Paper Citation Record · LEDGER

Spectral Gap for the Stochastic Exchange Model

As of 23 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 1 inbound Pith citation observation for arXiv:2504.13533.

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

pith.paper-citation-record.v1
2504.13533 v2

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T12:17:39.848399Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T01:01:44.982570Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-16T01:01:45.282191Z

Reference resolution

18 of 18 outbound references displayed

verified exact0
verified fuzzy16
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b1d7d73c-d27f-4533-8a58-28e1facbdd91 · outbound

This paper cites Caputo: Uniform Poincar´ e inequalities for unbounded conservative spin systems: the non-interacting case , Stoch.

Spectral Gap for the Stochastic Exchange Model Caputo: Uniform Poincar´ e inequalities for unbounded conservative spin systems: the non-interacting case , Stoch

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:40.074496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a6899891-d810-4c07-95d4-194ad87cf0e8 · outbound

This paper cites Caputo: On the spectral gap of the Kac walk and other binary collision processes , ALEA Lat.

Spectral Gap for the Stochastic Exchange Model Caputo: On the spectral gap of the Kac walk and other binary collision processes , ALEA Lat

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:40.061758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 23c5b2ef-8241-45f0-a254-22e5f04805bd · outbound

This paper cites ´Equations aux D´ eriv´ ees Partielles.

Spectral Gap for the Stochastic Exchange Model ´Equations aux D´ eriv´ ees Partielles

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:40.049535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 82dde5cc-825f-4238-b6c4-f7805dd6b8ec · outbound

This paper cites Carlen, M.

Spectral Gap for the Stochastic Exchange Model Carlen, M

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:40.039049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 0a0ac38b-4e43-4936-b2bc-c0f18f7c9122 · outbound

This paper cites Carlen, M.

Spectral Gap for the Stochastic Exchange Model Carlen, M

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:40.025810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 815889fb-187a-4b06-927c-825918e23818 · outbound

This paper cites an unresolved cited work.

Spectral Gap for the Stochastic Exchange Model Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:17:40.014489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f155427d-b0b8-4b6b-83b8-489428527307 · outbound

This paper cites an unresolved cited work.

Spectral Gap for the Stochastic Exchange Model Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:17:40.001196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9ea92a30-2fb4-4cbf-b889-f9cd663676e5 · outbound

This paper cites Carlen, J.

Spectral Gap for the Stochastic Exchange Model Carlen, J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:39.987400Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a06294e4-5a4b-46ad-8d51-d681c052a336 · outbound

This paper cites Gaspard, and T.

Spectral Gap for the Stochastic Exchange Model Gaspard, and T

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:39.975656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 47629079-4eff-4251-bd99-2b02a3e5b3f1 · outbound

This paper cites Gaspard, and T.

Spectral Gap for the Stochastic Exchange Model Gaspard, and T

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:39.964984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 493a62fb-b9be-4eb2-8fb4-a6585313685a · outbound

This paper cites Giroux and R.

Spectral Gap for the Stochastic Exchange Model Giroux and R

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:39.955219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 258bc4cf-907e-4053-adda-02cfb3a7c988 · outbound

This paper cites Grigo, K.

Spectral Gap for the Stochastic Exchange Model Grigo, K

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:39.945629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a1f3258c-6825-402e-a36d-c9a833d630cf · outbound

This paper cites Janvresse: Spectral gap for Kac’s model of Boltzmann equation , Ann.

Spectral Gap for the Stochastic Exchange Model Janvresse: Spectral gap for Kac’s model of Boltzmann equation , Ann

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:39.934967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 3cc888ba-a5b7-4cb8-a943-f11b63a76ad8 · outbound

This paper cites Kac: Foundations of kinetic theory , Proc.

Spectral Gap for the Stochastic Exchange Model Kac: Foundations of kinetic theory , Proc

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:39.923346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation abd30be4-c9c2-42ba-b069-56e206b17355 · outbound

This paper cites Kac: Probability and Related Topics in Physical Sciences, Interscience Publ.

Spectral Gap for the Stochastic Exchange Model Kac: Probability and Related Topics in Physical Sciences, Interscience Publ

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:39.912839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 18571bcf-c8bf-43c8-909f-535fdab86aab · outbound

This paper cites Sasada: On the Spectral Gap of the Kac Walk and Other Binary Collision Processes on d-Dimensional Lattice, in K.

Spectral Gap for the Stochastic Exchange Model Sasada: On the Spectral Gap of the Kac Walk and Other Binary Collision Processes on d-Dimensional Lattice, in K

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:39.901658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 2e59f8c4-100f-4201-8c40-38c1c5b97174 · outbound

This paper cites Sasada: Spectral gap for stochastic energy exchange model with nonuniformly positive rate function , Ann.

Spectral Gap for the Stochastic Exchange Model Sasada: Spectral gap for stochastic energy exchange model with nonuniformly positive rate function , Ann

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:39.890923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6bcacec4-0d5d-44b8-9d74-e5857550f555 · outbound

This paper cites Villani: Cercignani’s conjecture is sometimes true and always almost true.

Spectral Gap for the Stochastic Exchange Model Villani: Cercignani’s conjecture is sometimes true and always almost true

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:17:39.880019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

Observation ade5b912-a35c-4e25-ba64-bc54bf6d83f3 · inbound

Spectral gap of the KMP and other stochastic exchange models on arbitrary graphs cites this paper.

Spectral gap of the KMP and other stochastic exchange models on arbitrary graphs Spectral Gap for the Stochastic Exchange Model

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-16T01:01:45.290111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.