Paper Citation Record · LEDGER

A $\sigma$-morphic convex protoset

As of 13 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2507.20867.

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

pith.paper-citation-record.v1
2507.20867 v1

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T13:20:55.633417Z

measured 29 of 29 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 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

29 of 29 outbound references displayed

verified exact0
verified fuzzy23
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8d5b678e-b336-4847-8247-fba082150e70 · outbound

This paper cites Adams, The Tiling Book: An Introduction to the Mathematical Theory of Tilings, American Mathematical Society (2022).

A $\sigma$-morphic convex protoset Adams, The Tiling Book: An Introduction to the Mathematical Theory of Tilings, American Mathematical Society (2022)

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:56.112270Z

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 66edaeb3-aece-49e1-bf5c-f0fbbb158c02 · outbound

This paper cites Bašić, A.

A $\sigma$-morphic convex protoset Bašić, A

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:56.093285Z

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 a65fe712-2c41-4570-9a11-72342705457e · outbound

This paper cites Dolbilin, The countability of a tiling family and the p eriodicity of a tiling.

A $\sigma$-morphic convex protoset Dolbilin, The countability of a tiling family and the p eriodicity of a tiling

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:56.077336Z

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 70d2fd7b-c10d-431a-ae64-0530a0395e92 · outbound

This paper cites Danzer, and N.

A $\sigma$-morphic convex protoset Danzer, and N

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:56.061031Z

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 89729e88-a005-442f-8cd2-0050e15f9671 · outbound

This paper cites Grünbaum and G.

A $\sigma$-morphic convex protoset Grünbaum and G

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:56.044833Z

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 78a63e33-5c6c-49ad-b198-64300c394460 · outbound

This paper cites Grünbaum and G.

A $\sigma$-morphic convex protoset Grünbaum and G

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:56.029407Z

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 fa63f89e-d716-413a-8a78-2f3ff3c86153 · outbound

This paper cites Jeandel, R.

A $\sigma$-morphic convex protoset Jeandel, R

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:56.014644Z

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 c17948b0-c411-446c-b220-09a33161a304 · outbound

This paper cites Kari, A small aperiodic set of Wang tiles.

A $\sigma$-morphic convex protoset Kari, A small aperiodic set of Wang tiles

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.998144Z

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 02d3e30d-96c7-4ca6-8429-18cf89c883c3 · outbound

This paper cites an unresolved cited work.

A $\sigma$-morphic convex protoset Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T13:20:55.983043Z

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 c0b56bcd-df16-4f57-92c2-88237d7d46ea · outbound

This paper cites an unresolved cited work.

A $\sigma$-morphic convex protoset Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T13:20:55.968012Z

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 75f2f537-4f34-49f0-9d34-d4e8fa73cb6a · outbound

This paper cites Myers, Polyomino, polyhex and polyiamond tiling, https://www.polyomino.org.uk/mathematics/polyform-tiling/.

A $\sigma$-morphic convex protoset Myers, Polyomino, polyhex and polyiamond tiling, https://www.polyomino.org.uk/mathematics/polyform-tiling/

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.952148Z

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 cd1fedeb-f2bc-471f-8d0b-5cf60903146a · outbound

This paper cites Myers, Personal communication.

A $\sigma$-morphic convex protoset Myers, Personal communication

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.936174Z

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 f027a4c2-66be-4a4c-8145-ee95ab1f2986 · outbound

This paper cites Niven, Convex polygons which cannot tile the plane.

A $\sigma$-morphic convex protoset Niven, Convex polygons which cannot tile the plane

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.921184Z

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 3fc34551-ea37-4025-afaa-2ea3f0768dd5 · outbound

This paper cites Payne, Unit Distance Graphs with Ambiguous Chroma tic Number.

A $\sigma$-morphic convex protoset Payne, Unit Distance Graphs with Ambiguous Chroma tic Number

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.905460Z

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 d77276fa-1fd8-47e1-9c78-53432a21ae2f · outbound

This paper cites Penrose, Pentaplexity: A Class of Nonperiodic Thing s of the Plane, Eureka, 39, 1978, pp.

A $\sigma$-morphic convex protoset Penrose, Pentaplexity: A Class of Nonperiodic Thing s of the Plane, Eureka, 39, 1978, pp

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.889030Z

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 f10bf9a6-185b-4389-b6f7-2922c8823279 · outbound

This paper cites Exhaustive search of convex pentagons which tile the plane.

A $\sigma$-morphic convex protoset Exhaustive search of convex pentagons which tile the plane

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T13:20:55.575581Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e458b2b2-a521-4750-aaee-4cac2ae9b93d · outbound

This paper cites Reinhardt, Über die zerlegung der ebene in polygone.

A $\sigma$-morphic convex protoset Reinhardt, Über die zerlegung der ebene in polygone

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.872233Z

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 972b412b-42ab-4b10-93a1-b31d687e3a2c · outbound

This paper cites Reinhardt, Zwei Beweise für einen Satz über die Zerle gung der Ebene.

A $\sigma$-morphic convex protoset Reinhardt, Zwei Beweise für einen Satz über die Zerle gung der Ebene

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.855791Z

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 f8e5d3b5-3a8f-42ea-b0a4-0c0359df0ec7 · outbound

This paper cites Reinhardt, Zur Zerlegung der euklidischen Räume in k ongruente Polytope, Sitzungsber.

A $\sigma$-morphic convex protoset Reinhardt, Zur Zerlegung der euklidischen Räume in k ongruente Polytope, Sitzungsber

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.841616Z

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 019bd7c5-172c-46ba-a7e7-a538455f25c4 · outbound

This paper cites Schattschneider: Tiling the plane with congruent pe ntagons.

A $\sigma$-morphic convex protoset Schattschneider: Tiling the plane with congruent pe ntagons

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.825934Z

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 4121860f-8dc2-46e7-ae93-fbde44c56038 · outbound

This paper cites Schmitt, Pairs of tiles which admit ﬁnitely or counta bly inﬁnitely many tilings, Geom.

A $\sigma$-morphic convex protoset Schmitt, Pairs of tiles which admit ﬁnitely or counta bly inﬁnitely many tilings, Geom

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.810860Z

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 58a84da7-2b5c-4626-92de-4bdd60f96ed7 · outbound

This paper cites Schmitt, Polymorphic pairs of prototiles, Österreich.

A $\sigma$-morphic convex protoset Schmitt, Polymorphic pairs of prototiles, Österreich

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.795150Z

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 5ea6bf5e-e8ac-4f87-8d9a-aff4a93bb0f0 · outbound

This paper cites Schmitt, Sets of tiles with a prescribed number of til ings, Geom.

A $\sigma$-morphic convex protoset Schmitt, Sets of tiles with a prescribed number of til ings, Geom

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.777791Z

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 c88ca5a0-21a3-4616-bf09-ff3d78e5cc88 · outbound

This paper cites Schmitt, σ-morphic sets of prototiles, Discrete Comput.

A $\sigma$-morphic convex protoset Schmitt, σ-morphic sets of prototiles, Discrete Comput

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.762474Z

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 d793b3a3-4274-453f-a244-320f43c65ec5 · outbound

This paper cites Senechal, Quasicrystals and Geometry.

A $\sigma$-morphic convex protoset Senechal, Quasicrystals and Geometry

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.746830Z

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 3205fa58-c96c-42b7-a016-0f1e4cd86a18 · outbound

This paper cites Shelah and A.

A $\sigma$-morphic convex protoset Shelah and A

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:20:55.732863Z

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 7f14e82b-c3c0-4f5b-9892-00571de9e22a · outbound

This paper cites A chiral aperiodic monotile.

A $\sigma$-morphic convex protoset A chiral aperiodic monotile

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T13:20:55.624078Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a7b89bf-fc77-448a-ab07-20786d397acd · outbound

This paper cites An aperiodic monotile.

A $\sigma$-morphic convex protoset An aperiodic monotile

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T13:20:55.628603Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 26fc01dd-9e49-47ea-801a-e7aeb5c9f83e · outbound

This paper cites an unresolved cited work.

A $\sigma$-morphic convex protoset Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-06T13:20:55.717998Z

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.

Pith citing papers

No inbound Pith citation observations are available.