Paper Citation Record · LEDGER

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs

As of 12 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 1 inbound Pith citation observation for arXiv:2608.02503.

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

pith.paper-citation-record.v1
2608.02503 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T06:11:59.642462Z

measured 39 of 39 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 2026-08-05T11:27:08.464094Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T11:27:08.504354Z

Reference resolution

38 of 38 outbound references displayed

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unresolved38
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External citation measurements

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Outbound references

Observation 55a0fe21-bf3e-4ba4-897d-627aeeb45e91 · outbound

This paper cites Springer, 2016.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Springer, 2016

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.453014Z

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Observation 13e17746-ac62-4f02-b33b-b6faed169fdb · outbound

This paper cites A Quantitative Local Limit Theorem for Triangles in Random Graphs.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs A Quantitative Local Limit Theorem for Triangles in Random Graphs

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.459121Z

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Observation aa8add24-ce43-450c-b64d-f158d7c41763 · outbound

This paper cites # bis-hardness for 2-spin systems on bipartite bounded degree graphs in the tree non-uniqueness region.Journal of Computer and System Sciences, 82(5):690–711, 2016.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs # bis-hardness for 2-spin systems on bipartite bounded degree graphs in the tree non-uniqueness region.Journal of Computer and System Sciences, 82(5):690–711, 2016

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.464406Z

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Observation 1e6e9763-553c-40fb-8973-8298adaefc69 · outbound

This paper cites Pirogov–Sinai theory for the hard-core model beyond lattices.Communications in Mathematical Physics, 407:129, 2026.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Pirogov–Sinai theory for the hard-core model beyond lattices.Communications in Mathematical Physics, 407:129, 2026

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.469576Z

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Observation e01080c6-2dc2-4c13-bd70-6604cf406152 · outbound

This paper cites Counting independent sets in unbalanced bipartite graphs.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Counting independent sets in unbalanced bipartite graphs

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.475269Z

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Observation 39030114-7585-4245-a791-9e19254c4655 · outbound

This paper cites Computational thresholds for the fixed-magnetization ising model.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Computational thresholds for the fixed-magnetization ising model

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.480814Z

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Observation 49d058c0-36fc-48d9-9180-a53ea82dbaf3 · outbound

This paper cites Rapid mixing at the uniqueness threshold.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Rapid mixing at the uniqueness threshold

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.486472Z

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Observation 614a6775-36fc-4529-9795-322bdb4a4669 · outbound

This paper cites Uniqueness and rapid mixing in the bipartite hardcore model (extended abstract).

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Uniqueness and rapid mixing in the bipartite hardcore model (extended abstract)

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.491600Z

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Observation 1a6b4de2-7f80-4d25-8c47-13dd850dc9ba · outbound

This paper cites Zero-Freeness of the Hard-Core Model with Bounded Connective Constant.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Zero-Freeness of the Hard-Core Model with Bounded Connective Constant

Reference 9

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Observation 8e9c6992-d0f4-4ac8-a2d6-dbc276846b8d · outbound

This paper cites Sampling colorings and independent sets of random regular bipartite graphs in the non-uniqueness region.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Sampling colorings and independent sets of random regular bipartite graphs in the non-uniqueness region

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.502435Z

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Observation 7f3e2337-6b0f-4f78-a109-b8ff95603f79 · outbound

This paper cites Approximately counting independent sets of a given size in bounded-degree graphs.SIAM Journal on Computing, 52(2):618–640, 2023.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Approximately counting independent sets of a given size in bounded-degree graphs.SIAM Journal on Computing, 52(2):618–640, 2023

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.507744Z

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Observation 9f0440c4-392b-436f-8b5e-6a23d7527f02 · outbound

This paper cites an unresolved cited work.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.512673Z

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Observation 570ef8a4-94bf-4d15-a8d1-ede9aa32054a · outbound

This paper cites The relative complexity of approximate counting problems.Algorithmica, 38(3):471–500, 2004.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs The relative complexity of approximate counting problems.Algorithmica, 38(3):471–500, 2004

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.517489Z

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Observation 198d20c1-465a-4b71-8132-97b174bc9af1 · outbound

This paper cites An approximation trichotomy for boolean #csp.Journal of Computer and System Sciences, 76(3–4):267–277, 2010.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs An approximation trichotomy for boolean #csp.Journal of Computer and System Sciences, 76(3–4):267–277, 2010

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.522680Z

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Observation 43c7579f-cdfa-4397-8ac1-29520df1675f · outbound

This paper cites Relations between average case complexity and approximation complexity.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Relations between average case complexity and approximation complexity

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.527148Z

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Observation ce765d4a-d8fd-417b-898e-0cc6dc42a474 · outbound

This paper cites On cutting a few vertices from a graph.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs On cutting a few vertices from a graph

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.532074Z

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Observation a17e8504-7874-45db-aafb-34a4541e9746 · outbound

This paper cites Improved inapprox- imability results for counting independent sets in the hard-core model.Random Structures & Algorithms, 45(1):78–110, 2014.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Improved inapprox- imability results for counting independent sets in the hard-core model.Random Structures & Algorithms, 45(1):78–110, 2014

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.537678Z

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Observation a2f7cdc8-2bd8-47dd-a674-95dfe9aa0824 · outbound

This paper cites Inapproximability for antiferromagnetic spin systems in the tree nonuniqueness region.Journal of the ACM, 62(6):50:1–50:60, 2015.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Inapproximability for antiferromagnetic spin systems in the tree nonuniqueness region.Journal of the ACM, 62(6):50:1–50:60, 2015

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.542503Z

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Observation 8a7b33a8-8d28-4c73-9436-98a93a8a579a · outbound

This paper cites Inapproximability of the partition function for the antiferromagnetic ising and hard-core models.Combinatorics, Probability and Computing, 25(4):500–559, 2016.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Inapproximability of the partition function for the antiferromagnetic ising and hard-core models.Combinatorics, Probability and Computing, 25(4):500–559, 2016

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.547300Z

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Observation 26305145-22f4-4ea8-8611-a4bb7f35631e · outbound

This paper cites Some simplified np-complete problems.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Some simplified np-complete problems

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.552059Z

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Observation 665fe4d7-d992-41b1-8bce-cb2359f1d243 · outbound

This paper cites Walter de Gruyter, 2011.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Walter de Gruyter, 2011

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.557458Z

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Observation 5b5a4633-49b5-4db8-b058-2d948a2ad510 · outbound

This paper cites Algorithmic Pirogov–Sinai theory.Probability Theory and Related Fields, 176(3–4):851–895, 2020.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Algorithmic Pirogov–Sinai theory.Probability Theory and Related Fields, 176(3–4):851–895, 2020

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.562080Z

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Observation 9890fc48-5867-43f4-b0bc-dc4145b7b916 · outbound

This paper cites Optimal mixing of the down-up walk on independent sets of a given size.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Optimal mixing of the down-up walk on independent sets of a given size

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.567229Z

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Observation 7e16fc54-3d2b-4239-b100-92d93a84607d · outbound

This paper cites Approximate counting and sampling via local central limit theorems.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Approximate counting and sampling via local central limit theorems

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.572352Z

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Observation f4677c60-f46c-4f30-9806-b17e0e65a34a · outbound

This paper cites Algorithms for #BIS-hard problems on expander graphs.SIAM Journal on Computing, 49(4):681–710, 2020.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Algorithms for #BIS-hard problems on expander graphs.SIAM Journal on Computing, 49(4):681–710, 2020

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.577299Z

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Observation 52edfbd8-cb56-48cf-8dcc-58dc1edb0555 · outbound

This paper cites A refined graph container lemma and applications to the hard-core model on bipartite expanders.Random Structures & Algorithms, 68(1):e70041, 2026.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs A refined graph container lemma and applications to the hard-core model on bipartite expanders.Random Structures & Algorithms, 68(1):e70041, 2026

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.582496Z

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Observation 6cb26281-c8f2-4dc8-8777-e5f028d3b753 · outbound

This paper cites Approximately counting independent sets in bipartite graphs via graph containers.Random Structures & Algorithms, 63(1):215–241, 2023.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Approximately counting independent sets in bipartite graphs via graph containers.Random Structures & Algorithms, 63(1):215–241, 2023

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.587796Z

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Observation b502faf7-bb9e-4d0b-aed9-e16c7fc024cc · outbound

This paper cites Sampling from the Hardcore Model on Random Regular Bipartite Graphs above the Uniqueness Threshold.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Sampling from the Hardcore Model on Random Regular Bipartite Graphs above the Uniqueness Threshold

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.592858Z

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Observation fbac758d-5107-48fc-b8a6-2c82e63fd2a3 · outbound

This paper cites Fast and slow mixing of the Kawasaki dynamics on bounded-degree graphs.Random Structures & Algorithms, 67(4):e70038, 2025.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Fast and slow mixing of the Kawasaki dynamics on bounded-degree graphs.Random Structures & Algorithms, 67(4):e70038, 2025

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.598033Z

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Observation 545b94d9-24dd-400f-96d5-40b07c56b84f · outbound

This paper cites Counting independent sets and colorings on random regular bipartite graphs.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Counting independent sets and colorings on random regular bipartite graphs

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.602926Z

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Observation fa7630cd-62b0-4c4f-b921-ce0fc47a80ae · outbound

This paper cites Fptas for #BIS with degree bounds on one side.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Fptas for #BIS with degree bounds on one side

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.608569Z

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Observation 417d08a0-b39e-4f9f-a7e7-d71b72be75d1 · outbound

This paper cites Central limit theorems and the geometry of polynomials.Journal of the European Mathematical Society, 28(5):2261–2305, 2026.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Central limit theorems and the geometry of polynomials.Journal of the European Mathematical Society, 28(5):2261–2305, 2026

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.614177Z

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Observation e4a60ed9-ef41-4940-a459-f4b21c0ec4f4 · outbound

This paper cites Deterministic polynomial-time approximation algorithms for partition functions and graph polynomials.SIAM Journal on Computing, 46(6):1893–1919, 2017.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Deterministic polynomial-time approximation algorithms for partition functions and graph polynomials.SIAM Journal on Computing, 46(6):1893–1919, 2017

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.618874Z

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Observation 0e46b739-d839-46d3-8d05-c890cd230a64 · outbound

This paper cites On the hardness of finding balanced independent sets in random bipartite graphs.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs On the hardness of finding balanced independent sets in random bipartite graphs

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.623823Z

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Observation 63c81712-8f3d-46bf-9efe-5eaa92da7b0e · outbound

This paper cites Spatial mixing and the connective constant: Optimal bounds.Probability Theory and Related Fields, 168(1–2):153–197, 2017.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Spatial mixing and the connective constant: Optimal bounds.Probability Theory and Related Fields, 168(1–2):153–197, 2017

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.628402Z

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Observation 75ccc228-d6b8-4c31-bd14-8b0f19292d05 · outbound

This paper cites Computational transition at the uniqueness threshold.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Computational transition at the uniqueness threshold

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.632908Z

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Observation cf40aa86-8a07-4a50-a87d-5ebe72b6bbd4 · outbound

This paper cites Counting in two-spin models ond-regular graphs.The Annals of Probability, 42(6):2383–2416, 2014.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Counting in two-spin models ond-regular graphs.The Annals of Probability, 42(6):2383–2416, 2014

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.637927Z

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Observation 1d2e5cb8-2913-4e96-a025-5e00e0647c0a · outbound

This paper cites Counting independent sets up to the tree threshold.

Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs Counting independent sets up to the tree threshold

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-04T06:11:59.642462Z

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Pith citing papers

Observation 7d9aa399-d4a7-48fe-900a-277f9c2e942b · inbound

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities cites this paper.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-08-05T11:27:08.509456Z

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.