Paper Citation Record · LEDGER

Closure under factorization from a result of Furstenberg

As of 21 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2506.23214.

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

pith.paper-citation-record.v1
2506.23214 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:02:48.833473Z

measured 34 of 34 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

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Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Reference resolution

34 of 34 outbound references displayed

verified exact13
verified fuzzy4
unresolved16
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External citation measurements

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Outbound references

Observation bbacf292-5bdb-447c-b748-149e9a34c2d7 · outbound

This paper cites write newline toupdate empty.

Closure under factorization from a result of Furstenberg write newline toupdate empty

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:02:52.604174Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 37e43c74-69fe-4f6b-9f86-05d2ab8718eb · outbound

This paper cites an unresolved cited work.

Closure under factorization from a result of Furstenberg Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:44.811794Z

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Observation 4b386a6c-f508-4913-9512-56f4182c1679 · outbound

This paper cites http://dx.doi.org/10.1109/FOCS61266.2024.00138 Constant-Depth Arithmetic Circuits for Linear Algebra Problems.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.1109/FOCS61266.2024.00138 Constant-Depth Arithmetic Circuits for Linear Algebra Problems

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:44.883314Z

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Observation 4d75ca38-e343-4263-9793-a3877b3a5a64 · outbound

This paper cites Deterministic factorization of constant-depth algebraic circuits in subexponential time.

Closure under factorization from a result of Furstenberg Deterministic factorization of constant-depth algebraic circuits in subexponential time

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:02:50.432402Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 702f6b4f-15bb-426d-b844-34df61e15ed7 · outbound

This paper cites http://dx.doi.org/10.1145/3365667 Deterministic Factorization of Sparse Polynomials with Bounded Individual Degree.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.1145/3365667 Deterministic Factorization of Sparse Polynomials with Bounded Individual Degree

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:45.074059Z

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Observation b58eed5d-b9a2-49eb-be63-1e82d1c6b95c · outbound

This paper cites http://dx.doi.org/10.1007/S10208-002-0059-5 The Complexity of Factors of Multivariate Polynomials.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.1007/S10208-002-0059-5 The Complexity of Factors of Multivariate Polynomials

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:45.161087Z

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Observation 705afbc6-f668-4010-b0dc-44056abae85b · outbound

This paper cites http://dx.doi.org/10.4086/toc.2019.v015a013 Closure Results for Polynomial Factorization.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.4086/toc.2019.v015a013 Closure Results for Polynomial Factorization

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:45.244439Z

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Observation e84a3a69-e490-429f-8b2d-4cb7769234cb · outbound

This paper cites http://dx.doi.org/10.1145/3510359 Discovering the Roots: Uniform Closure Results for Algebraic Classes Under Factoring.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.1145/3510359 Discovering the Roots: Uniform Closure Results for Algebraic Classes Under Factoring

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:45.397556Z

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Observation 11b7ebb0-d63d-41ec-90a9-cd777f7a16f9 · outbound

This paper cites https://arxiv.org/abs/2411.17330 Derandomizing Multivariate Polynomial Factoring for Low Degree Factors , 2024.

Closure under factorization from a result of Furstenberg https://arxiv.org/abs/2411.17330 Derandomizing Multivariate Polynomial Factoring for Low Degree Factors , 2024

Reference 9

Resolution: verified exact; raw_fallback, observed 2026-08-06T22:02:51.801230Z

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Observation 162f4329-b1e1-41a3-93d2-5a236e1d28ed · outbound

This paper cites http://dx.doi.org/10.1137/080735850 Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.1137/080735850 Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:45.709368Z

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Observation 58068a8d-0e00-417d-90b7-1df39f1f529d · outbound

This paper cites Polynomial identity testing of read-once oblivious algebraic branching programs.

Closure under factorization from a result of Furstenberg Polynomial identity testing of read-once oblivious algebraic branching programs

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:02:52.395449Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 87d52dac-e95b-4698-9bab-f3f3ec5e8591 · outbound

This paper cites an unresolved cited work.

Closure under factorization from a result of Furstenberg Unresolved cited work

Reference 12

Resolution: verified exact; doi, observed 2026-08-06T22:02:50.251929Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 53dd1e02-0870-4924-a636-968fda65f06f · outbound

This paper cites Forbes and Amir Shpilka.

Closure under factorization from a result of Furstenberg Forbes and Amir Shpilka

Reference 13

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T22:02:51.592139Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8a5ad887-14c8-4217-88c6-3c89fd305969 · outbound

This paper cites http://dx.doi.org/https://doi.org/10.1016/0021-8693(67)90061-0 Algebraic functions over finite fields.

Closure under factorization from a result of Furstenberg http://dx.doi.org/https://doi.org/10.1016/0021-8693(67)90061-0 Algebraic functions over finite fields

Reference 14

Resolution: verified exact; doi, observed 2026-08-06T22:02:50.080423Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ea89e227-040a-4eda-9784-6b831c7ea902 · outbound

This paper cites an unresolved cited work.

Closure under factorization from a result of Furstenberg Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:46.779917Z

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Observation a1828e50-377c-4f30-ba44-5cdd5b9bba9c · outbound

This paper cites von zur Gathen and E.

Closure under factorization from a result of Furstenberg von zur Gathen and E

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:47.216870Z

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Observation 0754ce19-5a0c-4e72-a3fe-8d68b742493c · outbound

This paper cites Essential coding theory.

Closure under factorization from a result of Furstenberg Essential coding theory

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:02:52.250382Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f52b7fcf-7258-4d35-aca3-841b55b412f9 · outbound

This paper cites Explicit Implicit Function Theorem for All Fields.

Closure under factorization from a result of Furstenberg Explicit Implicit Function Theorem for All Fields

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:02:51.305463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e520768d-cb41-41b1-942d-5996f0cf11a2 · outbound

This paper cites Kaltofen.

Closure under factorization from a result of Furstenberg Kaltofen

Reference 19

Resolution: verified exact; doi, observed 2026-08-06T22:02:49.900230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 7ea968af-ef63-4124-9014-a855080848c3 · outbound

This paper cites http://dx.doi.org/10.1137/0214035 Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.1137/0214035 Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization

Reference 20

Resolution: verified exact; doi, observed 2026-08-06T22:02:49.687866Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e2c67980-38cd-4f2c-a1ad-646016bb3fbc · outbound

This paper cites https://users.cs.duke.edu/ elk27/bibliography/89/Ka89_slpfac.pdf Factorization of Polynomials Given by Straight-Line Programs.

Closure under factorization from a result of Furstenberg https://users.cs.duke.edu/ elk27/bibliography/89/Ka89_slpfac.pdf Factorization of Polynomials Given by Straight-Line Programs

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:02:52.111983Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ed975e44-facb-4ad1-99bf-ac20ee7a8164 · outbound

This paper cites http://dx.doi.org/10.1007/s00037-004-0182-6 D erandomizing Polynomial Identity Tests Means Proving Circuit Lower Bounds.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.1007/s00037-004-0182-6 D erandomizing Polynomial Identity Tests Means Proving Circuit Lower Bounds

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:47.703544Z

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Observation c43616a1-9347-4de6-9ee9-7d2d96f8820d · outbound

This paper cites Deterministic Algorithms for Low Degree Factors of Constant Depth Circuits.

Closure under factorization from a result of Furstenberg Deterministic Algorithms for Low Degree Factors of Constant Depth Circuits

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:02:49.554394Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f73c5af4-48a1-4f1e-84f1-1a1a2b6c8028 · outbound

This paper cites Towards Deterministic Algorithms for Constant-Depth Factors of Constant-Depth Circuits.

Closure under factorization from a result of Furstenberg Towards Deterministic Algorithms for Constant-Depth Factors of Constant-Depth Circuits

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:02:51.151334Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2e97004a-0012-4dca-b791-53ce5ca43dac · outbound

This paper cites http://dx.doi.org/10.1007/s00037-015-0102-y Equivalence of Polynomial Identity Testing and Polynomial Factorization.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.1007/s00037-015-0102-y Equivalence of Polynomial Identity Testing and Polynomial Factorization

Reference 25

Resolution: verified exact; doi, observed 2026-08-06T22:02:49.376873Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ce9d54d4-3af5-4159-8655-5e9c298c02ae · outbound

This paper cites Kaltofen and Barry M.

Closure under factorization from a result of Furstenberg Kaltofen and Barry M

Reference 26

Resolution: verified exact; raw_fallback, observed 2026-08-06T22:02:50.970147Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 111aa4e0-c2c0-4e25-9597-dcd9f538955d · outbound

This paper cites http://dx.doi.org/https://doi.org/10.1016/j.jsc.2007.01.003 Improved dense multivariate polynomial factorization algorithms.

Closure under factorization from a result of Furstenberg http://dx.doi.org/https://doi.org/10.1016/j.jsc.2007.01.003 Improved dense multivariate polynomial factorization algorithms

Reference 27

Resolution: verified exact; doi, observed 2026-08-06T22:02:49.183225Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d8d6b7f7-d1be-4f28-89ea-f3103e24bb5f · outbound

This paper cites http://dx.doi.org/10.1109/FOCS52979.2021.00083 Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.1109/FOCS52979.2021.00083 Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits

Reference 28

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Observation 97b66229-959a-4599-85f0-a4c928b0e451 · outbound

This paper cites http://dx.doi.org/10.1007/S00037-016-0130-2 Factors of low individual degree polynomials.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.1007/S00037-016-0130-2 Factors of low individual degree polynomials

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:48.424078Z

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Observation b1b1bb3f-ec6c-4abf-8e0b-29eff46d90e0 · outbound

This paper cites A ridiculously simple and explicit implicit function theorem.

Closure under factorization from a result of Furstenberg A ridiculously simple and explicit implicit function theorem

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:48.511993Z

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Observation 5087d3c3-2d59-4465-bd4d-01263ada98c0 · outbound

This paper cites http://dx.doi.org/10.4230/LIPIcs.CCC.2020.33 Factorization of Polynomials Given By Arithmetic Branching Programs.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.4230/LIPIcs.CCC.2020.33 Factorization of Polynomials Given By Arithmetic Branching Programs

Reference 31

Resolution: verified exact; doi, observed 2026-08-06T22:02:48.996929Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1dc9ceb6-b1e7-4dbf-91ff-0a0a7054a771 · outbound

This paper cites http://dx.doi.org/10.1017/CBO9780511609589 Enumerative Combinatorics - Volume 2.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.1017/CBO9780511609589 Enumerative Combinatorics - Volume 2

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:48.663717Z

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Observation 7276b65c-ebff-41d8-9f4f-97423275b9d8 · outbound

This paper cites http://dx.doi.org/10.1080/00029890.2023.2251344 Lagrange Inversion Formula by Induction.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.1080/00029890.2023.2251344 Lagrange Inversion Formula by Induction

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:48.756702Z

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Observation 7e6dfb24-01d1-45d5-af5e-f78bf2b60dc4 · outbound

This paper cites http://dx.doi.org/10.1017/CBO9781139856065 Modern Computer Algebra.

Closure under factorization from a result of Furstenberg http://dx.doi.org/10.1017/CBO9781139856065 Modern Computer Algebra

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-06T22:02:48.833473Z

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