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Paper Citation Record · LEDGER

Unit-Circle Moment Closure

As of 12 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2606.28894.

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

pith.paper-citation-record.v1
2606.28894 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-30T08:37:48.625740Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

32 of 32 outbound references displayed

  • verified exact1
  • verified fuzzy21
  • unresolved10
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5e963981-d4b8-40e9-a6cb-bda541c50f21 · outbound

This paper cites an unresolved cited work.

Unit-Circle Moment Closure Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-07-10T16:47:25.130287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:604920f754a5bcfa8c1a6e9360758e7573a52a4bbee9c5f201b4f411a07abc81

Observation 96628306-e1b3-48ed-a935-aad15e3a6fe8 · outbound

This paper cites an unresolved cited work.

Unit-Circle Moment Closure Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-07-10T16:47:25.132157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:5b59bde396189c8d38cb96520d4186c20cd1044545c4f07988c6a47f7378f6ae

Observation b64fdd29-c246-4924-980a-152cad48a669 · outbound

This paper cites Kuehn,Multiple Time Scale Dynamics, Applied Mathematical Sciences, Vol.

Unit-Circle Moment Closure Kuehn,Multiple Time Scale Dynamics, Applied Mathematical Sciences, Vol

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.109054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:28a7c8f2f9ce4457c3009674df8e7530df5c185ab1f552473bfd25c1ba8bda38

Observation f34173cb-a2a7-4480-810c-7314ddd36f62 · outbound

This paper cites Moment Closure - A Brief Review.

Unit-Circle Moment Closure Moment Closure - A Brief Review

Reference 4

Resolution
verified exact
local_arxiv, observed 2026-06-30T08:44:27.745561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:857bfcfb84a7a8e6d9c6c2b0d0cdfb25e6a8052ef72db7973209933b070d93a2

Observation f8ecf224-bb9b-4c34-b473-a49bf302e652 · outbound

This paper cites Grad, On the kinetic theory of rarefied gases, Com- munications on Pure and Applied Mathematics2, 331 (1949).

Unit-Circle Moment Closure Grad, On the kinetic theory of rarefied gases, Com- munications on Pure and Applied Mathematics2, 331 (1949)

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.140504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:130abb5b2db2d48f3778a47cac6bde97172e499487fe7afc5c84d547171cfd78

Observation 29b7b89e-8736-4474-ad2d-f664f35bee03 · outbound

This paper cites an unresolved cited work.

Unit-Circle Moment Closure Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-07-10T16:47:25.133066Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:6e4da907bf7a4e61011423c5521a1de57ee0180eb476b32562d98c624c36b3c3

Observation 7551d17d-86a8-404e-a023-5af69fbf2b34 · outbound

This paper cites an unresolved cited work.

Unit-Circle Moment Closure Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-07-10T16:47:25.126215Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:11ed9f9c97485699b7e8ee41efe70ea41b4aed83d5631d8e07efecbd4a64cc56

Observation 2d57c5ad-340d-4863-89a6-a9836da1543e · outbound

This paper cites an unresolved cited work.

Unit-Circle Moment Closure Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-07-10T16:47:25.152109Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:d495e2761cb07634f5f52f7e98d92de6a6ea448d90d98159bbdb1495182355a1

Observation f22f3544-aeb8-4832-9ed5-62f76f2080ef · outbound

This paper cites an unresolved cited work.

Unit-Circle Moment Closure Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-07-10T16:47:25.099795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:40a6609abf14413e16525cdd562dca6339161ec14e0a9778ab564ff672f8f8af

Observation 2cc97381-0696-42c7-baaf-ae1c00c37dc1 · outbound

This paper cites Froustey, J.

Unit-Circle Moment Closure Froustey, J

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.145903Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:ee3905f4e29c0707cd6e1acfb36e1cfda83c28c5169ab109a0405004960d8af8

Observation 4d9e01b3-46dc-435c-8b3d-9f9be4baa964 · outbound

This paper cites Alvarez Laguna and K.

Unit-Circle Moment Closure Alvarez Laguna and K

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.147938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:950fb9e76689cf7529285d69cc9157c8860800b02a4efa6dd5529522208dde0c

Observation df70b890-51c7-4f18-acdf-d0ad9586a032 · outbound

This paper cites Huang,Statistical Mechanics(Wiley, New York, NY, 1987).

Unit-Circle Moment Closure Huang,Statistical Mechanics(Wiley, New York, NY, 1987)

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.134801Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:c578446d8b5a39eab1b994b59c7105ac1bfe0370b872261c4cb96ee9da4caa3a

Observation 742c514c-b66f-4945-a7f6-75b2187358d1 · outbound

This paper cites Schnoerr, G.

Unit-Circle Moment Closure Schnoerr, G

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.101563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:4f04a1d76f725ba01e1902a7c1546519251fb0b61b0bddc681337aecd93032e2

Observation ffdbf2da-2f87-40ae-9aae-48507e6385ad · outbound

This paper cites Wuyts and J.

Unit-Circle Moment Closure Wuyts and J

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.139543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:17166bf8f85f344785a4fd7e2ce2000daaedbe0a6cd506a86742e561a94817b2

Observation 58efac1a-ae95-46dc-be55-cd39ddd30074 · outbound

This paper cites an unresolved cited work.

Unit-Circle Moment Closure Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-07-10T16:47:25.143527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:4e93c953fb8641147d46fe21ec9e660c0306c1bfdb36145b3720e87ab89354b8

Observation f153b7b0-7743-4bbc-8797-44d3e4436e3a · outbound

This paper cites Florencio and O.

Unit-Circle Moment Closure Florencio and O

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.128191Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:6294b96683921da81dffca365fc3f6a8441ba7d31288e2439458ce325932394f

Observation 73d13b31-04e7-4e1a-a6b9-bd2b1abceaaf · outbound

This paper cites Grima, A study of the accuracy of moment-closure ap- proximations for stochastic chemical kinetics, The Jour- nal of Chemical Physics136, 154105 (2012).

Unit-Circle Moment Closure Grima, A study of the accuracy of moment-closure ap- proximations for stochastic chemical kinetics, The Jour- nal of Chemical Physics136, 154105 (2012)

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.137571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:64a157d2a713c0f72f002cc9807e15bc8e20d29eeb70e8ca60b7f59370fe018c

Observation d917a21b-2a16-455e-a1b8-471e761b7f7b · outbound

This paper cites Blinnikov and R.

Unit-Circle Moment Closure Blinnikov and R

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.131486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:fae14db7892079d72f8d5f47475e36a3fe35e47e8fa857309a6ed6482ceaddc5

Observation 9be2cfd3-250c-4ae7-aba9-0056218ac8bc · outbound

This paper cites Brezinski (Springer US, Boston, MA, 2002) pp.

Unit-Circle Moment Closure Brezinski (Springer US, Boston, MA, 2002) pp

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.122114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:044eb3e3916ddd3dd5c703b28c2bb56b1d088d8ecabbeda52ee4ba9c25f6c69a

Observation c5f59fae-2b9a-45c9-b79b-4a677e657d39 · outbound

This paper cites an unresolved cited work.

Unit-Circle Moment Closure Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-07-10T16:47:25.119840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:7fabb1120ee9bd238c85a2dbb0c3d80026e4627439c83309ef0b93961189e7ec

Observation e4734003-cb13-4a2a-add1-bee33d9579a0 · outbound

This paper cites Starkschall and R.

Unit-Circle Moment Closure Starkschall and R

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.154016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:b3bf1c052f0edecff2dd36b5f2f6b502df2559a85fd0b04050272659d567c6da

Observation 9dc70c16-2d8d-4306-b4ba-7d19ba867f2d · outbound

This paper cites Liu, R.-H.

Unit-Circle Moment Closure Liu, R.-H

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.149359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:74148f47e4f7191136fb014c4ffed6efce5f5d08d1a0f11801d96873183d16ab

Observation dce53a20-a880-4446-ba68-e59cf30711d4 · outbound

This paper cites Simon,Orthogonal Polynomials on the Unit Circle: Part 1: Classical Theory(American Mathematial Soci- ety, Providence, Rhode Island, 2005).

Unit-Circle Moment Closure Simon,Orthogonal Polynomials on the Unit Circle: Part 1: Classical Theory(American Mathematial Soci- ety, Providence, Rhode Island, 2005)

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.117670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:1c55b6b83a0bcc8e4bb5833920e38a1e569fe947eea658ce8aae101dc042119f

Observation 5993ba77-fcd9-41d9-97eb-d8eb2a82d2f2 · outbound

This paper cites Simon,Orthogonal Polynomials on the Unit Circle: Part 2: Spectral Theory(American Mathematial Society, Providence, 2013).

Unit-Circle Moment Closure Simon,Orthogonal Polynomials on the Unit Circle: Part 2: Spectral Theory(American Mathematial Society, Providence, 2013)

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.101781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:7b7c42cc985f4152a6d122728f4cd5c85023403c967de8678750d950f83625ae

Observation f4f85781-b2fd-4632-a472-0a4e4dafc6ff · outbound

This paper cites an unresolved cited work.

Unit-Circle Moment Closure Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-07-10T16:47:25.155986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:5fa19d1d8d597e2666b53b1303469ce7a8050d0e5ba50b838e057dbe448fd252

Observation 299c2092-a615-4949-8fc1-38b650b87ef5 · outbound

This paper cites Zhang and E.

Unit-Circle Moment Closure Zhang and E

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.150056Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:81470338c98a5093e6b358d283e539d024f445ae58abbb4d7074bd323979ff6d

Observation 524278a3-bb9f-4f09-a4fc-d4be7191a34c · outbound

This paper cites Zhang, A.

Unit-Circle Moment Closure Zhang, A

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.145779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:bc1d02ef804cca4c6638cd16a3446dfae457fb6d00201061686a6356008b6994

Observation c3e36040-94a6-4cb4-8e41-33c6b5059767 · outbound

This paper cites Beylkin and L.

Unit-Circle Moment Closure Beylkin and L

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.136430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:59f718d139c252b5158159a9a3ebb998e63331b9f481f6f05574385bc4de95f1

Observation a233b96f-a58d-4c4c-a117-b5f41af90382 · outbound

This paper cites Zwanzig,Nonequilibrium Statistical Mechanics(Ox- ford u.a., 2010).

Unit-Circle Moment Closure Zwanzig,Nonequilibrium Statistical Mechanics(Ox- ford u.a., 2010)

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.147741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:4b88ded4c40eed1accf9f4bd117d848b91597b35f3eb5eab5828cb7b57d7f118

Observation 634f0ce8-afa2-495d-a867-34418d4821e4 · outbound

This paper cites Gu, Group-theoretical formalism of quantum mechan- ics based on quantum generalization of characteristic functions, Physical Review A32, 1310 (1985).

Unit-Circle Moment Closure Gu, Group-theoretical formalism of quantum mechan- ics based on quantum generalization of characteristic functions, Physical Review A32, 1310 (1985)

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.117241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:285cf891175cd56180325be8c21c0cf8dd37ed04b547a0ada475c8152d7becf9

Observation 2f05e6ab-b66f-4de5-8d3d-479e5b8e6e7c · outbound

This paper cites Ganoe and M.

Unit-Circle Moment Closure Ganoe and M

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T16:47:25.142367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:d338a5693bded7c1ac1a9fdd725bea1eb6402fe9cdcd6aafd32ab9aad49d7db8

Observation b70fa07c-7152-4e6c-a16b-a0fcd492007a · outbound

This paper cites an unresolved cited work.

Unit-Circle Moment Closure Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-07-10T16:47:25.105437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:6003eafc30b4ab61de4e15507d9dadf3bc3915ba8a02030a8f1147977c921dd0

Pith citing papers

No inbound Pith citation observations are available.