Paper Citation Record · LEDGER

Discrete Boltzmann distributions via multisets and their coefficients

As of 8 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2507.05719.

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

pith.paper-citation-record.v1
2507.05719 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:30:31.774936Z

measured 18 of 18 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

18 of 18 outbound references displayed

verified exact0
verified fuzzy10
unresolved6
parse uncertain0
malformed identifier2
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 873fdfb6-beae-4525-938f-0653226b4500 · outbound

This paper cites Benjamin and J.

Discrete Boltzmann distributions via multisets and their coefficients Benjamin and J

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:30:33.492961Z

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 4e490fc2-1cf2-40f0-861c-23cec8e05215 · outbound

This paper cites Dill and S.

Discrete Boltzmann distributions via multisets and their coefficients Dill and S

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:30:33.356944Z

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 fa75871a-87b2-40ba-bf1d-4c7c9ec70e1d · outbound

This paper cites Dragulescu and V.

Discrete Boltzmann distributions via multisets and their coefficients Dragulescu and V

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T19:30:30.806387Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d948c925-50fd-46f9-8e4c-7d43d7a0ccd5 · outbound

This paper cites Eisberg and R.

Discrete Boltzmann distributions via multisets and their coefficients Eisberg and R

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:30:33.239663Z

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 546f85c0-8871-49db-9bab-0f06a104d023 · outbound

This paper cites Graham, D.

Discrete Boltzmann distributions via multisets and their coefficients Graham, D

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:30:33.133031Z

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 afe7a68a-200c-44a3-8198-67b18528d1b6 · outbound

This paper cites an unresolved cited work.

Discrete Boltzmann distributions via multisets and their coefficients Unresolved cited work

Reference 6

Resolution: malformed identifier; no resolver link, observed 2026-08-06T19:30:31.019037Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ea428c6-3435-442a-b76e-7b7c31cf55ab · outbound

This paper cites an unresolved cited work.

Discrete Boltzmann distributions via multisets and their coefficients Unresolved cited work

Reference 7

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T19:30:33.039362Z

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 67d36c3a-9d3d-4833-be2f-cc5d3b6a047b · outbound

This paper cites an unresolved cited work.

Discrete Boltzmann distributions via multisets and their coefficients Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:30:32.919566Z

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 465f635a-503d-4c50-902d-e7deb6058961 · outbound

This paper cites Jacobs and M.

Discrete Boltzmann distributions via multisets and their coefficients Jacobs and M

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:30:32.779882Z

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 7c415941-23de-414d-be57-b8c825fe3cbe · outbound

This paper cites an unresolved cited work.

Discrete Boltzmann distributions via multisets and their coefficients Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T19:30:31.264394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5939528d-3480-42b6-803b-73607b97b61f · outbound

This paper cites Basic Category Theory.

Discrete Boltzmann distributions via multisets and their coefficients Basic Category Theory

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T19:30:31.344506Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d8fbbcdf-dc20-43c9-9b55-05fa76e7faaf · outbound

This paper cites Mac Lane.

Discrete Boltzmann distributions via multisets and their coefficients Mac Lane

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:30:32.673707Z

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 b107e431-c023-4b16-8a3a-d4492e516eef · outbound

This paper cites Multinomial coefficients.

Discrete Boltzmann distributions via multisets and their coefficients Multinomial coefficients

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:30:32.566148Z

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 cd8fb087-c0d6-4c23-803d-684b41b8a4ae · outbound

This paper cites Pathria and P.

Discrete Boltzmann distributions via multisets and their coefficients Pathria and P

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:30:32.462477Z

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 f046b740-fd7b-45bb-b933-bf19fa7ddc02 · outbound

This paper cites an unresolved cited work.

Discrete Boltzmann distributions via multisets and their coefficients Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:30:32.365799Z

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 26dd0955-65f9-4187-9788-b4be1f843a30 · outbound

This paper cites Tipler and R.

Discrete Boltzmann distributions via multisets and their coefficients Tipler and R

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:30:32.275183Z

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 ad519534-72a3-4727-95a8-de67ce02ab46 · outbound

This paper cites BD-1” is described with “States and occupation Discrete Boltzmann distributions 37 probabilities for six particles with total energy 8∆ E.

Discrete Boltzmann distributions via multisets and their coefficients BD-1” is described with “States and occupation Discrete Boltzmann distributions 37 probabilities for six particles with total energy 8∆ E

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:30:32.138246Z

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 c35e349f-a752-4631-9d44-e043540a8b40 · outbound

This paper cites an unresolved cited work.

Discrete Boltzmann distributions via multisets and their coefficients Unresolved cited work

Reference 2011

Resolution: unresolved; no resolver link, observed 2026-08-06T19:30:31.613411Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.