Paper Citation Record · LEDGER

Planar Perfect Matching Counting is as Hard as Determinants

As of 15 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2606.03975.

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

pith.paper-citation-record.v1
2606.03975 v1

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-28T07:13:05.776275Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

49 of 49 outbound references displayed

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verified fuzzy0
unresolved48
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b34edc93-67c3-4733-98f6-7799c5b84b29 · outbound

This paper cites A full dichotomy for Holant ^ c , inspired by quantum computation.

Planar Perfect Matching Counting is as Hard as Determinants A full dichotomy for Holant ^ c , inspired by quantum computation

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Unavailable: canonical work link unavailable.

Observation f2bb97c3-258b-4270-8c52-39b707e6c353 · outbound

This paper cites an unresolved cited work.

Planar Perfect Matching Counting is as Hard as Determinants Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 1c76ab36-1b50-4776-9209-9b8c545cec24 · outbound

This paper cites Beyond bilinear complexity: What works and what breaks with many modes? Electron.

Planar Perfect Matching Counting is as Hard as Determinants Beyond bilinear complexity: What works and what breaks with many modes? Electron

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 96421902-963d-4883-b4c4-8118d6d32762 · outbound

This paper cites Berkowitz.

Planar Perfect Matching Counting is as Hard as Determinants Berkowitz

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 0a181a68-ffd1-4bbc-9b22-7136ff77978a · outbound

This paper cites Bunch and John E.

Planar Perfect Matching Counting is as Hard as Determinants Bunch and John E

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 690d8376-0e07-4aac-94d8-58e50fb33bfe · outbound

This paper cites The complexity of partial derivatives.

Planar Perfect Matching Counting is as Hard as Determinants The complexity of partial derivatives

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 2e707104-35e2-494d-a302-2eb410de0950 · outbound

This paper cites Completeness classes in algebraic complexity theory.

Planar Perfect Matching Counting is as Hard as Determinants Completeness classes in algebraic complexity theory

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-07-02T07:06:43.916439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 462cf2b1-9555-4f2c-968c-eda473ce03cb · outbound

This paper cites Some results on matchgates and holographic algorithms.

Planar Perfect Matching Counting is as Hard as Determinants Some results on matchgates and holographic algorithms

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 8ee999a5-9a8d-418c-bd36-a85ff6c8bbc8 · outbound

This paper cites Complexity dichotomies for counting problems.

Planar Perfect Matching Counting is as Hard as Determinants Complexity dichotomies for counting problems

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation cfcfeaa8-5a17-4b82-a137-82701e9de2fd · outbound

This paper cites On the theory of matchgate computations.

Planar Perfect Matching Counting is as Hard as Determinants On the theory of matchgate computations

Reference 10

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Observation 7483abf0-ece4-405d-b2a1-f73876ff7704 · outbound

This paper cites Holographic algorithm with matchgates is universal for planar \# csp over boolean domain.

Planar Perfect Matching Counting is as Hard as Determinants Holographic algorithm with matchgates is universal for planar \# csp over boolean domain

Reference 11

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Observation 535efd1c-4862-4be4-b3f7-3b9522debe0d · outbound

This paper cites FKT is not universal - A planar H olant dichotomy for symmetric constraints.

Planar Perfect Matching Counting is as Hard as Determinants FKT is not universal - A planar H olant dichotomy for symmetric constraints

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 485a8d3c-1ad3-48f4-9fb9-73afd804d93f · outbound

This paper cites Matchgates revisited.

Planar Perfect Matching Counting is as Hard as Determinants Matchgates revisited

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation b62938bf-2d58-49be-85db-38a3752a73ea · outbound

This paper cites Holographic algorithms: From art to science.

Planar Perfect Matching Counting is as Hard as Determinants Holographic algorithms: From art to science

Reference 14

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Observation af03e140-ad8c-4579-a342-c5908fa0eeb4 · outbound

This paper cites Werner, and Freek Witteveen.

Planar Perfect Matching Counting is as Hard as Determinants Werner, and Freek Witteveen

Reference 15

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Observation d2c1753c-b019-4ead-9103-6001dc79b9f4 · outbound

This paper cites Dichotomy for H olant\( ^ \( _ \) \) problems on the boolean domain.

Planar Perfect Matching Counting is as Hard as Determinants Dichotomy for H olant\( ^ \( _ \) \) problems on the boolean domain

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 4738ce14-7a2f-4751-8f81-69c904c90ac4 · outbound

This paper cites Parameterizing the permanent: Hardness for fixed excluded minors.

Planar Perfect Matching Counting is as Hard as Determinants Parameterizing the permanent: Hardness for fixed excluded minors

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation a920e3bb-2f05-4c6f-a26b-5ef9c0637266 · outbound

This paper cites Paths, trees, and flowers.

Planar Perfect Matching Counting is as Hard as Determinants Paths, trees, and flowers

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 1b0c2f29-841f-43a0-8bc5-113aa3900548 · outbound

This paper cites Evenbly and G.

Planar Perfect Matching Counting is as Hard as Determinants Evenbly and G

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation c9bdb8a2-90b7-4eb7-b01c-b72040534177 · outbound

This paper cites On the expressive power of planar perfect matching and permanents of bounded treewidth matrices.

Planar Perfect Matching Counting is as Hard as Determinants On the expressive power of planar perfect matching and permanents of bounded treewidth matrices

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 2ef37188-c177-4946-95ba-8e246f4fee45 · outbound

This paper cites Nested dissection of a regular finite element mesh.

Planar Perfect Matching Counting is as Hard as Determinants Nested dissection of a regular finite element mesh

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 37658b49-05dc-4541-8bf1-415fb923b516 · outbound

This paper cites A dichotomy for real weighted H olant problems.

Planar Perfect Matching Counting is as Hard as Determinants A dichotomy for real weighted H olant problems

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 085f52e9-1671-4854-9b5e-58b32d38df84 · outbound

This paper cites Towards quantum machine learning with tensor networks.

Planar Perfect Matching Counting is as Hard as Determinants Towards quantum machine learning with tensor networks

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 368d6408-8475-4129-bca1-64726be56092 · outbound

This paper cites On the complexity of k- SAT.

Planar Perfect Matching Counting is as Hard as Determinants On the complexity of k- SAT

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 43cc78dd-b1bd-47c0-8b9d-8e982bb52191 · outbound

This paper cites Jaeger, D.

Planar Perfect Matching Counting is as Hard as Determinants Jaeger, D

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 3ff180d9-d28d-4abe-8b0b-7d561a30b5f7 · outbound

This paper cites an unresolved cited work.

Planar Perfect Matching Counting is as Hard as Determinants Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 2d4f3f26-a57d-4603-a09f-93dc0b557f10 · outbound

This paper cites Kaltofen and Pascal Koiran.

Planar Perfect Matching Counting is as Hard as Determinants Kaltofen and Pascal Koiran

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 9526b08c-6f52-43a4-99e1-e05d507db4b3 · outbound

This paper cites Lipton, Donald J.

Planar Perfect Matching Counting is as Hard as Determinants Lipton, Donald J

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 8da3aa17-ca88-43fa-a75c-e21f4d17198a · outbound

This paper cites Characterizing V aliant's algebraic complexity classes.

Planar Perfect Matching Counting is as Hard as Determinants Characterizing V aliant's algebraic complexity classes

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 78014962-135d-4ee8-b3bf-9cb3b15de83a · outbound

This paper cites Maximum matchings in planar graphs via gaussian elimination.

Planar Perfect Matching Counting is as Hard as Determinants Maximum matchings in planar graphs via gaussian elimination

Reference 30

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Observation 75d88de4-6e82-42a6-8f38-2db47b0418fb · outbound

This paper cites an unresolved cited work.

Planar Perfect Matching Counting is as Hard as Determinants Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 43f1bf40-2ec4-4eb6-85cf-aefc327b9b04 · outbound

This paper cites an unresolved cited work.

Planar Perfect Matching Counting is as Hard as Determinants Unresolved cited work

Reference 32

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Observation 47e46a3a-304f-48c8-9c72-3304883c415c · outbound

This paper cites A dichotomy for real boolean H olant problems.

Planar Perfect Matching Counting is as Hard as Determinants A dichotomy for real boolean H olant problems

Reference 33

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation df1f0610-f592-46fe-adb8-bed90324a184 · outbound

This paper cites Partial and total matrix multiplication.

Planar Perfect Matching Counting is as Hard as Determinants Partial and total matrix multiplication

Reference 34

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Observation bec4c6fd-902c-427f-9b77-f8d0f78a69eb · outbound

This paper cites Gaussian elimination is not optimal.

Planar Perfect Matching Counting is as Hard as Determinants Gaussian elimination is not optimal

Reference 35

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 57b180da-acd5-4a23-a7b6-0ae3f8ff72a1 · outbound

This paper cites an unresolved cited work.

Planar Perfect Matching Counting is as Hard as Determinants Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 39c88121-9c84-4a61-8cdd-771802982f04 · outbound

This paper cites Classes of arithmetic circuits capturing the complexity of computing the determinant.

Planar Perfect Matching Counting is as Hard as Determinants Classes of arithmetic circuits capturing the complexity of computing the determinant

Reference 37

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation e95730a1-199a-442b-8dd6-f3e8822145f7 · outbound

This paper cites an unresolved cited work.

Planar Perfect Matching Counting is as Hard as Determinants Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 1d97279c-56e9-47c7-a440-d458a2d2d005 · outbound

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Planar Perfect Matching Counting is as Hard as Determinants Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 67d6521d-27b2-4465-88a6-30ceeaed1a94 · outbound

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Planar Perfect Matching Counting is as Hard as Determinants Unresolved cited work

Reference 40

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation dc63403b-5f31-44a6-ab2c-9299f4077ed0 · outbound

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Planar Perfect Matching Counting is as Hard as Determinants Unresolved cited work

Reference 41

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 933b71f8-56dd-4778-9edb-fd30c946c571 · outbound

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Planar Perfect Matching Counting is as Hard as Determinants Unresolved cited work

Reference 42

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation ba14c954-9435-4340-89cd-a0f701797006 · outbound

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Planar Perfect Matching Counting is as Hard as Determinants Unresolved cited work

Reference 43

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Observation 61777bdb-64ae-4e2e-8226-ef2f6ead9821 · outbound

This paper cites Ryan Williams.

Planar Perfect Matching Counting is as Hard as Determinants Ryan Williams

Reference 44

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation f365043b-6db5-43b2-af9c-88f528a29d43 · outbound

This paper cites Complexity: Knots, Colourings and Countings.

Planar Perfect Matching Counting is as Hard as Determinants Complexity: Knots, Colourings and Countings

Reference 45

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 8b72929e-9195-43a4-ae4f-1dee652d7997 · outbound

This paper cites Determinant algorithms for random planar structures.

Planar Perfect Matching Counting is as Hard as Determinants Determinant algorithms for random planar structures

Reference 46

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 7fb73362-34fb-40a7-ae38-ddcfcd13544d · outbound

This paper cites Ryan Williams.

Planar Perfect Matching Counting is as Hard as Determinants Ryan Williams

Reference 47

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 7d484569-73bf-4c48-a81e-0d29dff8c0af · outbound

This paper cites Matrix sparsification for rank and determinant computations via nested dissection.

Planar Perfect Matching Counting is as Hard as Determinants Matrix sparsification for rank and determinant computations via nested dissection

Reference 48

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Observation 845abbad-2e25-4686-942c-180c05de470c · outbound

This paper cites Maximum matching in graphs with an excluded minor.

Planar Perfect Matching Counting is as Hard as Determinants Maximum matching in graphs with an excluded minor

Reference 49

Resolution: unresolved; no resolver link, observed 2026-06-28T07:13:05.776275Z

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Pith citing papers

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