Paper Citation Record · LEDGER

Generalized chip firing and critical groups of arithmetical structures on trees

As of 16 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 1 inbound Pith citation observation for arXiv:2505.05392.

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

pith.paper-citation-record.v1
2505.05392 v2

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T23:29:17.272402Z

measured 22 of 22 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-07T15:45:14.897070Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-12T00:11:14.015533Z

Reference resolution

21 of 21 outbound references displayed

verified exact9
verified fuzzy4
unresolved6
parse uncertain0
malformed identifier1
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 25c945e4-a676-4e54-a159-8a3de13b1c7c · outbound

This paper cites Bishop, Alexander Diaz-Lopez, Luis D.

Generalized chip firing and critical groups of arithmetical structures on trees Bishop, Alexander Diaz-Lopez, Luis D

Reference 1

Resolution: metadata mismatch; raw_fallback, observed 2026-08-15T23:29:17.693620Z

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.

Observation e99345ba-e83b-42f9-8194-84bb3ac7f639 · outbound

This paper cites an unresolved cited work.

Generalized chip firing and critical groups of arithmetical structures on trees Unresolved cited work

Reference 2

Resolution: malformed identifier; doi_truncated, observed 2026-08-15T23:29:17.568882Z

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.

Observation d8fd1c9f-2c5e-4243-b467-ce26768db5d3 · outbound

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

Generalized chip firing and critical groups of arithmetical structures on trees Chip-Firing and Riemann-Roch Theory for Directed Graphs

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T23:29:17.179553Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 09f19bcb-517b-4ccb-82ec-852f352ac5bf · outbound

This paper cites an unresolved cited work.

Generalized chip firing and critical groups of arithmetical structures on trees Unresolved cited work

Reference 4

Resolution: verified exact; doi, observed 2026-08-15T23:29:17.530806Z

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.

Observation a87fd85f-e1a0-4647-ad8e-fc1100fa7d3b · outbound

This paper cites an unresolved cited work.

Generalized chip firing and critical groups of arithmetical structures on trees Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T23:29:17.191766Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 63d190a4-b600-4899-b5ae-f3aa8b727055 · outbound

This paper cites Glass, Cyclic critical groups of graphs , Australas.

Generalized chip firing and critical groups of arithmetical structures on trees Glass, Cyclic critical groups of graphs , Australas

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:29:17.780320Z

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.

Observation d37c8669-64c6-4ab6-a812-182e8ee7275f · outbound

This paper cites an unresolved cited work.

Generalized chip firing and critical groups of arithmetical structures on trees Unresolved cited work

Reference 7

Resolution: verified exact; doi, observed 2026-08-15T23:29:17.496328Z

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.

Observation 0765503a-9ae5-440b-8b99-b05825c17562 · outbound

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

Generalized chip firing and critical groups of arithmetical structures on trees Martin, Gregg Musiker, and Carlos E

Reference 8

Resolution: verified exact; doi, observed 2026-08-15T23:29:17.479049Z

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.

Observation 8c0d5095-af28-479a-ac11-5a86b2ff23f6 · outbound

This paper cites Critical ideals of trees.

Generalized chip firing and critical groups of arithmetical structures on trees Critical ideals of trees

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-15T23:29:17.457704Z

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.

Observation accf8fa3-3b2d-4914-8284-b7a534bc5c3e · outbound

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

Generalized chip firing and critical groups of arithmetical structures on trees Valencia, Arithmetical structures on graphs , Linear Algebra Appl

Reference 10

Resolution: verified exact; doi, observed 2026-08-15T23:29:17.426792Z

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.

Observation 2d137daf-d4a2-40be-871c-f3abed946a55 · outbound

This paper cites Valencia, Arithmetical structures on graphs with connectivity one, J.

Generalized chip firing and critical groups of arithmetical structures on trees Valencia, Arithmetical structures on graphs with connectivity one, J

Reference 11

Resolution: verified exact; doi, observed 2026-08-15T23:29:17.409331Z

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.

Observation 65496129-37f4-4c36-bb67-97b6427d273f · outbound

This paper cites an unresolved cited work.

Generalized chip firing and critical groups of arithmetical structures on trees Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T23:29:17.227834Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47aa19b9-84fa-4bcf-8e5a-95e1b8528bec · outbound

This paper cites an unresolved cited work.

Generalized chip firing and critical groups of arithmetical structures on trees Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T23:29:17.232896Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fb0e8eb4-8dc0-422a-bb09-8f06fd51052e · outbound

This paper cites 22 KASSIE ARCHER, ALEXANDER DIAZ-LOPEZ, DARREN GLASS, AND JOEL LOUWSMA.

Generalized chip firing and critical groups of arithmetical structures on trees 22 KASSIE ARCHER, ALEXANDER DIAZ-LOPEZ, DARREN GLASS, AND JOEL LOUWSMA

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:29:17.764294Z

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.

Observation 9df856a0-fb81-42f1-a673-3221cd0066d4 · outbound

This paper cites Klivans, The mathematics of chip-firing , Discrete Mathematics and its Applications, CRC Press, Boca Raton, FL, 2019, https://doi.org/10.1201/9781315206899.

Generalized chip firing and critical groups of arithmetical structures on trees Klivans, The mathematics of chip-firing , Discrete Mathematics and its Applications, CRC Press, Boca Raton, FL, 2019, https://doi.org/10.1201/9781315206899

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T23:29:17.242742Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e8412f5-9c83-4e7f-8326-1a8e3a9e9faa · outbound

This paper cites an unresolved cited work.

Generalized chip firing and critical groups of arithmetical structures on trees Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:29:17.747953Z

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.

Observation d6ca74cb-e4af-4a55-a32a-0fadcd4ef131 · outbound

This paper cites 73 (1990), no.

Generalized chip firing and critical groups of arithmetical structures on trees 73 (1990), no

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:29:17.729770Z

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.

Observation a92cfae9-493c-4f6e-b970-247471d28ac4 · outbound

This paper cites Reine Angew.

Generalized chip firing and critical groups of arithmetical structures on trees Reine Angew

Reference 18

Resolution: verified exact; doi, observed 2026-08-15T23:29:17.349077Z

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.

Observation 955ad753-c830-4aac-ad33-6b23be729df8 · outbound

This paper cites Reine Angew.

Generalized chip firing and critical groups of arithmetical structures on trees Reine Angew

Reference 19

Resolution: verified exact; doi, observed 2026-08-15T23:29:17.332885Z

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.

Observation 76d08530-024a-4584-ab99-106eac45798e · outbound

This paper cites Number Theory 257 (2024), 215–248, https: //doi.org/10.1016/j.jnt.2023.10.009.

Generalized chip firing and critical groups of arithmetical structures on trees Number Theory 257 (2024), 215–248, https: //doi.org/10.1016/j.jnt.2023.10.009

Reference 20

Resolution: verified exact; doi, observed 2026-08-15T23:29:17.315860Z

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.

Observation f915c2f3-8f2c-4455-84e0-d471cb83eab1 · outbound

This paper cites Raynaud, Sp´ ecialisation du foncteur de Picard, Inst.

Generalized chip firing and critical groups of arithmetical structures on trees Raynaud, Sp´ ecialisation du foncteur de Picard, Inst

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:29:17.712227Z

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.

Pith citing papers

Observation e6044dac-a294-4969-9199-07e7256eee79 · inbound

Arithmetical Structures on Ladder Graphs cites this paper.

Arithmetical Structures on Ladder Graphs Generalized chip firing and critical groups of arithmetical structures on trees

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-12T00:11:14.029054Z

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.