Pith. sign in

Paper Citation Record · LEDGER

Unit-Circle Moment Closure

As of 11 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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:af874b42c7f9684cb519fb2339c751947f2ff2f712e827a04262e5efdd1f22da

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:bdbd1fac78c2b917f6ebe5f60b55919382bd54892a026990bccf7bbf190be94d

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:761bfba0d1ce86102a7cb89d928b7e76a6b724dcee8479d97959bc180c286caf

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:b9e2da08f817f55b5e7f037b21531fb3220bf224c34b629fcdf08819de597548

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:a719d2948784363f98da2fd93ce39c54b106bf4ceaeaf57900c341ac73b848f3

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:bc63256858bcd3b93eaf62c01deb782f2caee2016c080950810f343d879302be

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:b6782e81683b33d794ff8c5e41d8faca017bfd79530b019a52d32aad2382b1ab

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:66e9c2c2fd7157c98eb9b437b2f2bd5791330ebb30a94306f5b8d313b0595456

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:54da2092b23add301979511b4748c0a045dc33985e165cd647d12fefe2d776f5

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:1fc3752bac7a1ea52ea73bdd9756a581a097aecde1e2d0fdc79d28c40c6c6545

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:d2c04fbc686149d7df0dade238a5fb9dc41a79aaa39596864517a7ef90444124

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:50738ccaf0e61889f42ce7ecf4cdb787b47bf54077e596c492a78b2a0cafda70

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:65391ddc9a345538a6180069a81da59aefe754b758a44626ef0bfacda90f45a2

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:e26757ec31d29b5398f29ce16dc45d5da14db8d589e822587959d2bd3297e486

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:0dbd05f237574330f7a4a00e8e1f16fa849733c9a40ff819d4312fe60629462b

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:cb5257059d7a53ab2b9126f72719044f6773f48c34d71c2df46838b4f4a05987

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:54c5a173e4c22c9d0a38de99289daf04f0609b6a6cbe2789052213b4691fd073

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:fd4dde41b044191717de91ed0d9ebad8047757e588c500591ea086e5986b22ea

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:ca929fb8a83b34ea3552c007330493e8dbc5e7a799e2a2e630b7a8f7de46bb6d

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:a4d2b21a42ab0d50f74c1946ae00b57b4912ffb050f310fe736e112e4c01857e

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:fed437e46fefb04a62cd709499335b64a2bacdf66b9b0e07fdc905e5e1664653

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:b2d4bc18c717ace0b286c5d7b99f99119f3b5ef87ac7d9a57c9aa5bebf851894

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:dbda8ec01e1a1825075e53748cf46670b43aa4174143f36a6f40cfa75a8067b9

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:6354b8eab618abbb7a337b7ecb144f1dbf41bbe6f170317347521b2404690249

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:5cdac49a87f75b2bc99dedf884422c2542aa9b33cddba37e40e5aa7257047059

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:db0fb00572f5177293fe4bf89cab3024a598ed9e5be34db30913b98a53db35c2

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:431637694d25d6eacd544a4a898f54b177d2721f11d472bba9d4298dd5e2177c

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:eeeb2c1817d41e097e7eac23a8decd54c3feb34773fab1dfbbcf768c1813fa4e

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:5e6f2d2cd91c7766612f87efb6e6ef8ef27187df182329932903e8bb95d7e190

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:b914c9b4be87f5bda5b51047cc3dd1c213a1fa95551ba8ba38733c2ac23d16f5

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:7c30dc609508b3196d33abba0ff5bcc03444e2fee394eb2f7c09f09be25e6190

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 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-30T08:37:48.625740Z digest=sha256:b142932948f724d2f1b2d590e378072db4a8fb3c8efe9b502fd013991c9cdf43

Pith citing papers

No inbound Pith citation observations are available.