Paper Citation Record · LEDGER

Critical Parameters for Loop and Bernoulli Percolation

As of 20 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:1908.10213.

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

pith.paper-citation-record.v1
1908.10213 v1

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:06:22.429904Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

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

43 of 43 outbound references displayed

verified exact7
verified fuzzy31
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 61158e1a-39b3-40fb-bae8-a5fbe6e375d3 · outbound

This paper cites Percolation on finite graphs and isoperimetric inequalities.

Critical Parameters for Loop and Bernoulli Percolation Percolation on finite graphs and isoperimetric inequalities

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.261616Z

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 54d7960c-9be2-4c0e-82bb-2572af31c1c6 · outbound

This paper cites Strict monotonicity for critical points in percolation and ferromagnetic models.

Critical Parameters for Loop and Bernoulli Percolation Strict monotonicity for critical points in percolation and ferromagnetic models

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.247230Z

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 6e66f5df-46f8-47c3-a6f2-ecc4e02e7443 · outbound

This paper cites Geometric aspects of quantum spin states.

Critical Parameters for Loop and Bernoulli Percolation Geometric aspects of quantum spin states

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.233508Z

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

Observation 2daa4d6d-7e0c-42fb-9788-63e53cfbf50f · outbound

This paper cites Random infinite permutations and the cyclic time random walk.

Critical Parameters for Loop and Bernoulli Percolation Random infinite permutations and the cyclic time random walk

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.220267Z

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 4f168acc-4e0a-4819-96c1-c58f0d682c69 · outbound

This paper cites A numerical study of the 3d random interchange and random loop models.

Critical Parameters for Loop and Bernoulli Percolation A numerical study of the 3d random interchange and random loop models

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.206189Z

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 35e8d43c-75f6-43ba-89eb-d7802a77d37d · outbound

This paper cites Sharp threshold for percolation on expanders.

Critical Parameters for Loop and Bernoulli Percolation Sharp threshold for percolation on expanders

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.190565Z

Source-reported events for the cited work

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Observation d0452d80-948e-4266-b34a-a4b561d29fc7 · outbound

This paper cites Essential enhancements revisited.

Critical Parameters for Loop and Bernoulli Percolation Essential enhancements revisited

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-14T11:06:22.212060Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 41b933c9-e5bb-4111-bbaf-dddd90ab9069 · outbound

This paper cites Emergence of giant cycles and slowdown transition in random transpositions and k -cycles.

Critical Parameters for Loop and Bernoulli Percolation Emergence of giant cycles and slowdown transition in random transpositions and k -cycles

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.176689Z

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 d15bf9ff-93e1-4ede-8a7e-fe6bfb7688d5 · outbound

This paper cites Large cycles in random permutations related to the heisenberg model.

Critical Parameters for Loop and Bernoulli Percolation Large cycles in random permutations related to the heisenberg model

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.162162Z

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 4bc2fadc-997b-4e70-8d47-d6290d5faa6b · outbound

This paper cites The free energy in a class of quantum spin systems and interchange processes.

Critical Parameters for Loop and Bernoulli Percolation The free energy in a class of quantum spin systems and interchange processes

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.144727Z

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 edc803fd-522c-4a7e-85f5-083fb3b5b5dd · outbound

This paper cites Critical parameter of random loop model on trees.

Critical Parameters for Loop and Bernoulli Percolation Critical parameter of random loop model on trees

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.130240Z

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 b017c352-ed58-4f59-a457-01bb32cd88a9 · outbound

This paper cites Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction.

Critical Parameters for Loop and Bernoulli Percolation Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-14T11:06:22.258209Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a6c136fa-e62e-4a69-ba26-1428bfa4b7f3 · outbound

This paper cites Infinite cycles in the random stirring model on trees.

Critical Parameters for Loop and Bernoulli Percolation Infinite cycles in the random stirring model on trees

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.104338Z

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 0f42c904-c978-425d-be9c-d49a8372e6d4 · outbound

This paper cites Sharp phase transition in the random stirring model on trees.

Critical Parameters for Loop and Bernoulli Percolation Sharp phase transition in the random stirring model on trees

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.089405Z

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 33d40c7d-7ecb-4de0-886c-d3b772954f3c · outbound

This paper cites an unresolved cited work.

Critical Parameters for Loop and Bernoulli Percolation Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:06:23.072589Z

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 4c6285d0-aa5e-40c2-a254-45ee5296bdac · outbound

This paper cites The random interchange process on the hypercube.

Critical Parameters for Loop and Bernoulli Percolation The random interchange process on the hypercube

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.059817Z

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 18dd786d-59bc-4512-9bb0-20cadece74a5 · outbound

This paper cites Domination by product measures.

Critical Parameters for Loop and Bernoulli Percolation Domination by product measures

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.047149Z

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 e5aa2431-3097-46f9-b3a6-2527bc3b0208 · outbound

This paper cites Compositions of random transpositions.

Critical Parameters for Loop and Bernoulli Percolation Compositions of random transpositions

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.033437Z

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 206d4efa-402c-4368-8243-38b5a89391a7 · outbound

This paper cites Improved lower bound on the thermodynamic pressure of the spin 1/2 heisenberg ferromagnet.

Critical Parameters for Loop and Bernoulli Percolation Improved lower bound on the thermodynamic pressure of the spin 1/2 heisenberg ferromagnet

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.018053Z

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 222a4ad6-5ba7-47c3-a882-86a80887878e · outbound

This paper cites Random loop representations for quantum spin systems.

Critical Parameters for Loop and Bernoulli Percolation Random loop representations for quantum spin systems

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:23.001705Z

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 32ba8d79-a8e6-4021-8ef0-aebcce594a3e · outbound

This paper cites an unresolved cited work.

Critical Parameters for Loop and Bernoulli Percolation Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:06:22.983829Z

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 e8610e35-318e-4a11-b065-95d739344cc5 · outbound

This paper cites Improved lower bound on the thermodynamic pressure of the spin 1/2 Heisenberg ferromagnet.

Critical Parameters for Loop and Bernoulli Percolation Improved lower bound on the thermodynamic pressure of the spin 1/2 Heisenberg ferromagnet

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:22.966090Z

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 294caaa4-d927-47ba-90a8-1f2cfd4b0bb8 · outbound

This paper cites and Nachtergaele, B.

Critical Parameters for Loop and Bernoulli Percolation and Nachtergaele, B

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:22.945648Z

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 6d5dfd43-158a-4642-a03f-29fb128480d4 · outbound

This paper cites Random loop representations for quantum spin systems.

Critical Parameters for Loop and Bernoulli Percolation Random loop representations for quantum spin systems

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:22.922418Z

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 3c2500dc-ca4c-4d2c-b6ad-962d6adf2dfa · outbound

This paper cites Domination by product measures.

Critical Parameters for Loop and Bernoulli Percolation Domination by product measures

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:22.905038Z

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 9b83eee3-0580-4a97-af2f-e2d782ad4662 · outbound

This paper cites Statistical mechanics of lattice systems: a concrete mathematical introduction.

Critical Parameters for Loop and Bernoulli Percolation Statistical mechanics of lattice systems: a concrete mathematical introduction

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:22.890354Z

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 5f0a37c6-1f19-448a-b0cd-06d76ffc0607 · outbound

This paper cites and Barp, E.G.

Critical Parameters for Loop and Bernoulli Percolation and Barp, E.G

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:22.872154Z

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 2f4dc609-11fc-4822-ab27-025ef39623fa · outbound

This paper cites The interchange process with reversals on the complete graph.

Critical Parameters for Loop and Bernoulli Percolation The interchange process with reversals on the complete graph

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-08-14T11:06:22.568515Z

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 407bdbb4-1f03-4256-a774-e70579c9b17b · outbound

This paper cites Compositions of random transpositions.

Critical Parameters for Loop and Bernoulli Percolation Compositions of random transpositions

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:22.854447Z

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 4a4a5ff2-58b3-4fc6-a5d8-fb9b65841d07 · outbound

This paper cites and Mi o\' s , P.

Critical Parameters for Loop and Bernoulli Percolation and Mi o\' s , P

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:22.835774Z

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 cf181aa0-30db-4d68-9eab-43ac91c69edb · outbound

This paper cites Random Infinite Permutations and the Cyclic Time Random Walk.

Critical Parameters for Loop and Bernoulli Percolation Random Infinite Permutations and the Cyclic Time Random Walk

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:22.812173Z

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 120de41a-0ed6-4d8c-9796-75022126c000 · outbound

This paper cites Infinite cycles in the random stirring model on trees.

Critical Parameters for Loop and Bernoulli Percolation Infinite cycles in the random stirring model on trees

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:22.787886Z

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 f38cf739-36e2-437a-a46a-d0628f876688 · outbound

This paper cites Sharp phase transition in the random stirring model on trees.

Critical Parameters for Loop and Bernoulli Percolation Sharp phase transition in the random stirring model on trees

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:22.771390Z

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 f24affa5-17c7-4d11-858d-0a2e7499b5cb · outbound

This paper cites and Ueltschi, D.

Critical Parameters for Loop and Bernoulli Percolation and Ueltschi, D

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:22.754702Z

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 d87f675e-3228-4225-8609-2a4fc7103fdf · outbound

This paper cites Critical point for infinite cycles in a random loop model on trees.

Critical Parameters for Loop and Bernoulli Percolation Critical point for infinite cycles in a random loop model on trees

Reference 43

Resolution: verified exact; local_arxiv, observed 2026-08-14T11:06:22.504126Z

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 15763819-bf62-4aaf-b065-1668db1e1b23 · outbound

This paper cites Existence of a phase transition of the interchange process on the Hamming graph.

Critical Parameters for Loop and Bernoulli Percolation Existence of a phase transition of the interchange process on the Hamming graph

Reference 44

Resolution: verified exact; local_arxiv, observed 2026-08-14T11:06:22.477154Z

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 db6f3933-6f5a-4177-89f5-435448ce8ffb · outbound

This paper cites Large cycles in random permutations related to the Heisenberg model.

Critical Parameters for Loop and Bernoulli Percolation Large cycles in random permutations related to the Heisenberg model

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:22.739884Z

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 ba70e794-6342-4769-aa4b-7b6b985ea4ad · outbound

This paper cites The free energy in a class of quantum spin systems and interchange processes.

Critical Parameters for Loop and Bernoulli Percolation The free energy in a class of quantum spin systems and interchange processes

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:06:22.714213Z

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 82c02d77-6363-4fb2-90b3-2f1156c77d5a · outbound

This paper cites The mean-field quantum Heisenberg ferromagnet via representation theory.

Critical Parameters for Loop and Bernoulli Percolation The mean-field quantum Heisenberg ferromagnet via representation theory

Reference 47

Resolution: verified exact; local_arxiv, observed 2026-08-14T11:06:22.697957Z

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 b78efc52-6676-403d-814d-a8ec2e974d71 · outbound

This paper cites Quantum spins and random loops on the complete graph.

Critical Parameters for Loop and Bernoulli Percolation Quantum spins and random loops on the complete graph

Reference 48

Resolution: metadata mismatch; local_arxiv, observed 2026-08-14T11:06:22.588703Z

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 6f2947bb-8b77-474e-a1a2-c73d17821e33 · outbound

This paper cites Critical temperature of Heisenberg models on regular trees, via random loops.

Critical Parameters for Loop and Bernoulli Percolation Critical temperature of Heisenberg models on regular trees, via random loops

Reference 49

Resolution: verified exact; local_arxiv, observed 2026-08-14T11:06:22.535456Z

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 1e25f8b1-2293-4d3f-816c-14396f00ac04 · outbound

This paper cites Phase transition for loop representations of Quantum spin systems on trees.

Critical Parameters for Loop and Bernoulli Percolation Phase transition for loop representations of Quantum spin systems on trees

Reference 50

Resolution: verified exact; local_arxiv, observed 2026-08-14T11:06:22.615340Z

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 f05982cd-0db7-4b2e-968e-de6dae65bd20 · outbound

This paper cites Phase transition for the interchange and quantum Heisenberg models on the Hamming graph.

Critical Parameters for Loop and Bernoulli Percolation Phase transition for the interchange and quantum Heisenberg models on the Hamming graph

Reference 51

Resolution: verified exact; local_arxiv, observed 2026-08-14T11:06:22.671072Z

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.

Pith citing papers

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