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Paper Citation Record · LEDGER

Chip-Firing Games and Critical Groups

As of 16 August 2026, this Paper Citation Record lists 69 of 69 outbound references and 0 inbound Pith citation observations for arXiv:1908.04395.

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

pith.paper-citation-record.v1
1908.04395 v1

Coverage vector

measured 69 of 69 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T13:55:38.998298Z

measured 69 of 69 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

69 of 69 outbound references displayed

  • verified exact7
  • verified fuzzy30
  • unresolved32
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3f2538ba-78b0-45f6-879d-6178a67469f6 · outbound

This paper cites Alfaro and Carlos E.

Chip-Firing Games and Critical Groups Alfaro and Carlos E

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.986612Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.720905Z digest=sha256:4995d9e44483372d84fd0cf940b642f7222a5fc8cb69053e347803e57c1061a9

Observation b7c7f44f-4951-4758-8329-b278384b0718 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.974996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.725191Z digest=sha256:9e1036d90453bac9ab15ae5c40f5c901e7c7631bf2b31ddd0333da6fa429bee6

Observation ef1210b3-7223-4bd9-8698-5afbf5c4db23 · outbound

This paper cites Sigma 2 (2014), e24, 25 pp.

Chip-Firing Games and Critical Groups Sigma 2 (2014), e24, 25 pp

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.963759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.729378Z digest=sha256:688db1f05bee239ab38428f45b757d60d373d2372e27a7fcfb34eefd695e86de

Observation 0b5d9fe0-6e9c-4d4c-a1de-c39d69500d3d · outbound

This paper cites Arithmetical structures on bidents.

Chip-Firing Games and Critical Groups Arithmetical structures on bidents

Reference 4

Resolution
verified exact
local_arxiv, observed 2026-08-14T13:55:39.259750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.733387Z digest=sha256:ff6e9991bf15761591b70ff9b3c0e6f072b992a70eb19b5bb07933be97ea9fe3

Observation e48c2663-2e19-4ef5-a6e4-c7858d2ff1b6 · outbound

This paper cites Chip-Firing and Riemann-Roch Theory for Directed Graphs.

Chip-Firing Games and Critical Groups Chip-Firing and Riemann-Roch Theory for Directed Graphs

Reference 5

Resolution
verified exact
local_arxiv, observed 2026-08-14T13:55:39.244084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.737773Z digest=sha256:0c57cb2da8080500b365fc79c4cf3e1db7bfe68a7946a3b6c95d4dec0a9d3da4

Observation 89a971ba-77d6-44a5-95b4-da960c571b44 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 6

Resolution
unresolved
no resolver link, observed 2026-08-14T13:55:38.742255Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T13:55:38.742255Z digest=sha256:94cc29eb9709984c9a985f26939ae6e0fe2c0c8b9d56e47e5a412c3fa16534fe

Observation dd09e6a4-bf3a-418e-99cf-36c3e5d2f32c · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.943182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.747412Z digest=sha256:e32302ad148d86eea8cbef66e27f78f7594fa985461279ce0c3718ec9e2688df

Observation 2ab2b244-6850-464a-9704-124d0a08e18b · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.931023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.751157Z digest=sha256:6cccca9dfdfae3fa22eeb41f53f0dfbc53dbe1e77f1a01c2f968c3bfa8f3aa1b

Observation 5767ebd2-4816-4197-9ab9-6b50dc76f938 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.918846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.754718Z digest=sha256:5bb1b92c0b0c7f63a23222dcda709c982e1f0f2c93f93961e551a9457e76386d

Observation 2d50e80b-7826-4693-a6a7-00fd5f0fb713 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.906436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.758521Z digest=sha256:b48eb163a76a2364bad6ee8b99c1bc1e584e2b3f7c806b467277034b3dd99fc6

Observation 43807edf-7833-471e-84f2-a77d26d35dc9 · outbound

This paper cites Second edition.

Chip-Firing Games and Critical Groups Second edition

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.894668Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.762069Z digest=sha256:4fb3a7334c4e412dfc13044e66d484b4f4ddbcc063292c4abf75567eb483fc49

Observation fad4d194-67d4-4652-bfef-ea5fbfcd6008 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-14T13:55:38.765828Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T13:55:38.765828Z digest=sha256:53acdf8ba4daa31a83fecc512c470a8bd65d1b1a947acc31d09513ebf3281895

Observation 07723783-f47b-4923-9be9-4887dd2812e3 · outbound

This paper cites Algebraic Com- bin.

Chip-Firing Games and Critical Groups Algebraic Com- bin

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.873847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.769253Z digest=sha256:2fea87163016290c1cf1aa7bf1133b2ef958b89bc9f171746246741190966d43

Observation 20c41f31-5a68-4259-859c-8cfa4064c152 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.862367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.772838Z digest=sha256:b96b55ba8a289dcc365d138f0cca066c96424ec4e99e869b53f0992f318daab7

Observation b3b62b04-59be-4e0a-b134-78c69e9ca5b8 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.850199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.776270Z digest=sha256:6c406e1c49a00dee0dda03d93de01aeb7e4ac395cf3d117bfd2dfd47baf1da0c

Observation 95e4e62e-e540-447e-ad57-30c768fd9cbb · outbound

This paper cites Martin, Gregg Musiker, and Carlos E.

Chip-Firing Games and Critical Groups Martin, Gregg Musiker, and Carlos E

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.839290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.780123Z digest=sha256:0b07cf45494cfed24f3f78066518cd76b4eb19d06de95e982637445394a524e0

Observation 072d1e28-ea49-4ea9-911f-e670b0bef4e7 · outbound

This paper cites Brown, Jackson S.

Chip-Firing Games and Critical Groups Brown, Jackson S

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.826210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.783827Z digest=sha256:7a522cfe8a56472fa1e6b4a717a951a378b30db8c68b1c03c6809787ce49d29f

Observation f963a64e-d1da-4da5-abed-bbc6f29f4542 · outbound

This paper cites Chandler, Peter Sin, and Qing Xiang, The Smith and critical groups of Paley graphs, J.

Chip-Firing Games and Critical Groups Chandler, Peter Sin, and Qing Xiang, The Smith and critical groups of Paley graphs, J

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.814722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.787298Z digest=sha256:6d7cde8e3360cf618c3773279f32f75287c37ea9a107a4bde183cb9cda720498

Observation c6840fc7-855b-44c2-8dae-87bd30bb1210 · outbound

This paper cites 1, 255 – 258.

Chip-Firing Games and Critical Groups 1, 255 – 258

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.803919Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.790834Z digest=sha256:e1aa62c291354ca881f5c1e7767a3709cfe7e9730c648b8ab9bff7707cc0c2db

Observation 35ba2f6e-a06d-4ad4-bbf2-7975d458663a · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.791510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.794596Z digest=sha256:a2faf18071714338c8a969fb97a73b8368ced1c049fb012de2931c4f2a488489

Observation 8f0c073b-da76-4ad9-919a-54c087a49be6 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.779953Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.798332Z digest=sha256:7a8cde78fd897770f6a8f7f8d7b07bf6b2f8d2cfb52fa41e8df65f6593f419c1

Observation 35570a2b-7e7a-4bf2-9fd1-ad689824f407 · outbound

This paper cites Algebraic Combin.

Chip-Firing Games and Critical Groups Algebraic Combin

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.768500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.802012Z digest=sha256:c7b8ee57d6ce4e9d01092047a7960135fb47fa63c4b37124a8a7dbf1a79f6dfd

Observation 59f3ab56-ef67-4f5d-b09e-8e06d807db0b · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.756834Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.805912Z digest=sha256:bedd1ddf79367693df9266296c829a9bc47a455be53909cc26e60664765ac9a8

Observation debe6bb6-8ac1-43a7-8a22-b1728c0633a8 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.745503Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.809538Z digest=sha256:d20f400332219a6fb407c23308449067ae128b787d8be945948ef92f86c2cc3b

Observation 4a021df9-03fe-43ea-a9f1-e76574226f8e · outbound

This paper cites Le Borgne.

Chip-Firing Games and Critical Groups Le Borgne

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.734634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.813973Z digest=sha256:7b76a1f96bdd88215ee259265d5fbea23410b1ac2c80ad0389ca78873511672c

Observation c4814daf-dc9d-471f-b72c-c343aba2563e · outbound

This paper cites Com- bin.

Chip-Firing Games and Critical Groups Com- bin

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.723601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.818113Z digest=sha256:573fe4629588139197d606e6be7dd8ee8c8b336ac1bce8d0b4e2a8395f210a01

Observation cf4a72f4-fb45-4419-9cba-ca9ca14faef7 · outbound

This paper cites Cools, J.

Chip-Firing Games and Critical Groups Cools, J

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.712569Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.823511Z digest=sha256:f789c73de7347ec6276b9a1dede693e53da7981b68f36d71207e78ab2d1473c3

Observation 2b089b46-3fcc-415b-a4bc-4455084c7e5d · outbound

This paper cites V alencia, Arithmetical structures on graphs , Linear Algebra Appl.

Chip-Firing Games and Critical Groups V alencia, Arithmetical structures on graphs , Linear Algebra Appl

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.700437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.828605Z digest=sha256:2e421f858b06868c384621de184ff91396186b943b6a16a4d3224c9c677cad2f

Observation e69d5509-2364-4c1e-8450-fcd1d8ade2f4 · outbound

This paper cites Algebra Appl.

Chip-Firing Games and Critical Groups Algebra Appl

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.689261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.834832Z digest=sha256:dcf2581311a2d2634352903e2dd00bc6fb0892df33397a58c9eba31367249ad8

Observation ec9ea610-ac6d-413e-b271-751d07ded57c · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.679134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.839146Z digest=sha256:27ad32a8abf37f2d4cd225584fb318b6b5fb52b8b3efcda05267badbb0427a7a

Observation 093255cb-8e7e-4205-bca1-2aebbdad9796 · outbound

This paper cites Treewidth is a lower bound on graph gonality.

Chip-Firing Games and Critical Groups Treewidth is a lower bound on graph gonality

Reference 31

Resolution
verified exact
local_arxiv, observed 2026-08-14T13:55:39.225757Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.844341Z digest=sha256:2830d9f85b064a60f85ac7e13d21d7d71ef276be02d8dce04705a26c87dcb34e

Observation 126ff02c-2d53-43b6-8f24-4053c585f604 · outbound

This paper cites 4, 715–720.

Chip-Firing Games and Critical Groups 4, 715–720

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.668700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.848793Z digest=sha256:7e6504de8d4e2f522929cffd313006817149d86a4246f33f0ce2eb93e40762a8

Observation 11bf6d31-b09a-4d90-aaaf-fd9e58380e75 · outbound

This paper cites Ducey, Jonathan Gerhard, and Noah Watson, The Smith and Critical Groups of the Square Rook’s Graph and its Complement , Electr.

Chip-Firing Games and Critical Groups Ducey, Jonathan Gerhard, and Noah Watson, The Smith and Critical Groups of the Square Rook’s Graph and its Complement , Electr

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.658534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.852716Z digest=sha256:396465a1d0e8b3d701afdedbf9308109ee3df0855bc20693296ac9f8809ba2fc

Observation d49d7956-5e8b-47dc-a7cf-c0f09cf86b12 · outbound

This paper cites 341 (2018), no.

Chip-Firing Games and Critical Groups 341 (2018), no

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.646715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.857064Z digest=sha256:a732d0db7ef7b57de9ae1478868d9999f20e50e557eb9da6d01da1a144e5baff

Observation 2fe1cde3-2ce3-4aa0-9d7c-a99feceb26ab · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 35

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.635410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.861109Z digest=sha256:307f142e6d5742b23c33c5afea3d706d576790f06dfc129e39cd631ee313727c

Observation 80f265d5-dea9-47f5-89e8-00c2ee58130c · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 36

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.623822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.864914Z digest=sha256:2ea1cb7b5489b6925fa6b01c2c2a7b72abf22522934ef2bd0de35e2a7191906d

Observation 7352eba0-4a6c-4366-8670-9e2d9040c130 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 37

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.612325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.868630Z digest=sha256:0721f53feab2f7050811c92212dd04f913c6802e7edbb2f774991c06bb44be90

Observation e69908c6-3100-45bb-bd0f-a03f3f144991 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.601218Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.872687Z digest=sha256:e6614e541e509b7e50c64bd24e26353b2a40c3ab6eceea7b97903bafe83faefe

Observation ee73443a-fe8a-4965-a88d-eadcfc0b0fff · outbound

This paper cites 567 (2019), 138–142.

Chip-Firing Games and Critical Groups 567 (2019), 138–142

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.588472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.876567Z digest=sha256:5a215a722716bba8d096e7bd47f0dea1ba067c28ee476baeb158c4af5d05702e

Observation bfb4e113-c4be-49c6-9b24-cf2e1ace7e65 · outbound

This paper cites Gouvˆ ea, p-adic Numbers: An introduction , second ed., Universitext, Springer- V erlag, Berlin, 1997.

Chip-Firing Games and Critical Groups Gouvˆ ea, p-adic Numbers: An introduction , second ed., Universitext, Springer- V erlag, Berlin, 1997

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.576502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.880166Z digest=sha256:e4c9419ff538e7debe2cab2d24697185a523049c3f3509abf298a14776a207b2

Observation f5b3a891-9f8f-4523-8c2c-0055797606ad · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.564644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.883758Z digest=sha256:720d1daccfa289c834eadabb23d6e3b5ac828ec32ebbb8302a8bdc7a16cc55ad

Observation 49d54c8b-15aa-464d-999d-763c5da57fd0 · outbound

This paper cites 418 (2006), no.

Chip-Firing Games and Critical Groups 418 (2006), no

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.552924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.887310Z digest=sha256:f70359fd459390f81aa477e098bd6b45112563d15f93d9ff6f4d0e0574f46e00

Observation ac51ea65-1dc9-4d3e-885d-de04ccac9e1e · outbound

This paper cites 3, 231–250.

Chip-Firing Games and Critical Groups 3, 231–250

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.541571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.891068Z digest=sha256:8f36105b7a9757c9ea145cd901ab3faa099092323dc307d9bdeb313bdbac903c

Observation 36b395f5-665a-4b3c-aac0-a809bbfc6319 · outbound

This paper cites Electron.

Chip-Firing Games and Critical Groups Electron

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.530798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.894983Z digest=sha256:5a436a2d0abc9a3f581a4dcd81733e8f42b809ca7b527daf34516103c83f0d1f

Observation 7460729e-67fc-437c-95b1-19628da1cbdc · outbound

This paper cites Kirby, Roger B.

Chip-Firing Games and Critical Groups Kirby, Roger B

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.518618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.898946Z digest=sha256:b82b4f180a10664808aeb54032848140ca6e772486b9e562ddc0897fe38a4a74

Observation d471e981-56a8-408f-853b-bf87ad329d3b · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 46

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.506112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.902683Z digest=sha256:a5aa5bf340b5db36892381214165fe946bae6ab170474e841b5456ec2ab3b25f

Observation 96304ccb-2a1c-4201-96b2-6656f6cfbc9b · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 47

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.493142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.906178Z digest=sha256:74098a8903dad2c8a6ad14d00f7482fbf62ca230c66d9440b3468cf0c5f227e0

Observation 5850d2a1-e556-4216-9051-e10c98c2ca6e · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 48

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.481774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.909914Z digest=sha256:7389efd7566ee3954219292fcac6f17567a603e9512a7fef0ded52e71af7b075

Observation 7e35b435-30d3-4d50-b6b6-b37a542f057f · outbound

This paper cites Sandpile Groups of Random Bipartite Graphs.

Chip-Firing Games and Critical Groups Sandpile Groups of Random Bipartite Graphs

Reference 49

Resolution
verified exact
local_arxiv, observed 2026-08-14T13:55:39.206014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.914396Z digest=sha256:a046525c96a9d143a19094d3af3482f49c9cbfce875dff9be23cd8c7f9e413d1

Observation d68c3cec-17df-4a80-98d8-1bd2e619c55c · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 50

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.471276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.918628Z digest=sha256:1a3f1d523c0b6b1afa7909d24d7cf6871d903e74f6acf2fd9fb56a6487162814

Observation 00ba27fe-1d03-4b2e-a7b7-0c96701d727b · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.460694Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.922137Z digest=sha256:dc5d5234c02afa3473cb1da9737f5d7a202285f212176ec27fcf296734cd1072

Observation 78831175-259c-4a78-add7-9ed2ab13ec66 · outbound

This paper cites Lorenzini, Arithmetical graphs, Math.

Chip-Firing Games and Critical Groups Lorenzini, Arithmetical graphs, Math

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.449298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.926956Z digest=sha256:12a933c94817d75611e66742a6503bca95098d02f75e810fcd73cb925e6ce28b

Observation 9d7616f8-ddc8-4dc2-abb7-38c3e18d8f6a · outbound

This paper cites 73 (1990), no.

Chip-Firing Games and Critical Groups 73 (1990), no

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.438306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.931172Z digest=sha256:d7758ca3dcfefd90b1f763cc3c60422863fda65574713909c752885fe7c5fac4

Observation 135bd830-a73b-4f43-9eed-dd2c81afa926 · outbound

This paper cites 91 (1991), no.

Chip-Firing Games and Critical Groups 91 (1991), no

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.427136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.935139Z digest=sha256:31a999a4a4dc1b6970c5bff3ead184b06577fcc930291cfb6e2cb38a74739aa6

Observation b51c5773-dee6-4494-89e1-cb60449cb832 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 55

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.414858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.939674Z digest=sha256:090a89fde4c8d0be60972f630ff7bfc649c4ebd9dc42be99c2fab376ca205222

Observation ee9447e8-f6aa-4ae6-b4a7-6d4329a29f6f · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 56

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.403539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.943228Z digest=sha256:64a405e4394b65a7ccaf0a9ce1f6e3a60fc28f3f3c405abdbb3e10991c1c8fe5

Observation 8680cc93-fe08-4dcd-b13f-b171a65e9296 · outbound

This paper cites The distribution of sandpile groups of random regular graphs.

Chip-Firing Games and Critical Groups The distribution of sandpile groups of random regular graphs

Reference 57

Resolution
verified exact
local_arxiv, observed 2026-08-14T13:55:39.185672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.946931Z digest=sha256:235477f3261d7da1ac2cd48b84a40e641e3dc872cccddf1fc96e560ffe317f75

Observation 9c29c0a3-59b3-48d3-87c1-8fcb1e8cda26 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 58

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.390252Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.951102Z digest=sha256:d2201295aa6a9375f2b8011a184596b9cf8829a72e4b5daff13c8e7572d6847b

Observation 43fadcb9-e8c2-4bfc-8c1c-04abd013c577 · outbound

This paper cites Random integral matrices: universality of surjectivity and the cokernel.

Chip-Firing Games and Critical Groups Random integral matrices: universality of surjectivity and the cokernel

Reference 59

Resolution
verified exact
local_arxiv, observed 2026-08-14T13:55:39.169680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.955716Z digest=sha256:4b23f7b4b1f2c51ece9cb12224b6970389f47c2f412577202b09f2d70d861030

Observation 446cb5c1-3e43-43ce-9fed-61411dfcb328 · outbound

This paper cites 318 (2014), 10–40.

Chip-Firing Games and Critical Groups 318 (2014), 10–40

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.378755Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.959784Z digest=sha256:46727bec6a5e63882e4faa5fc3b90e98e60056a409d1d9b503673902f2d0408b

Observation 3413da62-43a1-4021-8bc1-80e81e0524a9 · outbound

This paper cites Sedl´ aˇ cek,On the minimal graph with a given number of spanning trees , Canad.

Chip-Firing Games and Critical Groups Sedl´ aˇ cek,On the minimal graph with a given number of spanning trees , Canad

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.366965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.963686Z digest=sha256:b0358f87986ae24382f61414931b94fe4b2808551519b697808f1592cb78841b

Observation c72e41c6-391c-486d-a4f7-6ed5bf6375da · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 62

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.355121Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.968479Z digest=sha256:89e138b554a713c1b4f58cb89221276d77913038fcbe07d5eadf592619183428

Observation 8e1b204a-9d81-4ed3-8779-fc78902f3947 · outbound

This paper cites Spielman, Graphs, vectors, and matrices, Bull.

Chip-Firing Games and Critical Groups Spielman, Graphs, vectors, and matrices, Bull

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.343450Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.972715Z digest=sha256:09419099cbd0015ee287d99e58ec95c267a38d9160628fa582d10ea566b2bec1

Observation ad746eeb-babb-49f8-a3c9-f452ccb9d7e3 · outbound

This paper cites Stanley, Smith normal form in combinatorics, J.

Chip-Firing Games and Critical Groups Stanley, Smith normal form in combinatorics, J

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:55:39.330286Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.978239Z digest=sha256:db6f99c995474c3ccfd68e3f3ca59878cf5c03e0ebeb45d985a79e022dd68706

Observation 800b1280-03be-4ad6-9de3-09e8fc69a36c · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 65

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.317078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.982266Z digest=sha256:0e3ecbb7bb467cac6f964bd754850cc70031a9fcfe2e62ab8da8bc5089bd04d7

Observation 4f5c0a94-d162-481b-9b8c-de2da379b3b5 · outbound

This paper cites The critical group of a directed graph.

Chip-Firing Games and Critical Groups The critical group of a directed graph

Reference 66

Resolution
verified exact
local_arxiv, observed 2026-08-14T13:55:39.153085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.985775Z digest=sha256:29b081965fc1d96ad0bfaf1e4cd9e1a0bf93cbe8983ce36f1399134e2cff3aeb

Observation b7ebef88-099c-43ae-ae2f-b89665eae500 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 67

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.301018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.989697Z digest=sha256:2b25231edd7bfae08f3f1d26913b2e874bf62e45824693640d3afbcc7a6ac2aa

Observation 29a5f872-0376-4a0f-b6b9-fe23a42c5468 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 68

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.287156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.994386Z digest=sha256:19b2f07a2bc9647e46793b7e827e2cffbcf1368498302c7aa64a4dc86e868db8

Observation 0a1ea980-bc2d-4eeb-ac00-b7e7b9088a13 · outbound

This paper cites an unresolved cited work.

Chip-Firing Games and Critical Groups Unresolved cited work

Reference 69

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:55:39.274331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.998298Z digest=sha256:0e998656c55db7e1d484e8ac0d737613ed4860edb4e2b8c27fe9a00ee2af501c

Pith citing papers

No inbound Pith citation observations are available.