Paper Citation Record · LEDGER

On the long-range order of the Spectre tilings

As of 21 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 2 inbound Pith citation observations for arXiv:2411.15503.

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

pith.paper-citation-record.v1
2411.15503 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T14:18:36.268434Z

measured 25 of 25 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-08T14:29:27.495710Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-08T14:29:27.634019Z

Reference resolution

23 of 23 outbound references displayed

verified exact6
verified fuzzy10
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5849b957-ac15-41fa-8b41-727d4a38394e · outbound

This paper cites An alternative proof for an aperiodic monotile.

On the long-range order of the Spectre tilings An alternative proof for an aperiodic monotile

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-12T14:18:37.132575Z

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 b8608583-4848-4604-b5cd-107e6d3ceb89 · outbound

This paper cites Anderson and I.F.

On the long-range order of the Spectre tilings Anderson and I.F

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:18:37.548652Z

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 95104f80-a641-476e-a8d6-6fafe3b04881 · outbound

This paper cites Algorithm for determining pure pointedness of self-affine tilings.

On the long-range order of the Spectre tilings Algorithm for determining pure pointedness of self-affine tilings

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-12T14:18:37.073892Z

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 a916fbfc-be9e-420c-816f-ab5fa8fefa88 · outbound

This paper cites Orbit separation dimension as complexity measure for primitive inflation tilings.

On the long-range order of the Spectre tilings Orbit separation dimension as complexity measure for primitive inflation tilings

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-12T14:18:36.095747Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e690d062-8a4b-41f3-a470-03507e8b0057 · outbound

This paper cites Baake, F.

On the long-range order of the Spectre tilings Baake, F

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-12T14:18:36.100030Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8e120ee-bfc7-43dd-93a3-6f843d63c2ff · outbound

This paper cites Baake, F.

On the long-range order of the Spectre tilings Baake, F

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:18:37.536465Z

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 10d01f28-4ab8-4824-8aba-58979c925d8b · outbound

This paper cites Baake and U.

On the long-range order of the Spectre tilings Baake and U

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-12T14:18:36.107151Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06d29253-21b6-4168-8f6c-798d20b96446 · outbound

This paper cites Baake and D.

On the long-range order of the Spectre tilings Baake and D

Reference 8

Resolution: verified exact; raw_fallback, observed 2026-08-12T14:18:36.786700Z

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 47092cd9-734b-4222-a613-ddc3497e777f · outbound

This paper cites Clark and L.

On the long-range order of the Spectre tilings Clark and L

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-12T14:18:36.115643Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9fe5974e-d07d-401d-88d7-fe7db53dd947 · outbound

This paper cites Elton, An ergodic theorem for iterated maps, Ergod.

On the long-range order of the Spectre tilings Elton, An ergodic theorem for iterated maps, Ergod

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:18:37.516070Z

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 cd70b71f-d1f9-4bb6-98e0-4a8194ec5a60 · outbound

This paper cites Frank and L.

On the long-range order of the Spectre tilings Frank and L

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:18:37.423588Z

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 f9561257-0d3d-4990-9e0e-bce363059359 · outbound

This paper cites Greither, On the two generator problem for the ideals of a one-dimensional ring, J.

On the long-range order of the Spectre tilings Greither, On the two generator problem for the ideals of a one-dimensional ring, J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:18:37.367944Z

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 5840cf09-8d17-4bf5-9e6e-317ec18efca6 · outbound

This paper cites Julien and L.

On the long-range order of the Spectre tilings Julien and L

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:18:37.354565Z

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 f8b14e48-0754-4a67-b33c-d1b51aa252aa · outbound

This paper cites Non Commutative Geometry of Tilings and Gap Labelling.

On the long-range order of the Spectre tilings Non Commutative Geometry of Tilings and Gap Labelling

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-12T14:18:36.470084Z

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 9c5b529f-f8c5-4439-8f28-cb245523f36d · outbound

This paper cites Maz´ aˇ c,Fractal and Statistical Phenomena in Aperiodic Order , PhD thesis, Bielefeld University, in preparation (2024).

On the long-range order of the Spectre tilings Maz´ aˇ c,Fractal and Statistical Phenomena in Aperiodic Order , PhD thesis, Bielefeld University, in preparation (2024)

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:18:37.341856Z

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 3d78d5f5-0ae1-4812-83b7-3aee0b06cab8 · outbound

This paper cites Moody, Uniform distribution in model sets, Can.

On the long-range order of the Spectre tilings Moody, Uniform distribution in model sets, Can

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:18:37.328602Z

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 9865aa63-4dde-471d-8417-72b86b3632af · outbound

This paper cites Sadun, Topology of Tiling Spaces, Amer.

On the long-range order of the Spectre tilings Sadun, Topology of Tiling Spaces, Amer

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:18:37.203852Z

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 5b4058b7-2af2-4f8d-9f1d-75217dcb5d71 · outbound

This paper cites An aperiodic monotile.

On the long-range order of the Spectre tilings An aperiodic monotile

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-12T14:18:36.151931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a1ff7986-fd37-4faa-9607-125d6b9b8743 · outbound

This paper cites A chiral aperiodic monotile.

On the long-range order of the Spectre tilings A chiral aperiodic monotile

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-12T14:18:36.195571Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 28a01ec8-afb8-4345-aabf-0eeb2dd174a5 · outbound

This paper cites Turtles, Hats and Spectres: Aperiodic structures on a Rhombic tiling.

On the long-range order of the Spectre tilings Turtles, Hats and Spectres: Aperiodic structures on a Rhombic tiling

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-12T14:18:36.387037Z

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 2f36f69b-562c-42be-945a-8b3c6f266755 · outbound

This paper cites An aperiodic hexagonal tile.

On the long-range order of the Spectre tilings An aperiodic hexagonal tile

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-12T14:18:36.310506Z

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 901e8d52-7071-47ac-ab17-bd246e071dc7 · outbound

This paper cites Solomyak, Dynamics of self-similar tilings, Ergod.

On the long-range order of the Spectre tilings Solomyak, Dynamics of self-similar tilings, Ergod

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:18:37.155207Z

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 7599d929-e36d-4b24-8340-c84a93853774 · outbound

This paper cites an unresolved cited work.

On the long-range order of the Spectre tilings Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-12T14:18:37.143137Z

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

Observation ae589d43-da3d-4e05-90a6-e814ded5f5a9 · inbound

Quasilattices of the Spectre monotile cites this paper.

Quasilattices of the Spectre monotile On the long-range order of the Spectre tilings

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-08T14:29:27.639035Z

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 8cd2860d-a93c-4956-9a8c-5186c919e0aa · inbound

Quantum error-correcting codes from aperiodic monotiles: the Hat and the Spectre cites this paper.

Quantum error-correcting codes from aperiodic monotiles: the Hat and the Spectre On the long-range order of the Spectre tilings

Reference 5

Resolution: malformed identifier; no resolver link, observed 2026-08-02T00:38:16.705406Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.