Paper Citation Record · LEDGER

Associative Pentagon Algebras

As of 20 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:2506.14216.

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

pith.paper-citation-record.v1
2506.14216 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T00:30:57.805433Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-10T17:51:57.020010Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T05:56:00.103056Z

Reference resolution

33 of 33 outbound references displayed

verified exact20
verified fuzzy6
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b9f3e952-f0ef-4d55-9b9c-661f98892172 · outbound

This paper cites Agore, A.

Associative Pentagon Algebras Agore, A

Reference 1

Resolution: verified exact; doi, observed 2026-08-07T00:30:58.107679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ce1351ec-923c-4bbb-9cae-590d552344cb · outbound

This paper cites an unresolved cited work.

Associative Pentagon Algebras Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-07T00:30:58.513484Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 729c77a1-0548-45a9-8570-77577628bf5f · outbound

This paper cites an unresolved cited work.

Associative Pentagon Algebras Unresolved cited work

Reference 3

Resolution: verified exact; doi, observed 2026-08-07T00:30:58.089597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 62efca26-bb9b-41eb-9196-1a38b546065c · outbound

This paper cites an unresolved cited work.

Associative Pentagon Algebras Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T00:30:58.502898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 67f66ef5-8933-440b-bf6b-45636a3a252b · outbound

This paper cites On commutative set-theoretic solutions of the Pentagon Equation.

Associative Pentagon Algebras On commutative set-theoretic solutions of the Pentagon Equation

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-07T00:30:58.412434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3f5812c8-430a-42c0-a17d-31f3fa80e870 · outbound

This paper cites Catino, M.

Associative Pentagon Algebras Catino, M

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T00:30:54.394666Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b0ab315b-2318-4b75-9802-91c5463d90a7 · outbound

This paper cites Catino, M.

Associative Pentagon Algebras Catino, M

Reference 7

Resolution: verified exact; doi, observed 2026-08-07T00:30:58.070981Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4ced3408-ba56-410a-af87-57feb41d5263 · outbound

This paper cites Colazzo, E.

Associative Pentagon Algebras Colazzo, E

Reference 8

Resolution: verified exact; doi, observed 2026-08-07T00:30:58.048998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ca7270d4-8be4-4f60-bd26-e89aaba489cc · outbound

This paper cites Colazzo, J.

Associative Pentagon Algebras Colazzo, J

Reference 9

Resolution: verified exact; raw_fallback, observed 2026-08-07T00:30:58.305454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3b67ce78-1502-4e66-85b0-ad02fe71dd9d · outbound

This paper cites Dimakis, F.

Associative Pentagon Algebras Dimakis, F

Reference 10

Resolution: verified exact; doi, observed 2026-08-07T00:30:58.031552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3cc38bec-3d67-4386-8fd4-0d9795b6fbd3 · outbound

This paper cites Doliwa, S.

Associative Pentagon Algebras Doliwa, S

Reference 11

Resolution: verified exact; doi, observed 2026-08-07T00:30:58.010959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation bd7eee53-1b02-4bef-9c83-558f57e67b2c · outbound

This paper cites an unresolved cited work.

Associative Pentagon Algebras Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T00:30:58.492039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 00da12e7-ef86-417f-bc65-4e45c2aa0125 · outbound

This paper cites an unresolved cited work.

Associative Pentagon Algebras Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T00:30:55.335795Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 154f917a-d575-4b4c-ac6b-cc4c103df7e9 · outbound

This paper cites Evripidou, P.

Associative Pentagon Algebras Evripidou, P

Reference 14

Resolution: verified exact; doi, observed 2026-08-07T00:30:57.978114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0a602f76-64e7-42b2-b104-c91b62529824 · outbound

This paper cites Jiang, M.

Associative Pentagon Algebras Jiang, M

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:30:58.482535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e64c3013-8948-4e82-833b-ca5827a3a304 · outbound

This paper cites Kashaev, Fully noncommutative discrete Liouville equation, in: Infinite analysis 2010– Developments in quantum integrable systems, RIMS Kôkyûroku Bessatsu, B28, Res.

Associative Pentagon Algebras Kashaev, Fully noncommutative discrete Liouville equation, in: Infinite analysis 2010– Developments in quantum integrable systems, RIMS Kôkyûroku Bessatsu, B28, Res

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:30:58.470884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4ff79aff-d81b-440a-9cbb-76c1a26945f8 · outbound

This paper cites an unresolved cited work.

Associative Pentagon Algebras Unresolved cited work

Reference 17

Resolution: verified exact; doi, observed 2026-08-07T00:30:57.963684Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f1bff4d0-0084-4e68-975b-6c70fa4f4ae5 · outbound

This paper cites an unresolved cited work.

Associative Pentagon Algebras Unresolved cited work

Reference 18

Resolution: verified exact; doi, observed 2026-08-07T00:30:57.952502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d2e5f89a-0321-49d9-b5af-e9ea101a2722 · outbound

This paper cites Kassotakis, Matrix factorizations and pentagon maps, Proc.

Associative Pentagon Algebras Kassotakis, Matrix factorizations and pentagon maps, Proc

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:30:58.459918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2ec7da73-795c-44d5-9a5b-9c01964f7aec · outbound

This paper cites Kawamura, Pentagon equation arising from state equations of a C*-Bialgebra, Lett.

Associative Pentagon Algebras Kawamura, Pentagon equation arising from state equations of a C*-Bialgebra, Lett

Reference 20

Resolution: verified exact; doi, observed 2026-08-07T00:30:57.940882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 92716fe5-6ef4-4f96-aa5a-b03a416b1148 · outbound

This paper cites Kimura, The structure of idempotent semigroups I, Pacific J.

Associative Pentagon Algebras Kimura, The structure of idempotent semigroups I, Pacific J

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:30:58.449794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 37197b3b-614b-4b61-8ae6-5dd3a3254e02 · outbound

This paper cites Pentagon relation and Biedenharn-Elliott identity.

Associative Pentagon Algebras Pentagon relation and Biedenharn-Elliott identity

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T00:30:56.837870Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b396e89c-c67a-48bf-8b35-e5deed496666 · outbound

This paper cites Maillet, Integrable systems and gauge theories, Nuclear Phys.

Associative Pentagon Algebras Maillet, Integrable systems and gauge theories, Nuclear Phys

Reference 23

Resolution: verified exact; doi, observed 2026-08-07T00:30:57.929679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 27b88a18-c63d-4baa-ad58-ac9d3f8abf92 · outbound

This paper cites Mazzotta, Idempotent set-theoretical solutions of the pentagon equation, Boll.

Associative Pentagon Algebras Mazzotta, Idempotent set-theoretical solutions of the pentagon equation, Boll

Reference 24

Resolution: verified exact; doi, observed 2026-08-07T00:30:57.919899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6a1b8ff5-57e9-4fdf-9105-d7bd1c48c2b7 · outbound

This paper cites Mazzotta, Set-theoretical solutions to the pentagon equation: a survey, Commun.

Associative Pentagon Algebras Mazzotta, Set-theoretical solutions to the pentagon equation: a survey, Commun

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:30:58.437822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 65da927e-c841-46f6-8873-04758cd9ff45 · outbound

This paper cites Mazzotta, V.

Associative Pentagon Algebras Mazzotta, V

Reference 26

Resolution: verified exact; doi, observed 2026-08-07T00:30:57.908097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3337e7b4-e585-40b5-904e-543d713002f5 · outbound

This paper cites Militaru, The Hopf modules category and the Hopf equation, Comm.

Associative Pentagon Algebras Militaru, The Hopf modules category and the Hopf equation, Comm

Reference 27

Resolution: verified exact; doi, observed 2026-08-07T00:30:57.894731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation dc1d7ac3-c448-4327-bf00-90affb084a21 · outbound

This paper cites Militaru, Heisenberg Double, Pentagon Equation, Structure and Classification of Finite- Dimensional Hopf Algebras, J.

Associative Pentagon Algebras Militaru, Heisenberg Double, Pentagon Equation, Structure and Classification of Finite- Dimensional Hopf Algebras, J

Reference 28

Resolution: verified exact; doi, observed 2026-08-07T00:30:57.884125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2e354468-c661-4431-bc39-5bf1af0e4ee8 · outbound

This paper cites Moore, N.

Associative Pentagon Algebras Moore, N

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-07T00:30:57.663077Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8f559e6-a5cf-4440-a6c0-76aa6eaee194 · outbound

This paper cites Müller-Hoissen, On the structure of set-theoretic polygon equations, SIGMA Symmetry Integrability Geom.

Associative Pentagon Algebras Müller-Hoissen, On the structure of set-theoretic polygon equations, SIGMA Symmetry Integrability Geom

Reference 30

Resolution: verified exact; doi, observed 2026-08-07T00:30:57.872639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 68a2404b-df54-4de4-97f2-7920476a08e3 · outbound

This paper cites an unresolved cited work.

Associative Pentagon Algebras Unresolved cited work

Reference 31

Resolution: verified exact; doi, observed 2026-08-07T00:30:57.861487Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fb798103-02da-4a79-922c-2196bdbdafc2 · outbound

This paper cites Yamada, Exclusive semigroups, J.

Associative Pentagon Algebras Yamada, Exclusive semigroups, J

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:30:58.424561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fbc2f41a-19d0-4fde-95c4-e160b4df8838 · outbound

This paper cites Zakrzewski, Poisson Lie groups and pentagonal transformations, Lett.

Associative Pentagon Algebras Zakrzewski, Poisson Lie groups and pentagonal transformations, Lett

Reference 33

Resolution: verified exact; doi, observed 2026-08-07T00:30:57.849470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation d4a31e3c-df75-443b-8cff-50871d9b834a · inbound

Multicomponent pentagon maps cites this paper.

Multicomponent pentagon maps Associative Pentagon Algebras

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:56:00.105875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.