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Paper Citation Record · LEDGER

Cluster volumes for the Gaussian free field on metric graphs

As of 12 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 3 inbound Pith citation observations for arXiv:2412.06772.

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

pith.paper-citation-record.v1
2412.06772 v1

Coverage vector

measured 44 of 44 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T19:26:56.761493Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T20:37:46.882838Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-08T14:41:54.094295Z

Reference resolution

44 of 44 outbound references displayed

  • verified exact3
  • verified fuzzy24
  • unresolved17
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2635e056-b5b5-4732-807c-74bff750a5eb · outbound

This paper cites Aizenman.

Cluster volumes for the Gaussian free field on metric graphs Aizenman

Reference 1

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation f3bbb505-b0c9-4d04-ab37-38673f69e76e · outbound

This paper cites Aizenman, F.

Cluster volumes for the Gaussian free field on metric graphs Aizenman, F

Reference 2

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 452c5ae0-9f37-4cdc-980b-0cbaa53c0899 · outbound

This paper cites an unresolved cited work.

Cluster volumes for the Gaussian free field on metric graphs Unresolved cited work

Reference 3

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 4c6ec2b0-b504-471c-bbcb-8d85c37dfaa1 · outbound

This paper cites an unresolved cited work.

Cluster volumes for the Gaussian free field on metric graphs Unresolved cited work

Reference 4

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation ef9055d8-e7f2-4107-8b3a-4f2f4109dfcc · outbound

This paper cites Bolthausen, J.-D.

Cluster volumes for the Gaussian free field on metric graphs Bolthausen, J.-D

Reference 5

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation effa0480-795b-42ed-ad58-7979f295a928 · outbound

This paper cites Bricmont, J.

Cluster volumes for the Gaussian free field on metric graphs Bricmont, J

Reference 6

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 8f646350-d9a4-4db3-b7af-942210b2979a · outbound

This paper cites One-arm exponent of critical level-set for metric graph Gaussian free field in high dimensions.

Cluster volumes for the Gaussian free field on metric graphs One-arm exponent of critical level-set for metric graph Gaussian free field in high dimensions

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-11T19:26:56.578869Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T19:26:56.578869Z digest=sha256:874392c496e7502cc69714537f82d1ebe89137762972f5bac30ea3e320ec6981

Observation 9b9e01e1-91bd-4c92-a48b-bb1eea7ed5bf · outbound

This paper cites One-arm Probabilities for Metric Graph Gaussian Free Fields below and at the Critical Dimension.

Cluster volumes for the Gaussian free field on metric graphs One-arm Probabilities for Metric Graph Gaussian Free Fields below and at the Critical Dimension

Reference 8

Resolution
unresolved
no resolver link, observed 2026-08-11T19:26:56.583761Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T19:26:56.583761Z digest=sha256:e1d3b06b1647a4506289fd8bd2ba687e620afb4a0f33bbc37a2a4b464269a45a

Observation 6444e940-9471-43ae-8e14-e1df34cd636c · outbound

This paper cites Universality classes for percolation models with long-range correlations.

Cluster volumes for the Gaussian free field on metric graphs Universality classes for percolation models with long-range correlations

Reference 9

Resolution
unresolved
no resolver link, observed 2026-08-11T19:26:56.588910Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T19:26:56.588910Z digest=sha256:afef80f92909800b12e03ea99965b3dc262319504fe9bac8fc409e015c076d6d

Observation 486b8d95-e364-4db1-8de5-2631a88a4e9e · outbound

This paper cites Contreras, S.

Cluster volumes for the Gaussian free field on metric graphs Contreras, S

Reference 10

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 646621ed-9c08-43d3-a360-32cf9075897d · outbound

This paper cites Ding and M.

Cluster volumes for the Gaussian free field on metric graphs Ding and M

Reference 11

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 37c6d88d-2db1-4f97-88ed-4cdf3c6b6bbe · outbound

This paper cites Drewitz, A.

Cluster volumes for the Gaussian free field on metric graphs Drewitz, A

Reference 12

Resolution
verified exact
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 2443b607-d9ec-4dab-9a27-5eaeb975cd45 · outbound

This paper cites Drewitz, A.

Cluster volumes for the Gaussian free field on metric graphs Drewitz, A

Reference 13

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation abdba362-4b60-48c7-ace8-9595b452c776 · outbound

This paper cites Drewitz, A.

Cluster volumes for the Gaussian free field on metric graphs Drewitz, A

Reference 14

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 2a92dd19-1d24-4c8c-9e20-42388d9c208e · outbound

This paper cites Drewitz, A.

Cluster volumes for the Gaussian free field on metric graphs Drewitz, A

Reference 15

Resolution
verified exact
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation d03cc08f-cbaa-43ec-a98b-7ac56b7a4d0d · outbound

This paper cites Drewitz, A.

Cluster volumes for the Gaussian free field on metric graphs Drewitz, A

Reference 16

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation b4795765-9dba-4d86-81c8-b0aba512308f · outbound

This paper cites Critical one-arm probability for the metric Gaussian free field in low dimensions.

Cluster volumes for the Gaussian free field on metric graphs Critical one-arm probability for the metric Gaussian free field in low dimensions

Reference 17

Resolution
unresolved
no resolver link, observed 2026-08-11T19:26:56.627980Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T19:26:56.627980Z digest=sha256:ec867775a767e81cc7bf763663c24d1c49aeb66f9fe74aa81e68d41a0101e143

Observation f9499d20-990f-4b6d-9eac-7b1a2002c494 · outbound

This paper cites Drewitz and P.-F.

Cluster volumes for the Gaussian free field on metric graphs Drewitz and P.-F

Reference 18

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation bdcf8eea-0b72-45d4-a45b-0f4e45a77995 · outbound

This paper cites An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d>6$.

Cluster volumes for the Gaussian free field on metric graphs An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d>6$

Reference 19

Resolution
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no resolver link, observed 2026-08-11T19:26:56.638090Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation efcac83f-1ae8-4fde-afbf-755d7d08a4dd · outbound

This paper cites Fitzner and R.

Cluster volumes for the Gaussian free field on metric graphs Fitzner and R

Reference 20

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 8e4dbef6-ade1-4d1a-98c5-e7ec151bc3d6 · outbound

This paper cites an unresolved cited work.

Cluster volumes for the Gaussian free field on metric graphs Unresolved cited work

Reference 21

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 55cfb111-b753-418f-a479-8772a9960918 · outbound

This paper cites The ant on loops: Alexander-Orbach conjecture for the critical level set of the Gaussian free field.

Cluster volumes for the Gaussian free field on metric graphs The ant on loops: Alexander-Orbach conjecture for the critical level set of the Gaussian free field

Reference 22

Resolution
unresolved
no resolver link, observed 2026-08-11T19:26:56.652357Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T19:26:56.652357Z digest=sha256:3c38be3a61b4e69807c50cb77106c61fd875da1d8a38a9491ae8439a9f01efe3

Observation da1a1095-e198-47d0-8777-faad5dfe7785 · outbound

This paper cites Goswami, P.-F.

Cluster volumes for the Gaussian free field on metric graphs Goswami, P.-F

Reference 23

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation cee32ab2-2124-41e6-8844-efde906fa11e · outbound

This paper cites Hara and G.

Cluster volumes for the Gaussian free field on metric graphs Hara and G

Reference 24

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 46cb10fc-a056-4c1e-a72f-63ff9583fbd4 · outbound

This paper cites Heydenreich and R.

Cluster volumes for the Gaussian free field on metric graphs Heydenreich and R

Reference 25

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation f44f962e-3a2a-45f7-9f21-f5ad403ea676 · outbound

This paper cites an unresolved cited work.

Cluster volumes for the Gaussian free field on metric graphs Unresolved cited work

Reference 26

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 95b33fad-0ec9-4a67-9c6c-f10aa60d6d9f · outbound

This paper cites an unresolved cited work.

Cluster volumes for the Gaussian free field on metric graphs Unresolved cited work

Reference 27

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation b1b97613-977b-43e3-8f3c-8855f780b461 · outbound

This paper cites an unresolved cited work.

Cluster volumes for the Gaussian free field on metric graphs Unresolved cited work

Reference 28

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 7d17a4d4-2758-484f-b9e4-e8ce1bf40b6d · outbound

This paper cites Kesten and Y.

Cluster volumes for the Gaussian free field on metric graphs Kesten and Y

Reference 29

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 8d3f5afb-f79c-4508-8712-0451cf629725 · outbound

This paper cites Kozma and A.

Cluster volumes for the Gaussian free field on metric graphs Kozma and A

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:57.467448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 31c4436f-9e89-4c43-bafb-888a7775162b · outbound

This paper cites an unresolved cited work.

Cluster volumes for the Gaussian free field on metric graphs Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:57.451676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 7e5b9715-7adc-4650-8c79-50c8111c69f6 · outbound

This paper cites an unresolved cited work.

Cluster volumes for the Gaussian free field on metric graphs Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:57.436552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 79476409-4c6a-406b-9603-8553f7e67dfe · outbound

This paper cites an unresolved cited work.

Cluster volumes for the Gaussian free field on metric graphs Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:57.420116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation a86c6c4a-a1fd-42d5-83b4-126d578fd756 · outbound

This paper cites Panagiotis and F.

Cluster volumes for the Gaussian free field on metric graphs Panagiotis and F

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:57.405232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 72266b08-a2cf-45d4-89ed-eea230c843c5 · outbound

This paper cites an unresolved cited work.

Cluster volumes for the Gaussian free field on metric graphs Unresolved cited work

Reference 35

Resolution
verified exact
raw_fallback, observed 2026-08-11T19:26:56.929345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 444cb01b-65a1-4f50-b01f-48e77e7bdaad · outbound

This paper cites Ráth and A.

Cluster volumes for the Gaussian free field on metric graphs Ráth and A

Reference 36

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 0166b0d9-4317-416a-8e99-f60a450ecee5 · outbound

This paper cites Rodriguez and A.-S.

Cluster volumes for the Gaussian free field on metric graphs Rodriguez and A.-S

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:57.368492Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation a248ec8d-a11a-4e09-acb3-b235cb25d6cb · outbound

This paper cites an unresolved cited work.

Cluster volumes for the Gaussian free field on metric graphs Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:57.350113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T19:26:56.732551Z digest=sha256:e7dc56f1b25d2d23c4c9cba603368a054475d7a1e5864d29c8e72df9166f5322

Observation d48ba261-741c-4f60-8799-8a08815e4792 · outbound

This paper cites Smirnov and W.

Cluster volumes for the Gaussian free field on metric graphs Smirnov and W

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:57.333635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T19:26:56.737347Z digest=sha256:7f3384b5a169a3b472c3a3e8286f11166420b467cf57c23d275089641ddcc172

Observation c483ea82-4f49-4504-9536-0c7db70854c4 · outbound

This paper cites Stauffer and A.

Cluster volumes for the Gaussian free field on metric graphs Stauffer and A

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:57.315389Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T19:26:56.741792Z digest=sha256:16b0a2a7378d0ff849cc83dd794ffe63daaa4e54dce7062f41efffb75e0bed5f

Observation fdb27e3f-7b7a-4d84-bdad-d54e901c86a4 · outbound

This paper cites Sznitman.

Cluster volumes for the Gaussian free field on metric graphs Sznitman

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:57.298523Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T19:26:56.747163Z digest=sha256:d151167a257077344b6446088e958dd6c6d28dab3fbe19388b4b4d3e5c6695ac

Observation 57307e1a-8ce6-499e-860d-60c0536e1b6b · outbound

This paper cites Sznitman.

Cluster volumes for the Gaussian free field on metric graphs Sznitman

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:57.280754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T19:26:56.751867Z digest=sha256:b234c507850c46b09fa56722707129afdc5b42b3755a559c0917aeea32c26636

Observation a61fbce3-0139-4625-b9e9-8c2304bdec09 · outbound

This paper cites Sznitman.

Cluster volumes for the Gaussian free field on metric graphs Sznitman

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:57.264441Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T19:26:56.756604Z digest=sha256:0bdd5bc65164d686169f9f1fce9fac82662a0d967881971718df070e2e426e97

Observation 7f4eb54f-5b96-4158-b8b5-8e65fb9b6eb3 · outbound

This paper cites an unresolved cited work.

Cluster volumes for the Gaussian free field on metric graphs Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:57.246766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T19:26:56.761493Z digest=sha256:2344642b783df19a35facaaddd3678726fe7f55df1300ec95fe23e5dc48888f4

Pith citing papers

Observation b2f93fc4-0e50-47c2-ba15-4a02961df530 · inbound

Quasi-multiplicativity and regularity for metric graph Gaussian free fields cites this paper.

Quasi-multiplicativity and regularity for metric graph Gaussian free fields Cluster volumes for the Gaussian free field on metric graphs

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-11T20:37:46.882838Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T20:37:46.882838Z digest=sha256:be1e956450912c6fdff9410eb0d23ae528de9532dae6c873d7d624ca38d2a0a6

Observation 80e5a270-1ca0-4f9a-a92c-a2981fa17458 · inbound

Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs cites this paper.

Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs Cluster volumes for the Gaussian free field on metric graphs

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-11T20:33:50.413676Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T20:33:50.413676Z digest=sha256:c10fc9983c6d55592d65a3c086a037c2780428d9eb4c2cfa7439dee5fd4e5e31

Observation da9e0a0a-c5e8-4c9b-9a5c-a9efed28ae00 · inbound

A switching identity for cable-graph loop soups and Gaussian free fields cites this paper.

A switching identity for cable-graph loop soups and Gaussian free fields Cluster volumes for the Gaussian free field on metric graphs

Reference 18

Resolution
verified exact
local_arxiv, observed 2026-08-08T14:41:54.097823Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-08T14:41:53.816273Z digest=sha256:9f99b4514da03855b8be533ad526357d9459ae3ccd1cf4fa7acec62f4d7be851