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Paper Citation Record · LEDGER

Unit-Circle Moment Closure

As of 8 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 2026-08-08T06:32:00.761636+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

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:a38d68e56e428b0b585b05f54f77f3894b7e4425098a0c995a48b9d5a659e064

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:8ab0c6ef9d2ed4041ff2417ab60a0753e478721d282774e36e3de103b4546897

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:e720ca013fd260a37b49b72742ee0cbd016f5c464758993f566d5b534531ea89

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:8c54c6459d8cccb05cb66bbe38ad588089b477a23df9cf5342719012225d31e9

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:a8c64dd112d328578f362b01f246c745248f45ab17583faacee1be6e31006840

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:f45fd4384844b21038a640eddbc5dc510b8938f4c22edc36aeeb374b98203c21

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:28330c8c681b3724e30214af359135309978f01b850040dc8af7b5a41853eb7c

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:31aebd114ab456eeb726fbf245dbccad9a7033471d8528eae564d61e40e2b5c7

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:360dd0ab0745cf686a1afbed81ae3fa7f8991ffa35a311780ac0df51e410e295

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:cf81caa9550f73504ba751701dbf300943b3a7cab7d69299e124447f5a1d37b8

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:1b7cb4de5c6cef2daf1a491fd5b9c24e4084719ab30ad1f0e780dff0feb29548

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:fa6003a000b255b3e0140f6fdef57bee6113b739e9f516824051ee760557f060

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:beee91aa1900c3e0a9915c1446794789f7d699700effbf8ad1b6f4369ffb88cd

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:ef600be116fde2d19e911b8495306ec70dbb99ce346460823da4bb25dd72bfca

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:8b926b1d27a8c9bab152944259035fb1127b6ad2dcc87d202b07b8e245043ecb

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:1388641fa6344d373a48cc0157fbc4882bd5b97b91c844aee7ba615754456060

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:d238dbbb0c12812b15645217646a302d4b56283cc07afb961cce6bd8031e91ed

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:4fc7027743381b4f0b470faa157af73fb5c565dc0a3a8b8c6d9cc9978891d484

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:07d5b0f2b88ae13d54e81aec32d9a555da6c2424877e055ea6a1722b17a6489e

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:a17e16a396dd149576afeef3f2d3345b933d01a8141b18bdcc707c7319f6adc8

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:fcea18230237ea48e153326ffb1de406487e3f5e6e9775e063472123b9b405ac

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:d97fa7ffe0a504734aae9979bb137ea78ca6e7220b900505cf19224ccd2c9feb

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:2dfe00099428dd263f27339a2999da0e72112bf74c19d9fe798665403ecb7ef1

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:2db0d02785efbc43c7c232c23366f459677971fef7109ee1e12415c16f8e6e1d

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:093221871be5f639a5c0ea72b7ce97db3d77fd7a340f09365651bfbe215227b5

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:7951739936ce1a0e9423ce98ea35a5f3f1f6997c79807af7360b3788349bb4d3

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:bfcb042f7b522323f99b2b939a39b0349f28aa498628a7a955e584619715d1f8

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:d86e1819d2541bed020d9f248db22e7a6e055cdfed6d272f4ee1c815bcec2481

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:cc643a92bab022bd28830217d80c9791687920ac833966f9d3b432b3ca4a27d4

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:a47c4ec145f20b51afa7c2fadb097ad73e324d5c038b6ed63daf0670b8ef1ae4

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:1c3861613302415e69e8fc2354b01b3d107eac3297e1aa264021f80141cfb1db

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:13c6b35d58b91cace82d5b14bfa5985867a6420df9a320c35d97a1f210a86ac6

Pith citing papers

No inbound Pith citation observations are available.