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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=sha256:7590cc18c4f1ab2944fa4d0e20d7bd91085044bc22484fd4d69c656b17bf36db

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:ee056e2d09e56f47ffa499628f5e397115629a043ed85958a213c242cb42f553

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:f6dc6293719559375b7189887f5110742af359579f66b29abfae32d9280ff36e

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:f96bc1246908512a16f1bba595e778e9e8d5192387581b90ea41eb17f4182701

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=sha256:3ccf775d100bceda6743bfb9bf94c24872ffaca19738ff0f0bd72f29ee427a1e

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=sha256:010c1e089d024fa527d7c1cdf3e58bf3f1fb62ee917f74c9aa94e56f7f18005c

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:d0a1e7e8e87b597d6061d042f75222baeda256e986e5eddd1982fc6a7c9ad221

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=sha256:5fcea7e529bf85e7afc52146dbbc9e76fd8cc135ce584d342f976f32e841de62

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=sha256:4d4b8d2207142df97664f128846f14793078b969ffc42a9249e4ae7b4224cd40

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:e3eb6fdd414f3326cabc5145c76bc937f73279552b24fc1c789f2f9e96eb37ac

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=sha256:841a082d35fd3e99edbf5babb3ca01dad6859e4669b9396e5df75ff333389775

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=sha256:6decacc85146663a38917cfcd9e29637be4bdea5ccba3a986ce576b20454ba3c

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=sha256:243c5a06a802f6b6f2506b804c8df095faa74c3a510289b5e35ffcbae64ca608

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=sha256:30cc6821bbdffc42b50789370d67176d1093629af2a39f6af41afad47b5e07ba

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=sha256:2e52ae98da0e8451921d46fcaf959a8b02691426f319750037bf83956e99c817

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:f9a4ab6ee9a8c24d7c392f6cb7fadcec42ae7b7202946e008b4d27e2171a57a7

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=sha256:4980b0fbc9172a00159a516330c619418f7ece5b3862c60f5408e1951d2bdc6e

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:dc4d12bbbf49372cc244e79db1bb3cd7acd81a5039edacea2b39ad8fa3e82996

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:dacff012251d0cf0fd76355addef91383e07262e8b63c6d30176d5e0bf165412

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=sha256:3969cc2bcc068a9c7e9871fe659869887c297533039108899520d047701df9a5

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=sha256:4ffb8a247f85217606ccccb40b78113750d19c8311fd9c06794c27dd29dcb9b2

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=sha256:4e33955ae18731e3a21065526bf11c064b24358a705d922eec899f28726d2b73

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:bbd61455ece5e88ae2ae8a376817c29d58ef88bd1ed426fee7dca0b1d94f5c2e

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=sha256:748b7ed056ba27f990121603581d2a8f12037dfb92de29a9e77b9fbcc1ad1c47

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:f7ccfee17b5ed35d2530f757315ec112d7060e510ab41c9110e01a2257b4ba8c

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=sha256:59a4971892bd22abe89795d977276955db1164722925b4f83ec71490fecede54

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:ca0ba27d5e9b1b4a0f77bed713d421ce5a45f51f7f31e2dde03bc0ca2c9befb0

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:c3cff0aae1c3bf3e629bda69cc6067a904893e6f184b6bfca44a7f2aa8ee53db

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=sha256:078b5f49a7e486249947d0da4fe9f4392d282aa82204f8d6c6706ba7782d45b2

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:ce98d1e10074dd711cb2cb9c8bb86b430aeb135630c6f57c6f116114b3297ace

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=sha256:45f1b8daf824efbcd39df2d0a633ac906d015b4d6a476798e1a3972374b62611

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:d4ccf53af5e4b09e0b271a525cb777a4da070a076dd5bf3cff3f6006cd5b282b

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=sha256:7320e8215e55cba78ecb30e808b0a5c530900851a6158d8e2523f608530eaf8c

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:f47e32d7b7a7f942adc3b5ba4a81c34119b53958e43f591c8ea45975284cf326

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=sha256:7e80757222f6fe2892a0ae1bf353d1907df054489a23c1a097c635329940117b

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:c89d4ec378a8a619b086a384212b199c802568f4b112e7bca0390bdf549aa8c3

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=sha256:14949a2eba7e6adc5bb9346f7b66b3fdcb0d48d393032f7bf321afa948e0b6ad

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=sha256:6bee88cdd4c9f058001829fdbfcfe2acad7a44a72f61e90e43db397e8cc8c86d

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=sha256:3508db5ec365e387e1e487067edec30ff1aa9397c0ee354d3269c80032bfc809

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=sha256:05f9d9e8496893d6d1b12fc970eeeca71cff11d940d47cde3341e450583742c5

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:d5a50d6aa1ffd3160e2c3517c8cb95058dfbfded4b00199947d6595182932891

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=sha256:75a4d253171a68bc4a140835b183e15b7bf6f2aa2b52a314c9066845a46fe7ab

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=sha256:693be9d4883998fbb77e6b3be4493afb9632b32907ec1920f3f7f812ce1814db

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=sha256:3c5e1f51862013b0c6d1372d0b5cdd093c06181ad324e455eca8483143f2180b

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=sha256:00a8a912efdd8f6357c0accb831dae80e0bf0abf69d8464cb5b9f98a1d6534e3

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=sha256:5ad3f02c88248bc17e68b0e259a03c6cc2729b6c0d92df74570f0b04e04fdb45

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=sha256:61e12929a186a0aaa7f4581e66ddf7fbf8f275874c09b44240b32f3e482416a3

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=sha256:4ba17d6c58b0c384481d25cb93c483c2766138ab15dbbace91452b7e72becb68

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=sha256:393e4c572d73cba38bcaec0615a45cf4728229a86a1ddeea28e4baa5ed387c74

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:f0310a09e51b87f2e99f32bbe72b52c98b00593ebefe7e716212e55f256157b8

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:a12805c1215841efb00fecd4edce4ae68bc8e05f7c941aed38ce221aa1aa8797

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:f65f23fc0ef1235e45b2a00583dd675db51594c0336fecf0bd1643358b4715b0

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:afb635ab95e9c68291ea24d29af405adc97db07bf52c57587b3995bde98bab65

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:c7687bef4a1baac2de33799a276147a035f504850955fa6edaadc60339917ccf

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=sha256:14310ab28dd294b762e8fa74b510356685e50b80a60177de73dccafcaae7c9d8

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=sha256:6f13040a64fe4c9232eedf91ff20576b791edb4afaf4cb20767633ddf60dd836

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=sha256:9b8990abba11e6265307dcc7a6c142c724a01a48bc590a8248ced18dbe89f350

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=sha256:8e3e2ac5f7cfde62c794e7393b03461ef11b3a79b40cd98d1be20a134bfddec6

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=sha256:988a638e30d81f9d3181c3f146c4921cbf3d6f5c50de6335339ade59440f4d53

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=sha256:5c60089f436540bc277481019ed1ad817ffe981dfb68b1088447c7e94e1e8a27

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:d69f51ebbbb71aea87c78aa29a7b979a618fea15370a67ca7ed04ce55a875342

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=sha256:25bb178dfe156797e3c44c45e80a3f027e74d9995d66a77595efb0d867e05837

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=sha256:70688aa4bb19ddfa43a9ff7025f97c029e7199eddf237e37c06100256624124b

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=sha256:5c9d9be3aacf35a0a8f1886c27adcebeaf48ca86c5a80b904a9c364ab3e2de09

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=sha256:17b02088d79f88bd2b2475f51a247018694931a990793d7be6d8d5d0cc84b83b

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=sha256:6d9fb90d1c56d87de4f6cf61aba34a8496be04c58123a732e251a14704e4be2f

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:ca9b55aa0bfd62a02711a322f5f853683333ad226db12c55cb2a3cf7b7f867ca

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=sha256:4d29e19d11e115d065576bbbe2e2961f2d3f10026764367e8c37be0548156a5d

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=sha256:392ea758164f2f4bd381683944a359d9bd1a8841aa963a25235d2a7cb44a1138

Pith citing papers

No inbound Pith citation observations are available.