polynomial to the unit circle Algorithms in real algebraic geometry

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.924623Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 02217cc1-4cb5-47b7-b3a4-253dba7fda92 · outbound

This paper cites Palindromic and per- turbed polynomials: zeros location.

Dragging the roots of a polynomial to the unit circle Palindromic and per- turbed polynomials: zeros location

Reference 4

Resolution: verified exact; doi, observed 2026-08-14T14:40:10.365662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fd112482-fc80-44cc-906c-3ae7f5514253 · outbound

This paper cites Unimodality, log-concavity, real-rootedness and be- yond.

Dragging the roots of a polynomial to the unit circle Unimodality, log-concavity, real-rootedness and be- yond

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.906284Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2f03577c-1cc7-4d7c-a6a9-ee1218f8cf42 · outbound

This paper cites Proof of the monotone column permanent con- jecture.

Dragging the roots of a polynomial to the unit circle Proof of the monotone column permanent con- jecture

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.889751Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3b4115fe-f77c-4344-a53e-50fd496a2429 · outbound

This paper cites Computing symmetry groups of polyhedra.

Dragging the roots of a polynomial to the unit circle Computing symmetry groups of polyhedra

Reference 7

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation cfee48a0-76ec-44e4-9882-881735cafc77 · outbound

This paper cites QEPCAD B: a program for computing with semi-algebraic sets using CADs.

Dragging the roots of a polynomial to the unit circle QEPCAD B: a program for computing with semi-algebraic sets using CADs

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.858879Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 53a18479-a0fd-423b-8c2d-d9e54b005fa3 · outbound

This paper cites Polytopes, rings, and K-theory.

Dragging the roots of a polynomial to the unit circle Polytopes, rings, and K-theory

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-14T14:40:09.852341Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 03e80839-3abb-4ea0-bc1a-e6fa49ecfd85 · outbound

This paper cites On the polynomials with all their zeros on the unit circle.

Dragging the roots of a polynomial to the unit circle On the polynomials with all their zeros on the unit circle

Reference 10

Resolution: verified exact; raw_fallback, observed 2026-08-14T14:40:10.558521Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation bf015495-8fa1-4df6-93c4-36d0782c000d · outbound

This paper cites The roots of the indepen- dence polynomial of a clawfree graph.

Dragging the roots of a polynomial to the unit circle The roots of the indepen- dence polynomial of a clawfree graph

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-14T14:40:09.863083Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4463d6e1-b346-48e5-8a3f-196fa4b52ef0 · outbound

This paper cites A course in computational algebraic number theory.

Dragging the roots of a polynomial to the unit circle A course in computational algebraic number theory

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-14T14:40:09.868375Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4088d409-8544-4a51-98e3-d0dd20c0180d · outbound

This paper cites Roots on a Circle.

Dragging the roots of a polynomial to the unit circle Roots on a Circle

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.842134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 560d86b0-82bf-4d21-bdac-7092388d05e6 · outbound

This paper cites Zeros and irreducibility of polynomi- als with gcd powers as coeﬃcients.

Dragging the roots of a polynomial to the unit circle Zeros and irreducibility of polynomi- als with gcd powers as coeﬃcients

Reference 14

Resolution: verified exact; doi, observed 2026-08-14T14:40:10.302980Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0f3e8ebc-1d61-4b6d-b631-d0c27a18e6b2 · outbound

This paper cites Combinatorial convexity and algebraic geometry.

Dragging the roots of a polynomial to the unit circle Combinatorial convexity and algebraic geometry

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-14T14:40:09.883093Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a41fbed-319b-4c07-a7a4-8bce5f9240eb · outbound

This paper cites Polynomials, roots, and interlacing.

Dragging the roots of a polynomial to the unit circle Polynomials, roots, and interlacing

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-14T14:40:09.887593Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b6e2a312-8603-4c98-8870-ba5cb44ee9a2 · outbound

This paper cites Hecke operators on rational functions. I.

Dragging the roots of a polynomial to the unit circle Hecke operators on rational functions. I

Reference 17

Resolution: verified exact; doi, observed 2026-08-14T14:40:10.274870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7237895d-c482-4268-87a5-e50224c747af · outbound

This paper cites Zeros of some self-reciprocal polynomials.

Dragging the roots of a polynomial to the unit circle Zeros of some self-reciprocal polynomials

Reference 18

Resolution: malformed identifier; raw_fallback, observed 2026-08-14T14:40:10.825023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7193ff01-1970-40f6-ab94-89b0d523fe22 · outbound

This paper cites Self-inversive polynomials, curves, and codes.

Dragging the roots of a polynomial to the unit circle Self-inversive polynomials, curves, and codes

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.807689Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a04b4bf8-1487-4ef2-9ebc-52caaa8b7c93 · outbound

This paper cites A su ﬃcient condition for all the roots of a polyno- mial to be real.

Dragging the roots of a polynomial to the unit circle A su ﬃcient condition for all the roots of a polyno- mial to be real

Reference 20

Resolution: verified exact; doi, observed 2026-08-14T14:40:10.256160Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 55727684-2164-407d-b8c1-a23c1096ac8c · outbound

This paper cites Reciprocal polynomials with all zeros on the unit cir- cle.

Dragging the roots of a polynomial to the unit circle Reciprocal polynomials with all zeros on the unit cir- cle

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.789826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 994e9fe8-11d2-4436-9e41-cb9dd45e93ce · outbound

This paper cites Circular interlacing with re- ciprocal polynomials.

Dragging the roots of a polynomial to the unit circle Circular interlacing with re- ciprocal polynomials

Reference 22

Resolution: malformed identifier; raw_fallback, observed 2026-08-14T14:40:10.774144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 56cafeca-d3d1-4f0f-944e-794e6cf330d0 · outbound

This paper cites On zeros of reciprocal poly- nomials of odd degree.

Dragging the roots of a polynomial to the unit circle On zeros of reciprocal poly- nomials of odd degree

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.757449Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 68715ca4-78f7-4044-9e20-720a692f805e · outbound

This paper cites Polynomials with all zeros on the unit circle.

Dragging the roots of a polynomial to the unit circle Polynomials with all zeros on the unit circle

Reference 24

Resolution: verified exact; doi, observed 2026-08-14T14:40:10.214731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 01351709-7fb0-4189-80b4-6027b41e8505 · outbound

This paper cites Self-inversive polynomials whose zeros are on the unit circle.

Dragging the roots of a polynomial to the unit circle Self-inversive polynomials whose zeros are on the unit circle

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.738612Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 171e4ca3-140f-469c-b514-f537153d2343 · outbound

This paper cites Variations of the Ramanu- jan polynomials and remarks on ζ(2 j + 1)/n2 j+1.

Dragging the roots of a polynomial to the unit circle Variations of the Ramanu- jan polynomials and remarks on ζ(2 j + 1)/n2 j+1

Reference 26

Resolution: malformed identifier; doi_truncated, observed 2026-08-14T14:40:10.194318Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a2476f96-08b5-479e-9a6a-9111a73e0f49 · outbound

This paper cites Unimodularity of zeros of self- inversive polynomials.

Dragging the roots of a polynomial to the unit circle Unimodularity of zeros of self- inversive polynomials

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.719828Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 32c94102-220b-4338-8472-1578e52d4b48 · outbound

This paper cites Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model.

Dragging the roots of a polynomial to the unit circle Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.700388Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 00344002-18fe-42f1-b381-3fa465cafe8e · outbound

This paper cites Large finite products of small fractions.

Dragging the roots of a polynomial to the unit circle Large finite products of small fractions

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-14T14:40:10.440109Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e625d793-bff5-45d5-a039-269f51b83635 · outbound

This paper cites Geometry of polynomials.

Dragging the roots of a polynomial to the unit circle Geometry of polynomials

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.682942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 419bb7e8-861f-45ea-b0ee-ec230a2075fd · outbound

This paper cites Conjugate recip- rocal polynomials with all roots on the unit circle.

Dragging the roots of a polynomial to the unit circle Conjugate recip- rocal polynomials with all roots on the unit circle

Reference 31

Resolution: malformed identifier; doi_truncated, observed 2026-08-14T14:40:10.159038Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4b21f5a5-3115-429f-ba84-16b0e81f56d9 · outbound

This paper cites an unresolved cited work.

Dragging the roots of a polynomial to the unit circle Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:40:10.665334Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 89ebd332-32c0-42cc-9cad-a4abb01a7c74 · outbound

This paper cites SageMath, the Sage Mathematics Software Sys- tem (Version 8.2).

Dragging the roots of a polynomial to the unit circle SageMath, the Sage Mathematics Software Sys- tem (Version 8.2)

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.644625Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a3747f41-4623-43a4-b0fa-0b11da57b913 · outbound

This paper cites The s-Eulerian polynomials have only real roots.

Dragging the roots of a polynomial to the unit circle The s-Eulerian polynomials have only real roots

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.624124Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 93f9858c-19c3-4ca1-853b-add3ea5fa2de · outbound

This paper cites The Fourier transform of functions of the great- est common divisor.

Dragging the roots of a polynomial to the unit circle The Fourier transform of functions of the great- est common divisor

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.607792Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6148ea3f-b0df-4592-8383-e1338c9512fa · outbound

This paper cites Arithmetical functions.

Dragging the roots of a polynomial to the unit circle Arithmetical functions

Reference 36

Resolution: verified exact; doi, observed 2026-08-14T14:40:10.132488Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b12320ed-ca6b-4dbc-9e85-40723acfa348 · outbound

This paper cites Sheil-Small.

Dragging the roots of a polynomial to the unit circle Sheil-Small

Reference 37

Resolution: verified exact; doi, observed 2026-08-14T14:40:10.116532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fbdcf105-dd2c-4df0-b51c-10a851279f2d · outbound

This paper cites The discrete Fourier transform of r-even functions.

Dragging the roots of a polynomial to the unit circle The discrete Fourier transform of r-even functions

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:40:10.589904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e32226e7-d8b9-4a2f-8568-fa4fdcd95389 · outbound

This paper cites How to count the number of zeros that a polynomial has on the unit circle?.

Dragging the roots of a polynomial to the unit circle How to count the number of zeros that a polynomial has on the unit circle?

Reference 39

Resolution: verified exact; local_arxiv, observed 2026-08-14T14:40:10.415752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0230b2d3-7207-4909-b296-a25fba7b8a2a · outbound

This paper cites Polynomials with Symmetric Zeros.

Dragging the roots of a polynomial to the unit circle Polynomials with Symmetric Zeros

Reference 40

Resolution: malformed identifier; raw_fallback, observed 2026-08-14T14:40:10.574161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c9f6f060-8b77-455c-902f-e57d4c6a625f · outbound

This paper cites Polynomials with real zeros and Pólya frequency sequences.

Dragging the roots of a polynomial to the unit circle Polynomials with real zeros and Pólya frequency sequences

Reference 41

Resolution: verified exact; doi, observed 2026-08-14T14:40:10.101354Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 00fe9bc8-a646-4ea3-ad08-dca631c1d7d6 · outbound

This paper cites A one-line high school algebra proof of the uni- modality of the Gaussian polynomials [ n k] for k < 20.

Dragging the roots of a polynomial to the unit circle A one-line high school algebra proof of the uni- modality of the Gaussian polynomials [ n k] for k < 20

Reference 42

Resolution: malformed identifier; no resolver link, observed 2026-08-14T14:40:10.031115Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc0b4727-c331-454f-b41d-2b9fe0bee0ca · outbound

This paper cites an unresolved cited work.

Dragging the roots of a polynomial to the unit circle Unresolved cited work

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-14T14:40:10.036297Z

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Unavailable: canonical work link unavailable.

Observation ec7eebd3-d199-4188-b5b8-1222fb289842 · outbound

This paper cites an unresolved cited work.

Dragging the roots of a polynomial to the unit circle Unresolved cited work

Reference 78

Resolution: unresolved; no resolver link, observed 2026-08-14T14:40:09.835653Z

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Unavailable: canonical work link unavailable.

Observation 22295077-26a3-4d74-bb6b-201f52ad9e17 · outbound

This paper cites an unresolved cited work.

Dragging the roots of a polynomial to the unit circle Unresolved cited work

Reference 101

Resolution: verified exact; doi, observed 2026-08-14T14:40:10.176600Z

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Observation 1e197e3e-1477-4657-8620-088d8b283530 · outbound

This paper cites an unresolved cited work.

Dragging the roots of a polynomial to the unit circle Unresolved cited work

Reference 769

Resolution: verified exact; doi, observed 2026-08-14T14:40:10.235804Z

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Observation 1201f760-cfc3-4475-b2e8-47a54f8925b8 · outbound

This paper cites REFERENCES 61.

Dragging the roots of a polynomial to the unit circle REFERENCES 61

Reference 1466

Resolution: unresolved; no resolver link, observed 2026-08-14T14:40:09.991428Z

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Unavailable: canonical work link unavailable.

Pith citing papers

Observation bf11908a-f1da-4075-8ca6-46d3bb13f3e9 · inbound

Large finite products of small fractions cites this paper.

Large finite products of small fractions Dragging the roots of a polynomial to the unit circle

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-14T15:38:57.372852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.