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Paper Citation Record · LEDGER

Cluster volumes for the Gaussian free field on metric graphs

As of 13 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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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
raw_fallback, observed 2026-08-11T19:26:57.724900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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=sha256:33890f987dbbc4828e5587a65f3e190cb06deb3fc5b66cd646ad954f609361da

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:e1a589706dac24bb92f6f74b5e4b2f938ac9e90ebd37cdd5e8f113e7b8d376de

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:c8ed998eeba8424bc4ce85dedbad7117c15e33bdf7dbe4cf7cadf78c49933de4

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 2026-08-13T06:32:02.005865+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
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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:c7c6a7f4cd4839c195d0633b475ddb64e8de9c4d55acac1bfd46b6dbc319ba86

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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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=sha256:6399732a00e78153627f454d8633b317421d1838aed33c214d10840c40f5e09b

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
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T19:26:56.713488Z digest=sha256:e5436cc80352e97a20890dfe270ce3199b9f75e505ba2c96847de7a56c731e27

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T19:26:56.718322Z digest=sha256:18502f4753d8962d2cf3d83344c5f7aa5217b71f4882eb9d4774f88cccfcc527

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
raw_fallback, observed 2026-08-11T19:26:57.388619Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T19:26:56.723303Z digest=sha256:3c627962fbd68a63a7c5784a64f52c208a2553a51b2502f1a8faf78a4691c9ee

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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+00:00.

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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
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T19:26:56.737347Z digest=sha256:26c9c892cace445391305d4493a32efca57561a7fc119e6c0a4e421f1aa1a493

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T19:26:56.741792Z digest=sha256:c4cd7534210bad5e56b1546b281c0282482f4240f149810eb09c5ce73294e61c

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T19:26:56.747163Z digest=sha256:3eda235bd9ea9b8dcb4a508252ee9417425fd94cca04f97cadc84451f28f1b12

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T19:26:56.751867Z digest=sha256:789716c3ebec137cdb617e46b205b11afb2559b13522480d2a5fa5940ce98985

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T19:26:56.756604Z digest=sha256:d4408f3840b325bb67409e39f4d3b72a03b8b430d15156e62376a248be62116f

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T19:26:56.761493Z digest=sha256:f84665fe1152fa7c034a9475ab115651f543ccf24ad290d788480af0fc208e30

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:a9b9c88c556655377d5a1aaa19fe700c2e802560611f2788024fbc3a1b86009b

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=sha256:8ae22715cb8b2453b5e09160106daf4ece8cf1514bbc3766c4931f95241b4211

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-08T14:41:53.816273Z digest=sha256:90e66c38e92bf64223166944a9a8ede03fbc0186bab0e2bc974bed957b037b3e