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Paper Citation Record · LEDGER

The polynomial growth of effective resistances in one-dimensional critical long-range percolation

As of 18 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 1 inbound Pith citation observation for arXiv:2504.21378.

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

pith.paper-citation-record.v1
2504.21378 v2

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T05:13:25.876835Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:35:41.189108Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T15:35:41.231106Z

Reference resolution

24 of 24 outbound references displayed

  • verified exact0
  • verified fuzzy10
  • unresolved14
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0cab6dfe-de24-4f5b-887f-f366fe1ec00a · outbound

This paper cites Aizenman and C.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Aizenman and C

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:27.589342Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.185747Z digest=sha256:91b44f1400e1a3cad7bdab88f07f959a691452c67e7416194a52efe213e9092d

Observation b7bf31eb-0fd2-4479-9eaf-c1fe8fb3027d · outbound

This paper cites Aldous and J.-A.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Aldous and J.-A

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:27.483938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.193753Z digest=sha256:411288714cf9596085bd2c284571e3e79517303588338c8cd196c7b7b61b871a

Observation 62c7bcde-a51e-4c5a-9f3c-eff4268a4ee5 · outbound

This paper cites an unresolved cited work.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:13:27.468035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.236119Z digest=sha256:f5a4971e0822303874bdee03e4b30425e7fb0d227ecec5733f82646ad378e9b1

Observation f3765c0d-df62-400e-ae8b-800ebddd5801 · outbound

This paper cites an unresolved cited work.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:13:27.393368Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.285481Z digest=sha256:e990f6012a0f458115e2d2ea9e8eac298805c56b6815d53c08191f6c2835d90e

Observation 5b5a0df9-4ece-468e-969d-7b85c7e99a81 · outbound

This paper cites an unresolved cited work.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Unresolved cited work

Reference 5

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:25.290323Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T05:13:25.290323Z digest=sha256:6342c68998de0dfc6b5e4e534bb474030bbe9f54b4d10129f75511970d2b85e5

Observation 55e0f74e-6014-4322-ba1a-e32c69155d18 · outbound

This paper cites Scaling limits for random walks on long range percolation clusters.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Scaling limits for random walks on long range percolation clusters

Reference 6

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:25.295371Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T05:13:25.295371Z digest=sha256:ac8e20bec443354a5054253dcdc08046bb3db9f1a3e4ab22e2f693cf3a7bfc40

Observation de1cf5ce-2996-453e-8651-d0ad2e9bada9 · outbound

This paper cites Biskup, J.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Biskup, J

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:27.293789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.302220Z digest=sha256:9e9a78138ac0ffdf7448f6995ac9a70821d44449600baa934f0524c650907ac6

Observation bb56debd-33e5-4910-b426-e63a108cb429 · outbound

This paper cites Can, D.A.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Can, D.A

Reference 8

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:25.307257Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T05:13:25.307257Z digest=sha256:baf7eed5ba81a32dea45cb47b056fd32090cdf83a2c108e186cb2c5570d31286

Observation 8030a386-38a8-4931-ab30-ca9b3840f42a · outbound

This paper cites Crawford and A.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Crawford and A

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:27.170945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.339502Z digest=sha256:2ec82bb9fa3e210775c7e51ecca7877c8af30bb8f79ac94d197a901d4cdd9732

Observation bf809242-1d1d-4bae-b1bd-9c0c01ad3875 · outbound

This paper cites an unresolved cited work.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:13:27.098969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.432510Z digest=sha256:99feb517275ae62e09ea51ff741302bba74b93386264f47805bfee4c4a1cf499

Observation 644c056e-361a-49cd-89f9-51929b9bc473 · outbound

This paper cites an unresolved cited work.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:13:26.974951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.468097Z digest=sha256:bd172c697057c2dbbf2a67dc0f4718c1e60d6dccd43cfba6a02202d413ab45c3

Observation 1b574775-3ab5-454c-9dea-195fedbf86a6 · outbound

This paper cites an unresolved cited work.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:13:26.901731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.472403Z digest=sha256:cbc0a2f3153dd86bf6e4170f45829781bf904837bdfca9abd8b1937b6b6b2035

Observation 33d72c8b-631c-4051-bfd6-57eec0e7c94d · outbound

This paper cites Ding and E.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Ding and E

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:26.835240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.477291Z digest=sha256:e4c0a3d4bc35b0261dbf8266562a291b7fe38b00774126b247b42d598371ac03

Observation 416b6f72-6e97-41c1-801e-b3b61d0e1435 · outbound

This paper cites Distances in critical long range percolation.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Distances in critical long range percolation

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:25.482897Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T05:13:25.482897Z digest=sha256:3724d7796927e1cabbb5ede92eebe032618f87386b6b81d54ded5d137b101729

Observation f6fd704d-092e-448b-8407-f5fe2d03137b · outbound

This paper cites Duminil-Copin, C.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Duminil-Copin, C

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:26.766752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.488889Z digest=sha256:54741db6967587bccba0b5cfb258e3d51dd47373035c19dbcc678f4ca5c74506

Observation 8a54abb0-8655-4c98-be30-18d10d2a166d · outbound

This paper cites Gwynne and J.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Gwynne and J

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:26.678631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.643140Z digest=sha256:02c6e9487a0aaa88cc5f98b651ffffdba11adc5413ec49fa9b51cb4a9000ff93

Observation e826cd2f-23dc-4b1f-a025-8900e65118c0 · outbound

This paper cites an unresolved cited work.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:13:26.583348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.753256Z digest=sha256:499728f1769eb00e5874f49427c7cf22e42c828202dc4dd9fe6e644ec50fee46

Observation 3c693d73-412c-4454-919c-221d674ee406 · outbound

This paper cites Kumagai and J.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Kumagai and J

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:26.468873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.757992Z digest=sha256:8bdc15092295cde168e21d6291813209abc9b9d51a21173c7a3efecc137aaf24

Observation 56fb3552-0188-42bf-b726-3986f48cc109 · outbound

This paper cites Levin, Y.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Levin, Y

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:26.380385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.764030Z digest=sha256:7787d176c104eb21fd383ea63522e6bbd042b36d888a57d79e3b4a10db81495e

Observation f5c28f63-a037-4fa4-95a9-029605a5878f · outbound

This paper cites an unresolved cited work.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:13:26.363586Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.769027Z digest=sha256:c2bb7b0f8546814a3b4c554462f5f3604026414b6cdc5c2f3474e5caa2607028

Observation cb30ec64-ee75-4965-a9d5-c3c25cc305e7 · outbound

This paper cites Newman and L.S.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Newman and L.S

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:26.089048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.775756Z digest=sha256:68eeab48c9e08a6d6ad93cb5ec79e2f13911888351bbfc6ecbc2c5aad52be91e

Observation 7258e79c-cd3a-444c-b4d9-5203593fbf35 · outbound

This paper cites Schulman.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Schulman

Reference 22

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:25.827035Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T05:13:25.827035Z digest=sha256:c5c1e736f388d392ff64b85e85b2f6defd24c62f538345ff3244227d9f492541

Observation 224296d3-e583-4c1c-b3bb-e0f8d62a70c2 · outbound

This paper cites an unresolved cited work.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:13:26.012740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-16T05:13:25.872012Z digest=sha256:1af679cea55b5c8c8a2d8f2f18b3d5fa701f709261219f965138979ddcd9c286

Observation 6f80b0ee-052a-4a21-bb05-693d76c46f17 · outbound

This paper cites Zhang, F.C.

The polynomial growth of effective resistances in one-dimensional critical long-range percolation Zhang, F.C

Reference 24

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:25.876835Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T05:13:25.876835Z digest=sha256:2deea639cd9cdcc551f52641903a6d0aabe78fc68a58053b16abfb3c34ebac92

Pith citing papers

Observation 8320a8ec-779b-4085-aee5-bd48a6a76cd5 · inbound

Spectral dimensions for one-dimensional critical long-range percolation cites this paper.

Spectral dimensions for one-dimensional critical long-range percolation The polynomial growth of effective resistances in one-dimensional critical long-range percolation

Reference 10

Resolution
verified exact
local_arxiv, observed 2026-08-07T15:35:41.235663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T15:35:41.189108Z digest=sha256:fea830f661caaeab54930eb922e6d9fe39347fe898ef436407c1ebb0e0e1a770