Paper Citation Record · LEDGER

Undecidability of Translational Tiling with Three Tiles

As of 13 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 2 inbound Pith citation observations for arXiv:2412.10646.

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

pith.paper-citation-record.v1
2412.10646 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T15:56:09.248642Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T00:53:26.193379Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T20:09:22.958752Z

Reference resolution

25 of 25 outbound references displayed

verified exact2
verified fuzzy11
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7c4f609f-75b9-44e7-bf2e-3fb89cf00239 · outbound

This paper cites Beauquier, M.

Undecidability of Translational Tiling with Three Tiles Beauquier, M

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:56:09.614247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d6fe092e-4f6b-4b1a-9a06-95b92841a857 · outbound

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

Undecidability of Translational Tiling with Three Tiles Berger, The undecidability of the domino problem, Memoirs of the American Mathematical Society , 66(1966), 1-72

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:56:09.603641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 14c65757-d192-4f2b-9c88-38e2d4af6d58 · outbound

This paper cites Bhattacharya, Periodicity and decidability of tilings of Z2.

Undecidability of Translational Tiling with Three Tiles Bhattacharya, Periodicity and decidability of tilings of Z2

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:56:09.591897Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c3dbb420-208b-4202-90bb-4584288b2abd · outbound

This paper cites Tiling with Three Polygons is Undecidable.

Undecidability of Translational Tiling with Three Tiles Tiling with Three Polygons is Undecidable

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-11T15:56:09.169601Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 46b05151-ef22-4693-ab1d-b3dfc5171974 · outbound

This paper cites Greenfeld, T.

Undecidability of Translational Tiling with Three Tiles Greenfeld, T

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T15:56:09.174190Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c28954e8-44b9-4a5d-b389-36477a70427f · outbound

This paper cites Greenfeld, T.

Undecidability of Translational Tiling with Three Tiles Greenfeld, T

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:56:09.572497Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b482c4b9-0682-4edc-8bfb-4c26a81370f0 · outbound

This paper cites Greenfeld, T.

Undecidability of Translational Tiling with Three Tiles Greenfeld, T

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:56:09.561195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 14e9f502-8b78-474d-a2fd-acde37aaded5 · outbound

This paper cites Undecidability of translational monotilings.

Undecidability of Translational Tiling with Three Tiles Undecidability of translational monotilings

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T15:56:09.185314Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 91cae3a1-c9ba-4f37-94ed-3c730dc4a9ac · outbound

This paper cites Gr¨ unbaum, G.

Undecidability of Translational Tiling with Three Tiles Gr¨ unbaum, G

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:56:09.549929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d8715c2b-8d4c-4a66-8c4e-e201a2eee251 · outbound

This paper cites Jeandel, N.

Undecidability of Translational Tiling with Three Tiles Jeandel, N

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:56:09.538413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 41726683-2956-4a67-9b69-bd463d2b76f1 · outbound

This paper cites an unresolved cited work.

Undecidability of Translational Tiling with Three Tiles Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T15:56:09.196348Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 430df2d4-a96f-463a-bfa3-b8ac96609421 · outbound

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

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

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:56:09.518594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation df0df446-dcf3-498a-914a-4a4c36c5ead0 · outbound

This paper cites Sidorenko, Periodicity of one-dimensional tilings.

Undecidability of Translational Tiling with Three Tiles Sidorenko, Periodicity of one-dimensional tilings

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:56:09.498170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 652fc189-8119-493e-8278-530470a68745 · outbound

This paper cites An aperiodic monotile.

Undecidability of Translational Tiling with Three Tiles An aperiodic monotile

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T15:56:09.211251Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dee80230-15c9-4d06-86be-cf872b81ca04 · outbound

This paper cites A chiral aperiodic monotile.

Undecidability of Translational Tiling with Three Tiles A chiral aperiodic monotile

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-11T15:56:09.215199Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12f0e396-f0b4-46d3-9fb4-d203e35da26a · outbound

This paper cites an unresolved cited work.

Undecidability of Translational Tiling with Three Tiles Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:56:09.486422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9b7b2c14-7ad8-4032-ada0-b6eb807491f1 · outbound

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

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

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:56:09.474582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f8a8ebbf-7ffd-40e7-b0ac-3a3ed0fd0226 · outbound

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

Undecidability of Translational Tiling with Three Tiles Winslow, An optimal algorithm for tiling the plane with a translate d polyomino, In: K

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:56:09.462134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation bdb0512d-85bc-42c7-be53-68b61924326c · outbound

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

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

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T15:56:09.229961Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f3f93a50-c74b-47ce-b91a-866d49074dcc · outbound

This paper cites Yang, On the undecidability of tiling the plane with a set of 9 polyo minoes (in Chinese), (2024), to appear in SCIENTIA SINICA Mathematica.

Undecidability of Translational Tiling with Three Tiles Yang, On the undecidability of tiling the plane with a set of 9 polyo minoes (in Chinese), (2024), to appear in SCIENTIA SINICA Mathematica

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T15:56:09.233590Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac44a078-1615-47aa-9720-356af01c3448 · outbound

This paper cites an unresolved cited work.

Undecidability of Translational Tiling with Three Tiles Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T15:56:09.237261Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a6e4b23-e7e8-4ea5-8ec8-435fcda01ea2 · outbound

This paper cites an unresolved cited work.

Undecidability of Translational Tiling with Three Tiles Unresolved cited work

Reference 22

Resolution: verified exact; raw_fallback, observed 2026-08-11T15:56:09.396645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ab206487-df39-42a3-a0be-615b22e0914e · outbound

This paper cites Undecidability of Translational Tiling of the 3-dimensional Space with a Set of 6 Polycubes.

Undecidability of Translational Tiling with Three Tiles Undecidability of Translational Tiling of the 3-dimensional Space with a Set of 6 Polycubes

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T15:56:09.244777Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 869ce81e-ed32-4f68-bfa5-1ab84897b35e · outbound

This paper cites Undecidability of Translational Tiling of the 4-dimensional Space with a Set of 4 Polyhypercubes.

Undecidability of Translational Tiling with Three Tiles Undecidability of Translational Tiling of the 4-dimensional Space with a Set of 4 Polyhypercubes

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-11T15:56:09.299766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 092a4697-a75a-486e-adb6-935a301a98dc · outbound

This paper cites an unresolved cited work.

Undecidability of Translational Tiling with Three Tiles Unresolved cited work

Reference 5457

Resolution: unresolved; no resolver link, observed 2026-08-11T15:56:09.203911Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 765481b5-b631-4483-ae04-4653161d20e4 · inbound

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

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

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T00:53:26.193379Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e17900f8-2d81-4e94-9dc7-b8a3e7de94c0 · inbound

Undecidability of Translational Tiling with 2 Polycubes cites this paper.

Undecidability of Translational Tiling with 2 Polycubes Undecidability of Translational Tiling with Three Tiles

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-05T20:09:23.066540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.