Paper Citation Record · LEDGER

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice

As of 8 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 0 inbound Pith citation observations for arXiv:2505.21950.

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

pith.paper-citation-record.v1
2505.21950 v1

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:48:38.393775Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

17 of 17 outbound references displayed

verified exact0
verified fuzzy15
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5bb4ba20-6fb1-4070-967c-a0e7f61de80a · outbound

This paper cites A direct construction of non-transitive dice sets, 2016.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice A direct construction of non-transitive dice sets, 2016

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:42.825697Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6857f77f-d283-43b4-afd0-ed5dad67aba9 · outbound

This paper cites an unresolved cited work.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:48:42.558976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a929cb6b-ff40-4ad8-8eb5-38e36baf8a74 · outbound

This paper cites Maximally nontransitive dice.The American Mathe- matical Monthly, 125:387–399, 05 2018.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice Maximally nontransitive dice.The American Mathe- matical Monthly, 125:387–399, 05 2018

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:42.296624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 96d06530-5d13-4f1f-9d85-69948108151a · outbound

This paper cites The paradox of the nontransitive dice and the elusive principle of indifference.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice The paradox of the nontransitive dice and the elusive principle of indifference

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:42.057034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e80b3c0d-7266-4f36-920e-79d51a3a0af9 · outbound

This paper cites Possible probability and irreducibility of balanced nontransitive dice.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice Possible probability and irreducibility of balanced nontransitive dice

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:41.836090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f95ff032-0133-4234-9803-e6c717e3bb9a · outbound

This paper cites Joyce, A.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice Joyce, A

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:41.564665Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6672b4b1-557a-4dc9-9ba0-da6b5b36fefd · outbound

This paper cites Balanced nontransitive dice: Existence and probability.The Electronic Journal of Combinatorics, 31:Not available, 1 2024.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice Balanced nontransitive dice: Existence and probability.The Electronic Journal of Combinatorics, 31:Not available, 1 2024

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:41.323648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a71c87b2-7a64-4bbe-bd48-07877a4052ab · outbound

This paper cites Balanced nontransitive 4-dice.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice Balanced nontransitive 4-dice

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:41.015141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c14385ee-8894-4b17-ba67-8912d03bb4d5 · outbound

This paper cites Nontransitive random variables and nontransitive dice.The American Mathematical Monthly, 128(5):423–434, 2021.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice Nontransitive random variables and nontransitive dice.The American Mathematical Monthly, 128(5):423–434, 2021

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:40.744838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 45cd7e44-d1e9-42e7-bfc7-7c096cd2da56 · outbound

This paper cites an unresolved cited work.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:48:40.467304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e2db4f25-77e6-42ba-823b-5289f7d92349 · outbound

This paper cites Savage, R.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice Savage, R

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:40.199112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4240fb07-7b2c-4821-b13a-ba41437feb3e · outbound

This paper cites Schaefer.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice Schaefer

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:39.929210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6038f605-6858-4917-ba59-d366ca1ed9da · outbound

This paper cites Balanced non-transitive dice ii: Tournaments, 2017.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice Balanced non-transitive dice ii: Tournaments, 2017

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:39.700853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c94509d4-56e9-4ef9-a44a-2d3b4a13c1e6 · outbound

This paper cites Balanced nontransitive dice.The College Mathematics Journal, 48:10–16, 1 2017.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice Balanced nontransitive dice.The College Mathematics Journal, 48:10–16, 1 2017

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:39.462412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d4360f5c-9e19-436b-8a27-62d70ff314eb · outbound

This paper cites On a paradox in applied probabilities.Bulletin of the Polish Academy of Sciences, 7(6):675–680, 1959.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice On a paradox in applied probabilities.Bulletin of the Polish Academy of Sciences, 7(6):675–680, 1959

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:39.166561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 15f546b7-189d-4421-a93e-8d27facbaa52 · outbound

This paper cites Trybu la.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice Trybu la

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:38.857358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 28f8990f-02a5-46d9-a7c8-1e260b1ef804 · outbound

This paper cites Trybu la.

Winning Probabilities of Balanced and Nontransitive n-tuples of Dice Trybu la

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:48:38.634471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.