Paper Citation Record · LEDGER

Between Markov and restriction. Two more monads on categories for relations

As of 22 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 1 inbound Pith citation observation for arXiv:2508.20054.

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

pith.paper-citation-record.v1
2508.20054 v2

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:58:06.868089Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T05:51:26.543451Z

measured 1 of 1 external citation measurements

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

Source: pith, observed 2026-08-10T05:30:23.456663Z

Reference resolution

27 of 27 outbound references displayed

verified exact0
verified fuzzy22
unresolved5
parse uncertain0
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External citation measurements

0
pith, observed 2026-08-10T05:30:23.456663Z

Outbound references

Observation b53f5ce3-5561-4d90-986c-ab6da9a8c5c3 · outbound

This paper cites Monoidal functors, species and Hopf algebras, volume 29 of CRM Monograph Series.

Between Markov and restriction. Two more monads on categories for relations Monoidal functors, species and Hopf algebras, volume 29 of CRM Monograph Series

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.351436Z

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 e837b966-20be-4a47-ad4c-a0718d25d325 · outbound

This paper cites Semiring-based constraint satisfaction and optimization.

Between Markov and restriction. Two more monads on categories for relations Semiring-based constraint satisfaction and optimization

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.336768Z

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 f14d2864-1d05-433f-91fa-ba159a3a167b · outbound

This paper cites String diagram rewrite theory I: Rewriting with Frobenius structure.

Between Markov and restriction. Two more monads on categories for relations String diagram rewrite theory I: Rewriting with Frobenius structure

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.322462Z

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 9904be36-817e-4d7f-9782-049986fa23e2 · outbound

This paper cites Disintegration and Bayesian inversion via string diagrams.

Between Markov and restriction. Two more monads on categories for relations Disintegration and Bayesian inversion via string diagrams

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.306978Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0464711e-38ca-408a-83e8-95c3e3db2e47 · outbound

This paper cites A taxonomy of categories for relations.

Between Markov and restriction. Two more monads on categories for relations A taxonomy of categories for relations

Reference 5

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dc2e1490-3940-44d6-86b3-0248ae05572c · outbound

This paper cites Cockett and Stephen Lack.

Between Markov and restriction. Two more monads on categories for relations Cockett and Stephen Lack

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.291543Z

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 3c5462fd-1c8a-4d49-acd6-ab6f91444c73 · outbound

This paper cites Cockett and Stephen Lack.

Between Markov and restriction. Two more monads on categories for relations Cockett and Stephen Lack

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.277546Z

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 cb2b26f0-3378-4937-a27f-39c49495f760 · outbound

This paper cites An algebraic presentation of term graphs, via gs-monoidal categories.

Between Markov and restriction. Two more monads on categories for relations An algebraic presentation of term graphs, via gs-monoidal categories

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.263603Z

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 e5aa31fe-0b66-4dcf-a97a-68cf6afb1a11 · outbound

This paper cites Rewriting on cyclic structures: Equiv- alence between the operational and the categorical description.

Between Markov and restriction. Two more monads on categories for relations Rewriting on cyclic structures: Equiv- alence between the operational and the categorical description

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.249147Z

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 c0401ddd-fafd-487f-8159-ee43086706d6 · outbound

This paper cites Evidential decision theory via partial markov categories.

Between Markov and restriction. Two more monads on categories for relations Evidential decision theory via partial markov categories

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.235274Z

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 e619a048-87b2-44a2-bef4-67200f8e448e · outbound

This paper cites Coalgebras and cartesian categories.

Between Markov and restriction. Two more monads on categories for relations Coalgebras and cartesian categories

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.219731Z

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 2a8591c8-fc72-4e66-9bdd-b8c5119d4363 · outbound

This paper cites A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics.

Between Markov and restriction. Two more monads on categories for relations A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.206044Z

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 2d0f5790-49ab-4677-97e1-3898c6c40fcf · outbound

This paper cites Weakly Markov categories and weakly affine monads.

Between Markov and restriction. Two more monads on categories for relations Weakly Markov categories and weakly affine monads

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.190995Z

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 135825aa-2e5c-4352-899b-b2dd4508b740 · outbound

This paper cites From gs- monoidal to oplax cartesian categories: Constructions and functorial completeness.

Between Markov and restriction. Two more monads on categories for relations From gs- monoidal to oplax cartesian categories: Constructions and functorial completeness

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.177090Z

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 5df85774-5827-4b5a-8629-5174c93c9a9f · outbound

This paper cites Empirical Measures and Strong Laws of Large Numbers in Categorical Probability.

Between Markov and restriction. Two more monads on categories for relations Empirical Measures and Strong Laws of Large Numbers in Categorical Probability

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T16:58:06.818239Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation edc454c3-8a9d-47cc-86b8-d4073ba06a65 · outbound

This paper cites On The Algebraic Approach To Concurrent Term Rewriting.

Between Markov and restriction. Two more monads on categories for relations On The Algebraic Approach To Concurrent Term Rewriting

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.162501Z

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 f5d87566-ec30-4237-9acb-f1e50aaffdb6 · outbound

This paper cites an unresolved cited work.

Between Markov and restriction. Two more monads on categories for relations Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:58:07.148454Z

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 ef41e8be-ccaf-41fc-82fa-b03dbc34098e · outbound

This paper cites Golubtsov.

Between Markov and restriction. Two more monads on categories for relations Golubtsov

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.134265Z

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 8f06143c-0be4-42f0-b8be-3a1c3be71a38 · outbound

This paper cites Affine monads and side-effect-freeness.

Between Markov and restriction. Two more monads on categories for relations Affine monads and side-effect-freeness

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.120274Z

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 29d882e5-87af-4606-9077-75c493f47806 · outbound

This paper cites From probability monads to commutative effectuses.

Between Markov and restriction. Two more monads on categories for relations From probability monads to commutative effectuses

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.106198Z

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 eb3e8a96-224b-495a-9004-51c912a69207 · outbound

This paper cites Traced monoidal categories.Mathe- matical Proceedings of the Cambridge Philosophical Society, 119(3):447–468, 1996.

Between Markov and restriction. Two more monads on categories for relations Traced monoidal categories.Mathe- matical Proceedings of the Cambridge Philosophical Society, 119(3):447–468, 1996

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.091626Z

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 4bddf85e-9865-40f6-97bf-85ca411d7694 · outbound

This paper cites Monads on symmetric monoidal closed categories.

Between Markov and restriction. Two more monads on categories for relations Monads on symmetric monoidal closed categories

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.075729Z

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 252bb28f-bd56-4a71-8814-c621a00c0363 · outbound

This paper cites Strong functors and monoidal monads.

Between Markov and restriction. Two more monads on categories for relations Strong functors and monoidal monads

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.060765Z

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 0946de1f-9f7c-4c0c-b7b1-1e8c546a2ef0 · outbound

This paper cites Semirings, Automata, Languages , volume 5 of EATCS Monographs on Theoretical Computer Science.

Between Markov and restriction. Two more monads on categories for relations Semirings, Automata, Languages , volume 5 of EATCS Monographs on Theoretical Computer Science

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.044864Z

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 10c660a8-6b11-4cc2-b3b6-23aa7f8d2f87 · outbound

This paper cites Partial markov categories.

Between Markov and restriction. Two more monads on categories for relations Partial markov categories

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-15T16:58:06.860079Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1d5a4396-2257-4002-bb67-19954ae83150 · outbound

This paper cites an unresolved cited work.

Between Markov and restriction. Two more monads on categories for relations Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:58:07.029404Z

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 bcce3533-3626-4a35-af13-e27723b7b1d7 · outbound

This paper cites Categories of partial maps.

Between Markov and restriction. Two more monads on categories for relations Categories of partial maps

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:58:07.013673Z

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

Observation cb403a90-b2c9-498c-adaf-1e9e224bb4c7 · inbound

Partializations of Markov categories cites this paper.

Partializations of Markov categories Between Markov and restriction. Two more monads on categories for relations

Reference 2025

Resolution: verified exact; local_arxiv, observed 2026-08-05T05:51:27.157127Z

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.