Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T13:20:55.633417Z
Paper Citation Record · LEDGER
A $\sigma$-morphic convex protoset
As of 22 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.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+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.
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 2026-08-22T06:32:14.747728+00:00.
Pith citing papers
No inbound Pith citation observations are available.