Paper Citation Record · LEDGER

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

As of 14 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2608.03848.

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

pith.paper-citation-record.v1
2608.03848 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T11:27:08.476973Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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

37 of 37 outbound references displayed

verified exact4
verified fuzzy28
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7f6dd92b-d6f7-4393-94a1-4be79bfe6069 · outbound

This paper cites Entropic Independence I: Modified Log-Sobolev Inequalities for Fractionally Log-Concave Distributions and High-Temperature Ising Models.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Entropic Independence I: Modified Log-Sobolev Inequalities for Fractionally Log-Concave Distributions and High-Temperature Ising Models

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-05T11:27:08.379865Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aeaa5430-7474-48d8-90ae-0653c798d39f · outbound

This paper cites Trickle-down in localization schemes and applications.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Trickle-down in localization schemes and applications

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.951776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 45ad28ab-4f5a-4213-a95a-20a309344ab4 · outbound

This paper cites A very simple proof of the LSI for high temperature spin systems.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities A very simple proof of the LSI for high temperature spin systems

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.942539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 40ba65f6-4cf5-4157-989e-e36af7136733 · outbound

This paper cites Spectral gap in random bipartite biregular graphs and applications.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Spectral gap in random bipartite biregular graphs and applications

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.933972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4837576a-7dbb-46ff-85c7-2fbb3474bcfc · outbound

This paper cites an unresolved cited work.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:27:08.925601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d501b9c0-c1ee-458b-88eb-8e806e8801e1 · outbound

This paper cites Rapid mixing on random regular graphs beyond uniqueness, 2025.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Rapid mixing on random regular graphs beyond uniqueness, 2025

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-05T11:27:08.396644Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 260a5da2-7ef5-4e9c-ae81-8dc064539ae3 · outbound

This paper cites \# bis-hardness for 2-spin systems on bipartite bounded degree graphs in the tree non-uniqueness region.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities \# bis-hardness for 2-spin systems on bipartite bounded degree graphs in the tree non-uniqueness region

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.917074Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b34563fe-bec4-45ff-be9d-ad856fa05d2f · outbound

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

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Sampling colorings and independent sets of random regular bipartite graphs in the non-uniqueness region

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.908662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e003cd54-ee68-4baa-a3e2-ab026a3f8b34 · outbound

This paper cites Pirogov-- S inai theory for the hard-core model beyond lattices.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Pirogov-- S inai theory for the hard-core model beyond lattices

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.900448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 60d932bc-2825-43f6-8ade-a09b7b9e967c · outbound

This paper cites an unresolved cited work.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:27:08.891557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d708c4ad-ad80-48c0-8b94-3ff8465f8ca8 · outbound

This paper cites The relative complexity of approximate counting problems.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities The relative complexity of approximate counting problems

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.883246Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d4fac6e3-d632-4077-8871-b2b556708179 · outbound

This paper cites An approximation trichotomy for boolean \#csp.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities An approximation trichotomy for boolean \#csp

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.875261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d7be5ecd-bdaf-4d77-b1e0-57abdac6f2f8 · outbound

This paper cites A spectral condition for spectral gap: Fast mixing in high-temperature Ising models.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities A spectral condition for spectral gap: Fast mixing in high-temperature Ising models

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.867704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 115c24c3-9c9b-4fee-a85b-5916bc75b047 · outbound

This paper cites A proof of Alon 's second eigenvalue conjecture.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities A proof of Alon 's second eigenvalue conjecture

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.859539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 63c0007d-57ba-48f4-8119-11dc0f7fe194 · outbound

This paper cites A simple proof of rapid mixing on random regular graphs beyond uniqueness.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities A simple proof of rapid mixing on random regular graphs beyond uniqueness

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-05T11:27:08.607378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 691b3e86-5eed-4ffc-b1e8-f86f83672432 · outbound

This paper cites Inapproximability of the partition function for the antiferromagnetic I sing and hard-core models.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Inapproximability of the partition function for the antiferromagnetic I sing and hard-core models

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.851592Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d16d2f3a-97df-4be5-8f40-28fa0a6a7a83 · outbound

This paper cites Expander graphs and their applications.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Expander graphs and their applications

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.843514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c0542c4f-1dd5-4d84-91c5-6aedf6d74f18 · outbound

This paper cites On the critical fugacity of the hard-core model on regular bipartite graphs, 2026.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities On the critical fugacity of the hard-core model on regular bipartite graphs, 2026

Reference 18

Resolution: verified exact; raw_fallback, observed 2026-08-05T11:27:08.594447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8012dc29-c622-45e4-b1de-32e5846c16a0 · outbound

This paper cites Algorithmic pirogov--sinai theory.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Algorithmic pirogov--sinai theory

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.834525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 372dc077-8c73-465b-b9a4-da68037aca9d · outbound

This paper cites Calculation of partition functions.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Calculation of partition functions

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.826101Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4fbbe821-3596-4e04-b301-dcc37eeab434 · outbound

This paper cites Algorithms for \#bis -hard problems on expander graphs.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Algorithms for \#bis -hard problems on expander graphs

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.818205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7a406108-9fa8-4e57-91cc-3418addd17c4 · outbound

This paper cites A refined graph container lemma and applications to the hard-core model on bipartite expanders.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities A refined graph container lemma and applications to the hard-core model on bipartite expanders

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.809623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1506ffe5-2b9f-4bf4-8b12-cfb898a71ef4 · outbound

This paper cites Approximately counting independent sets in bipartite graphs via graph containers.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Approximately counting independent sets in bipartite graphs via graph containers

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.800955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 10b10bc2-6528-442a-a147-85026b5dfbc1 · outbound

This paper cites Umbrella sampling.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Umbrella sampling

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.792259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 14667b95-6dcc-444a-b6ba-7792783fa5ed · outbound

This paper cites Spectral gap for G lauber type dynamics for a special class of potentials.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Spectral gap for G lauber type dynamics for a special class of potentials

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.783544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9fc438b7-e504-4823-be2a-49c76520f4e2 · outbound

This paper cites Sampling approximately low-rank Ising models: MCMC meets variational methods.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Sampling approximately low-rank Ising models: MCMC meets variational methods

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.775356Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4f0de50c-d46d-420a-9bf5-e6eef3d2efac · outbound

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

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Sampling from the Hardcore Model on Random Regular Bipartite Graphs above the Uniqueness Threshold

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-05T11:27:08.521968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c20e48d3-d22e-4b82-8f8e-07f499436c11 · outbound

This paper cites Cluster expansion for abstract polymer models.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Cluster expansion for abstract polymer models

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.767234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7eb21329-ab2c-414a-93dd-4c4e2bcaf5e7 · outbound

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

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Counting independent sets and colorings on random regular bipartite graphs

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.758679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f1b0e336-bcae-4c28-850a-8ec6238b7101 · outbound

This paper cites Structured logconcave sampling with a restricted gaussian oracle.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Structured logconcave sampling with a restricted gaussian oracle

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.750582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 44ee427a-a208-4191-8199-d7c8c8aaed5b · outbound

This paper cites On the hardness of sampling independent sets beyond the tree threshold.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities On the hardness of sampling independent sets beyond the tree threshold

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.742529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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

This paper cites Computational Thresholds for Balanced and Fixed-Slice Independent Sets in Bipartite Graphs.

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 2026-08-14T06:32:32.682623+00:00.

Observation 1ccd230b-202e-4a8e-ba71-f7737f63a59d · outbound

This paper cites Computational transition at the uniqueness threshold.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Computational transition at the uniqueness threshold

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.733777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ffcca03b-b5f5-4a57-802b-3dafbb9d8c55 · outbound

This paper cites Counting in two-spin models on \(d\)-regular graphs.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Counting in two-spin models on \(d\)-regular graphs

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.724560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6603aa5d-6d46-453c-b9f7-77a16c390344 · outbound

This paper cites Michael Tanner.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Michael Tanner

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.715643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 86f51b2d-d213-4901-b9be-f68224ef8dfb · outbound

This paper cites an unresolved cited work.

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:27:08.707097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7b1671d2-4d76-4f5e-bb7e-9e0549c1c3a8 · outbound

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

The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities Counting independent sets up to the tree threshold

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:27:08.697266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

No inbound Pith citation observations are available.