Paper Citation Record · LEDGER

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds

As of 14 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 1 inbound Pith citation observation for arXiv:2505.22903.

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

pith.paper-citation-record.v1
2505.22903 v2

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:05:35.447744Z

measured 42 of 42 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-11T08:52:05.032610Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

41 of 41 outbound references displayed

verified exact2
verified fuzzy36
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 21e23f4e-060f-49ed-ab1f-4fda896e8f78 · outbound

This paper cites Albritton, S.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Albritton, S

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:41.810964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation fc618857-a780-4434-8c31-baa0a30c4013 · outbound

This paper cites Arendt, A.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Arendt, A

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:41.656648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0a2487c1-0d11-4265-80ec-60198a5b8dca · outbound

This paper cites Arnold, A formula connecting sample and moment stability of linear stochastic systems, SIAM Journal on Applied Mathe- matics 44 (1984), no.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Arnold, A formula connecting sample and moment stability of linear stochastic systems, SIAM Journal on Applied Mathe- matics 44 (1984), no

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:41.489454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4031b0d2-edf2-4092-b3fe-567837ecedc5 · outbound

This paper cites Arnold, Random dynamical systems , 1st ed., Springer Monographs in Mathematics, Springer Berlin, Heidelberg, 1998.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Arnold, Random dynamical systems , 1st ed., Springer Monographs in Mathematics, Springer Berlin, Heidelberg, 1998

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:41.351386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a532363a-4ec6-43d6-b72f-9f81a857ef07 · outbound

This paper cites Ayyer and M.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Ayyer and M

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:41.107890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3b06ab74-a820-4579-894d-f16e22ef0132 · outbound

This paper cites an unresolved cited work.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:05:40.814279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation cb69ccb3-07f9-4e02-80b6-1103c1d2d7af · outbound

This paper cites H Baxendale, A stochastic hopf bifurcation, Probability Theory and Related Fields 99 (1994), 581–616.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds H Baxendale, A stochastic hopf bifurcation, Probability Theory and Related Fields 99 (1994), 581–616

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:40.539458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b51f4bc8-d499-48d1-ad99-0d5e448b7a7e · outbound

This paper cites H Baxendale, Invariant measures for nonlinear stochastic differential equations , Lyapunov exponents: Proceedings of a conference held in oberwolfach, may 28–june 2, 1990, 2006, pp.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds H Baxendale, Invariant measures for nonlinear stochastic differential equations , Lyapunov exponents: Proceedings of a conference held in oberwolfach, may 28–june 2, 1990, 2006, pp

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:40.222380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 21652ccd-47d3-4aaf-a311-308bdb3a2b8b · outbound

This paper cites Baxendale and D.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Baxendale and D

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:40.002159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d8ca666d-191f-4468-8386-46cfa8152df1 · outbound

This paper cites Bedrossian, A.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Bedrossian, A

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:39.750222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 636bcc5a-810f-49d9-8c4d-2d2e72ba71f5 · outbound

This paper cites Bedrossian, A.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Bedrossian, A

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:39.457873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b8fe603c-6047-4107-8c51-011c6781c4f2 · outbound

This paper cites Bedrossian and K.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Bedrossian and K

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:39.263286Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 628c3c49-f782-4514-a920-e717f92376bf · outbound

This paper cites Stationary measures for stochastic differential equations with degenerate damping.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Stationary measures for stochastic differential equations with degenerate damping

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:05:35.687013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c7d85738-c66c-4c14-9331-3507b17551f7 · outbound

This paper cites Bedrossian and S.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Bedrossian and S

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:38.971734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation bf837ffe-d9ea-44b7-9e9d-5a8ed0167c7c · outbound

This paper cites Stochastic Persistence.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Stochastic Persistence

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T13:05:33.567759Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac6a76a7-c32c-46d1-a2a9-667b156ae244 · outbound

This paper cites Blumenthal, M.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Blumenthal, M

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:38.760969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4e04aea9-a8b6-4531-97e5-6db7ef2f1155 · outbound

This paper cites Blumenthal, J.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Blumenthal, J

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:38.591317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7c3677a0-7813-42f6-80c6-cdfd7a9c292c · outbound

This paper cites Chemnitz and M.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Chemnitz and M

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:38.493821Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8cc8b1d6-62c1-48b1-948c-b2870617f944 · outbound

This paper cites Coti Zelati and M.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Coti Zelati and M

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:38.332213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d2cf95ed-6721-4e1a-86bc-0966e091b3a6 · outbound

This paper cites Dolgopyat, V.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Dolgopyat, V

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:38.230116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 33a55858-b5c9-415c-97a1-fe0bea734f0b · outbound

This paper cites Ruelle, Ergodic theory of chaos and strange attractors , Reviews of modern physics 57 (1985), no.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Ruelle, Ergodic theory of chaos and strange attractors , Reviews of modern physics 57 (1985), no

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:38.092351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c0114234-12fc-447a-8606-15801ab9dc21 · outbound

This paper cites S Ellis, Entropy, large deviations, and statistical mechanics, Springer, 2007.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds S Ellis, Entropy, large deviations, and statistical mechanics, Springer, 2007

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:37.962134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 046f2335-62f9-4d76-8bdb-56bb352865f5 · outbound

This paper cites Hairer and J.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Hairer and J

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:37.853877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 47bfcb98-9868-4702-8597-941b5eda3261 · outbound

This paper cites Non-equilibrium steady state for a three-mode energy cascade model.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Non-equilibrium steady state for a three-mode energy cascade model

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:05:35.586814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 378a8d6e-66da-4a8f-b340-fa57d2a77ee1 · outbound

This paper cites Hening and D.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Hening and D

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:37.714949Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 648db196-52da-4405-840d-36ef6e94911d · outbound

This paper cites P Herzog and J.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds P Herzog and J

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:37.616162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f4eab431-0df3-47a7-b888-2fb8495dff66 · outbound

This paper cites H ¨ormander, Hypoelliptic second order differential equations, Acta Mathematica 119 (1967), no.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds H ¨ormander, Hypoelliptic second order differential equations, Acta Mathematica 119 (1967), no

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:37.510284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 791a45f7-e9dd-48f5-a736-79bca41c8260 · outbound

This paper cites Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, vol.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, vol

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:37.370969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1f689530-82b8-45a0-afea-1b1f1ab467ea · outbound

This paper cites 1, 1985), 361–368.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds 1, 1985), 361–368

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:37.269624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9c55c8d2-1862-48e3-8687-8e08230e298d · outbound

This paper cites Jurdjevic,Geometric control theory, Cambridge university press, 1997.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Jurdjevic,Geometric control theory, Cambridge university press, 1997

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:37.141907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 09c33b68-097a-4da3-b1b4-41a779ed1cdf · outbound

This paper cites Kifer,Ergodic theory of random transformations, V ol.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Kifer,Ergodic theory of random transformations, V ol

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:37.044494Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3e411bd1-005b-4a17-b9ff-069b4ba8519b · outbound

This paper cites Lian and M.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Lian and M

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:36.935643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 69d97761-8bb9-4f40-9fb5-188fec25bec2 · outbound

This paper cites N Lorenz, Predictability: A problem partly solved, Proc.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds N Lorenz, Predictability: A problem partly solved, Proc

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:36.814595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation cafcd80f-c77a-4ddc-8ef4-c11448a8c88b · outbound

This paper cites C Mattingly, Ergodicity of 2d navier–stokes equations with random forcing and large viscosity, Communications in mathe- matical physics 206 (1999), 273–288.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds C Mattingly, Ergodicity of 2d navier–stokes equations with random forcing and large viscosity, Communications in mathe- matical physics 206 (1999), 273–288

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:36.721054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c4ca9aa6-a6cd-4fb8-87b6-0046f5e8ecd3 · outbound

This paper cites P Meyn and R.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds P Meyn and R

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:36.605136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 729ef1be-f47b-4a33-bea5-5f94910a75d1 · outbound

This paper cites Punshon-Smith, L-96 cap: Computer-assisted proof for lorenz 96 model hypoellipticity , GitHub, 2025.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Punshon-Smith, L-96 cap: Computer-assisted proof for lorenz 96 model hypoellipticity , GitHub, 2025

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:36.489027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation aa871000-2705-499a-b2b0-a94921a2de7b · outbound

This paper cites Punshon-Smith, L96-matrix-cap, Google Colab, 2025.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Punshon-Smith, L96-matrix-cap, Google Colab, 2025

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:36.371752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation cc8d96e3-fb23-4668-9df6-de3ce337ac40 · outbound

This paper cites Revuz and M.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Revuz and M

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:36.232346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 46965d06-45a9-4e73-b2f4-5a6210003d10 · outbound

This paper cites an unresolved cited work.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:05:36.123021Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9fc4c281-59b8-4a7b-9a49-a11213176c77 · outbound

This paper cites Triebel, Theory of function spaces II, Birkhauser, 1992.

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds Triebel, Theory of function spaces II, Birkhauser, 1992

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:35.979566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 54a7397b-df43-4c22-82af-294b4f0de893 · outbound

This paper cites W Warner, Foundations of Differentiable Manifolds and Lie Groups, Graduate texts in mathematics, Springer, 2010 (en).

Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds W Warner, Foundations of Differentiable Manifolds and Lie Groups, Graduate texts in mathematics, Springer, 2010 (en)

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:05:35.832361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

Observation b3e8ff4b-c3f8-4f52-b70d-12cb6acacfbe · inbound

Asymptotics of Lyapunov Exponents and Phase Transitions for Fluids with Degenerate Forcing cites this paper.

Asymptotics of Lyapunov Exponents and Phase Transitions for Fluids with Degenerate Forcing Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-11T08:52:05.032610Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.