Paper Citation Record · LEDGER

Undecidability of Translational Tiling of the Plane with Four Tiles

As of 22 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2506.19295.

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

pith.paper-citation-record.v1
2506.19295 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:44:02.496919Z

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+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

18 of 18 outbound references displayed

verified exact1
verified fuzzy11
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a826b0ef-3d8d-40c2-af17-3b18bf1d0709 · outbound

This paper cites Ammann, B.

Undecidability of Translational Tiling of the Plane with Four Tiles Ammann, B

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:44:02.877326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c94b2aa1-bfdf-4f59-89dc-d07afa750549 · outbound

This paper cites Beauquier, M.

Undecidability of Translational Tiling of the Plane with Four Tiles Beauquier, M

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:44:02.858444Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ad4d01d2-016e-47f1-87c5-893be6e8e73e · outbound

This paper cites Berger, The undecidability of the domino problem,Memoirs of the American Mathemat- ical Society,66(1966), 1-72.

Undecidability of Translational Tiling of the Plane with Four Tiles Berger, The undecidability of the domino problem,Memoirs of the American Mathemat- ical Society,66(1966), 1-72

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:44:02.840740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 50112b5b-c3d8-4a94-9e80-28b1991d5712 · outbound

This paper cites Bhattacharya, Periodicity and decidability of tilings ofZ 2.American Journal of Mathe- matics,142(2020), 255-266.

Undecidability of Translational Tiling of the Plane with Four Tiles Bhattacharya, Periodicity and decidability of tilings ofZ 2.American Journal of Mathe- matics,142(2020), 255-266

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:44:02.823923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 72d53266-6746-4937-9a7d-32b16950c6ad · outbound

This paper cites Greenfeld, T.

Undecidability of Translational Tiling of the Plane with Four Tiles Greenfeld, T

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:44:02.807776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 162f9c9a-9509-4063-a75c-6927a07c5911 · outbound

This paper cites Greenfeld, T.

Undecidability of Translational Tiling of the Plane with Four Tiles Greenfeld, T

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:44:02.789513Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 33ca66ba-8e9a-4514-961b-eb509f132a06 · outbound

This paper cites Undecidability of translational monotilings.

Undecidability of Translational Tiling of the Plane with Four Tiles Undecidability of translational monotilings

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T18:44:02.439171Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 66d4627a-8f99-4fe7-af52-89ecdaf89d66 · outbound

This paper cites Kim, Undecidability of tiling the plane with a set of 5 polyominoes, (2025), a manuscript.

Undecidability of Translational Tiling of the Plane with Four Tiles Kim, Undecidability of tiling the plane with a set of 5 polyominoes, (2025), a manuscript

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T18:44:02.444386Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c7346c6-94b8-4521-a77d-7d858530bfb8 · outbound

This paper cites Ollinger, Tiling the plane with a fixed number of polyominoes, In: A.H.

Undecidability of Translational Tiling of the Plane with Four Tiles Ollinger, Tiling the plane with a fixed number of polyominoes, In: A.H

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:44:02.756226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 367f9f51-1027-4239-beeb-b2474bca9e7a · outbound

This paper cites an unresolved cited work.

Undecidability of Translational Tiling of the Plane with Four Tiles Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:44:02.738154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a0a49bd3-1b95-49d6-ad33-c7408ae927cf · outbound

This paper cites Wang, Proving theorems by pattern recognition-II,Bell System Technical Journal, 40(1961) 1-41.

Undecidability of Translational Tiling of the Plane with Four Tiles Wang, Proving theorems by pattern recognition-II,Bell System Technical Journal, 40(1961) 1-41

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:44:02.719990Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f6386434-0849-4482-9fcd-6af3c4b047a1 · outbound

This paper cites Winslow, An optimal algorithm for tiling the plane with a translated polyomino, In: K.

Undecidability of Translational Tiling of the Plane with Four Tiles Winslow, An optimal algorithm for tiling the plane with a translated polyomino, In: K

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:44:02.702524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0e2e1fa3-e5ef-4c2c-a586-78a8da68d493 · outbound

This paper cites Yang, Tiling the plane with a set of ten polyominoes,International Journal of Computa- tional Geometry & Applications,33(03n04)(2023), 55-64.

Undecidability of Translational Tiling of the Plane with Four Tiles Yang, Tiling the plane with a set of ten polyominoes,International Journal of Computa- tional Geometry & Applications,33(03n04)(2023), 55-64

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:44:02.684285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c87f2082-9020-4a32-8da8-f33991e87e44 · outbound

This paper cites Yang, On the undecidability of tiling the plane with a set of 9 polyominoes (in Chinese), SCIENTIA SINICA Mathematica,55(6)(2025), 1113-1122.

Undecidability of Translational Tiling of the Plane with Four Tiles Yang, On the undecidability of tiling the plane with a set of 9 polyominoes (in Chinese), SCIENTIA SINICA Mathematica,55(6)(2025), 1113-1122

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:44:02.666862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f27d23cf-91f3-41a5-899d-85051db39206 · outbound

This paper cites an unresolved cited work.

Undecidability of Translational Tiling of the Plane with Four Tiles Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T18:44:02.480109Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d6db1482-317c-4afb-b3d3-ba3cc5c60fa9 · outbound

This paper cites Translational Aperiodic Sets of 7 Polyominoes.

Undecidability of Translational Tiling of the Plane with Four Tiles Translational Aperiodic Sets of 7 Polyominoes

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T18:44:02.485667Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0fa724b2-5068-453f-abef-a3770154dac3 · outbound

This paper cites Undecidability of Translational Tiling with Three Tiles.

Undecidability of Translational Tiling of the Plane with Four Tiles Undecidability of Translational Tiling with Three Tiles

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T18:44:02.491583Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f43894c1-8520-421c-81d0-a71573e03228 · outbound

This paper cites Undecidability of Translational Tiling of the Plane with Orthogonally Convex Polyominoes.

Undecidability of Translational Tiling of the Plane with Four Tiles Undecidability of Translational Tiling of the Plane with Orthogonally Convex Polyominoes

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:44:02.592670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

No inbound Pith citation observations are available.