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Paper Citation Record · LEDGER

Collisions of random walks on comb graphs with a planar base

As of 20 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 2 inbound Pith citation observations for arXiv:2508.19814.

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

pith.paper-citation-record.v1
2508.19814 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T15:35:47.930701Z

measured 25 of 25 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-12T06:08:15.459958Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

23 of 23 outbound references displayed

  • verified exact0
  • verified fuzzy21
  • unresolved2
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3a3123df-b40a-4a85-a203-ecc5e048eab2 · outbound

This paper cites an unresolved cited work.

Collisions of random walks on comb graphs with a planar base Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-05T15:35:48.192329Z

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.

source=pdf_text observed=2026-08-05T15:35:47.848313Z digest=sha256:9fb33fc613882f6b86d0949f2e4bae4bb1c0025ea59c21c4750bf04af0bea4b6

Observation 3328c3d6-7151-4714-9943-7988b8a3b796 · outbound

This paper cites Randomwalksonsupercriticalpercolationclusters.

Collisions of random walks on comb graphs with a planar base Randomwalksonsupercriticalpercolationclusters

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.182577Z

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.

source=pdf_text observed=2026-08-05T15:35:47.852868Z digest=sha256:b46ebffcf6fb6c560c7b1a254efb47990fa5d77d3b9addc88e9c8750a1100bac

Observation 45c8b855-430c-49d9-a89c-a70ec35f7b23 · outbound

This paper cites Random walks and heat kernels on graphs, volume438of London Mathematical Society Lecture Note Series.

Collisions of random walks on comb graphs with a planar base Random walks and heat kernels on graphs, volume438of London Mathematical Society Lecture Note Series

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.172333Z

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.

source=pdf_text observed=2026-08-05T15:35:47.857661Z digest=sha256:465b36e0b789ecf78078f5c90d23b973aeb53ba5c086a0e40be2cc23d29d2151

Observation 295c9bb2-e92c-493d-92bb-2d8b6debd2a5 · outbound

This paper cites Barlow, T.

Collisions of random walks on comb graphs with a planar base Barlow, T

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.161157Z

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.

source=pdf_text observed=2026-08-05T15:35:47.861399Z digest=sha256:0fa8d4641afd96c0dc667d11f8ac69cfe9dc25a0a1fb2583e960c85837fdaabd

Observation a64e025f-bf1c-4a4b-a72a-9cf9c832f8fd · outbound

This paper cites Barlow, Y.

Collisions of random walks on comb graphs with a planar base Barlow, Y

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.150537Z

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.

source=pdf_text observed=2026-08-05T15:35:47.865394Z digest=sha256:7dd8542e89c9a75a9a31e2e29308722f3e8046e0b4c35d36084f5bbfec8ff584

Observation cc1f50fb-d7ec-4767-be50-81ceb502a664 · outbound

This paper cites Boivin and C.

Collisions of random walks on comb graphs with a planar base Boivin and C

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.140616Z

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.

source=pdf_text observed=2026-08-05T15:35:47.869272Z digest=sha256:f8ff07e5ef883311b563679099f4b31bdc17567670c1030f42d5e8b5b8c7d8a9

Observation d197afab-18c4-4abe-8f55-954fb6ed3e6b · outbound

This paper cites an unresolved cited work.

Collisions of random walks on comb graphs with a planar base Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-05T15:35:48.130525Z

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.

source=pdf_text observed=2026-08-05T15:35:47.873242Z digest=sha256:b65fff878c43a4cd03bf6787fb7b511b07bd85ea6b2137f193b9450382795470

Observation aabf98e4-ecc1-4a4b-a772-9fb10d302970 · outbound

This paper cites Chen and D.

Collisions of random walks on comb graphs with a planar base Chen and D

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.120468Z

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.

source=pdf_text observed=2026-08-05T15:35:47.876615Z digest=sha256:35a333222e8a9d0a9d9de6ff2c4fc7ea923e671809503bd594589fd4e63954b0

Observation 0961eb53-c948-41de-ba4e-1de95e47298f · outbound

This paper cites Chen and D.

Collisions of random walks on comb graphs with a planar base Chen and D

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.110530Z

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.

source=pdf_text observed=2026-08-05T15:35:47.880847Z digest=sha256:ca1dc1bd7500a432799f819da563c0ef5caf5edf20bea37fbdc81c2a636117d2

Observation 0a86d95d-f619-4330-ab75-72148ae6d6d4 · outbound

This paper cites Croydon and Umberto De Ambroggio.

Collisions of random walks on comb graphs with a planar base Croydon and Umberto De Ambroggio

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.099299Z

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.

source=pdf_text observed=2026-08-05T15:35:47.884285Z digest=sha256:d7e3278a396ca977e2314c275a4b2d3f24940904484afe6cda964dceabaccaaf

Observation 53bfeae7-1472-455e-bd0a-77454b8b6596 · outbound

This paper cites Dembo, Y.

Collisions of random walks on comb graphs with a planar base Dembo, Y

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.089759Z

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.

source=pdf_text observed=2026-08-05T15:35:47.887543Z digest=sha256:b91ed99c3ee4039842a9ff4450fef7666dc62c0aef81fa8c22179920e86b7c42

Observation 1e861237-45ac-4c2a-9a4f-d60cf9663392 · outbound

This paper cites Devulder.

Collisions of random walks on comb graphs with a planar base Devulder

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.079773Z

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.

source=pdf_text observed=2026-08-05T15:35:47.891486Z digest=sha256:11a6c81e20ad4a7a9e4a2a1f26051a343edc80d9e62861a7975b65d945b539c3

Observation 0554d482-391a-4d16-b884-2fd9c32432fc · outbound

This paper cites Devulder, N.

Collisions of random walks on comb graphs with a planar base Devulder, N

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.069676Z

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.

source=pdf_text observed=2026-08-05T15:35:47.894833Z digest=sha256:70c39d60d00e9d39a242d36408e4a7f0f671c914cb644cb6cc696c890373cb29

Observation c51c118c-6956-4220-ab73-00ef0e72efab · outbound

This paper cites Devulder, N.

Collisions of random walks on comb graphs with a planar base Devulder, N

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.059061Z

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.

source=pdf_text observed=2026-08-05T15:35:47.898238Z digest=sha256:4e301ccb03151fc429f4c9be0afe54831393165170e86b3df11e1b25acf92261

Observation cbd406fe-7068-4a6c-9e71-55ffe1d1f61f · outbound

This paper cites Erdős and S.

Collisions of random walks on comb graphs with a planar base Erdős and S

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.048257Z

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.

source=pdf_text observed=2026-08-05T15:35:47.901509Z digest=sha256:e5fdd6a3abfdf69035c15356fa63bd36fa15b5084a19806a801f2e2533259d60

Observation 3e7495b5-bb52-4d4a-b97d-e0be6df847d2 · outbound

This paper cites Grimmett.Percolation.

Collisions of random walks on comb graphs with a planar base Grimmett.Percolation

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.037756Z

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.

source=pdf_text observed=2026-08-05T15:35:47.905655Z digest=sha256:4383384671328bf272c4b23faf281def3214054cda3ca14b16ec3899f39e0416

Observation 68ca7adb-b573-4bcf-ac00-a14bb4a1de33 · outbound

This paper cites Halberstam and T.

Collisions of random walks on comb graphs with a planar base Halberstam and T

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.026967Z

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.

source=pdf_text observed=2026-08-05T15:35:47.908889Z digest=sha256:be943b76808b7622bc9b0544a2a057b99b2747ba65eee38a07ad5e60c3f9aa0d

Observation fa9233eb-fd28-40b3-a21a-df90bbe3574a · outbound

This paper cites Hutchcroft and Y.

Collisions of random walks on comb graphs with a planar base Hutchcroft and Y

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.015760Z

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.

source=pdf_text observed=2026-08-05T15:35:47.912426Z digest=sha256:d76a79e64a7a8ac908312a1bf16314ad12e9c613bd395c4e20954daf9400447b

Observation db93a69d-49c0-4f27-8a04-5c98b6fabb97 · outbound

This paper cites Krishnapur and Y.

Collisions of random walks on comb graphs with a planar base Krishnapur and Y

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:48.004365Z

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.

source=pdf_text observed=2026-08-05T15:35:47.915858Z digest=sha256:f10878948604ba660cfea9612e23fe04e2f91eb9af741ccd26f8de7a0dc33889

Observation 19789a72-473f-4247-a377-dc158d78301f · outbound

This paper cites Coupling from the past.

Collisions of random walks on comb graphs with a planar base Coupling from the past

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:47.993522Z

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.

source=pdf_text observed=2026-08-05T15:35:47.919242Z digest=sha256:e7f9758e7dba25881bed9532b7ecfee708ec3285ffc3120a6ad546d032ec2072

Observation ee1c897a-6ed2-44dc-acd4-34b9eac5227b · outbound

This paper cites Lyons and Y.

Collisions of random walks on comb graphs with a planar base Lyons and Y

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:47.982791Z

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.

source=pdf_text observed=2026-08-05T15:35:47.922514Z digest=sha256:0f7a54bb4efc5376a13a07c652c94079cdf21e6056ca8ee4ba8b69d15ea31cbc

Observation 8f267655-b18e-4911-af3b-b93b82cebfd5 · outbound

This paper cites Sapozhnikov.

Collisions of random walks on comb graphs with a planar base Sapozhnikov

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:47.972261Z

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.

source=pdf_text observed=2026-08-05T15:35:47.927251Z digest=sha256:5bf41efeae69b276c2b5934f413be1fae0ff57becb4e6df1639643ddaa5e1173

Observation e62d0543-fa70-4088-b4d2-d1d6c227047f · outbound

This paper cites Watanabe.

Collisions of random walks on comb graphs with a planar base Watanabe

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T15:35:47.961063Z

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.

source=pdf_text observed=2026-08-05T15:35:47.930701Z digest=sha256:80a837d92b0a4f6338b5d006380f659126f93c4af893e745d0981c9ae293592e

Pith citing papers

Observation 6d2262e5-3990-4254-8b15-d77738e302a9 · inbound

Infinite collisions of simple random walks on random recursive trees generated by Bernoulli sequences cites this paper.

Infinite collisions of simple random walks on random recursive trees generated by Bernoulli sequences Collisions of random walks on comb graphs with a planar base

Reference 10

Resolution
unresolved
no resolver link, observed 2026-07-12T06:08:15.459958Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-12T06:08:15.459958Z digest=sha256:738199cfbc0f92f12583a4f08a88fd48cd18612950ead945c454accb4ff25b17

Observation e82f375d-5d12-4144-ae0f-e9760b2e90fd · inbound

Collisions of random walks in unimodular random graphs: applications to the random geometric graph and long-range percolation cites this paper.

Collisions of random walks in unimodular random graphs: applications to the random geometric graph and long-range percolation Collisions of random walks on comb graphs with a planar base

Reference 3

Resolution
unresolved
no resolver link, observed 2026-07-11T22:23:21.358379Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-11T22:23:21.358379Z digest=sha256:5f7a474ee899ec2789fedbfa13d5ddafe10d9d67f28feda9105583de69b08d5f