Pith. sign in

Paper Citation Record · LEDGER

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC

As of 16 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:1908.02234.

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

pith.paper-citation-record.v1
1908.02234 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T15:07:27.374519Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

34 of 34 outbound references displayed

  • verified exact1
  • verified fuzzy32
  • unresolved1
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 42692979-f69b-475c-9113-9e32add1492c · outbound

This paper cites Bleher and X.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Bleher and X

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:28.850330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.073590Z digest=sha256:b8d201bd841a1b2957293d28808f58d3c25a971a02746b675b063f9c2a42ae9e

Observation 9375c689-36a8-46f1-953e-9b502a8fd813 · outbound

This paper cites Bloch and G.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Bloch and G

Reference 2

Resolution
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raw_fallback, observed 2026-08-14T15:07:28.825736Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.083899Z digest=sha256:ddeebcb7a78eaf76d786e7e75b829970f18a1f45d5d20d7da2543d97aedd2049

Observation 8255a318-f93e-463d-a800-282db1276471 · outbound

This paper cites an unresolved cited work.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Unresolved cited work

Reference 3

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unresolved
raw_fallback, observed 2026-08-14T15:07:28.797944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.091420Z digest=sha256:50bf5e84dd3d489a511806f07fea692c198041798d36022dd9d44257f7d76624

Observation 8cdc7f8d-efc1-4a97-97c8-13533add7268 · outbound

This paper cites Bogomolny, O.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Bogomolny, O

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:28.769542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.100236Z digest=sha256:4178d7c33fc56120933ca26ff103ac4916836ebd99c7970c716bbc5edccefbf9

Observation 94fa71b9-526f-41fd-a0a4-4e996e83f7b1 · outbound

This paper cites Edelman and E.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Edelman and E

Reference 5

Resolution
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raw_fallback, observed 2026-08-14T15:07:28.736286Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.108088Z digest=sha256:4142176ab6e9bbf7198a52c05fccaccd5a9714745bcaf4a8c85f4e4df619c089

Observation bba5d70c-3d56-4656-83b7-6d1a681358e8 · outbound

This paper cites Erd˝ os and A.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Erd˝ os and A

Reference 6

Resolution
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raw_fallback, observed 2026-08-14T15:07:28.711635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.118169Z digest=sha256:0401c4875b16c0fc0c812250ca7f0daaa40f89bd9046f5eb48dac745f6d1dcca

Observation c90bba10-c553-447c-a1e2-5e3b076c3e38 · outbound

This paper cites Erd˝ os and P.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Erd˝ os and P

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:28.684312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.126352Z digest=sha256:7ab65f936c9de5d0aeb0f8f6a3beece7216b0434ae40841b49485714acf9ad1b

Observation 0dba1700-aef5-434c-90fd-39ac888a3bf8 · outbound

This paper cites Farahmand, Topics in random polynomials, Pitman Res.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Farahmand, Topics in random polynomials, Pitman Res

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:28.485239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.135019Z digest=sha256:0aa95edc41b5a45f1d72df8818299bd5786f8b7b033dac2188e1db235a0fedf6

Observation 6604d3d4-1a7f-432d-9f25-a926b5ee2d93 · outbound

This paper cites Farahmand, On the variance of the number of real zeros of a random trignometric polynomial, J.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Farahmand, On the variance of the number of real zeros of a random trignometric polynomial, J

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:28.453159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.145305Z digest=sha256:bae1fb2edfd7a57397b14d97f69b19c8a0d4e8225f536cd34c2c2ef4c4ea86f8

Observation ac009e9e-cfb6-407c-988e-da00c11622dc · outbound

This paper cites Fairley, Roots of random polynomials, Ph.D.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Fairley, Roots of random polynomials, Ph.D

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:28.425228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.155218Z digest=sha256:e6f88d12bc5c14fd6b2b5c9c5519b09ece9b5c9a9d65f98c4ea71913d66e3d3f

Observation 278a8ae0-7a48-4b4a-a34f-189b53f9c9d1 · outbound

This paper cites Forrester and G.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Forrester and G

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:28.386605Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.162639Z digest=sha256:8b824e9ff91d5e699c3f3471aa8b5c04f655d15b7d1101720981993f8528526d

Observation a26936b6-e439-4602-9ee4-ff0bf04bd4c4 · outbound

This paper cites Granville and I.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Granville and I

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:28.343749Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.169673Z digest=sha256:cd7144e58830ffc2557d2aa71b30aeabe4f4ee7a6ba8d23bbc062fb5cece8407

Observation 3b7c205b-13c2-47cf-b354-f212b1ff214c · outbound

This paper cites Hammersley, The zeros of a random polynomial, Proc.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Hammersley, The zeros of a random polynomial, Proc

Reference 13

Resolution
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raw_fallback, observed 2026-08-14T15:07:28.305636Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.189188Z digest=sha256:f8803f23497d3628a6591fc4b819d7d332676d83453737861b02c2b78e3eff01

Observation 9fc40455-b1f6-4ecd-a354-7abaa1776360 · outbound

This paper cites Hannay, Chaotic analytic zero points: exact statistics for t hose of a random spin state, J.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Hannay, Chaotic analytic zero points: exact statistics for t hose of a random spin state, J

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:28.271093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.200053Z digest=sha256:6f45f8dc1fb17692739a23b75d41433bfe02c739f47e3bfc70e843a52d49d6fa

Observation cfe480b7-b85c-4fd4-bca0-cd3753412b90 · outbound

This paper cites Hough, M.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Hough, M

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:28.239748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.212995Z digest=sha256:31a621c67f6780471743fa9c07a648b733f3856680248b96f989a3fab4f66446

Observation fa67128c-3527-4ed3-aef5-4139e0a88146 · outbound

This paper cites Jamrom, On the average number of real roots of a random a lgebraic polynomial, Vestnik Leningrad.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Jamrom, On the average number of real roots of a random a lgebraic polynomial, Vestnik Leningrad

Reference 16

Resolution
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raw_fallback, observed 2026-08-14T15:07:28.209195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.228992Z digest=sha256:48bb75fc9611f0c04d25f1eede76a3d85bbbecb9509ef2c76a18fe92379c5591

Observation 5a74db5f-e472-40a9-aaa0-ca4be34775d5 · outbound

This paper cites Jamrom, The average number of real zeros of random polyn omials, Soviet Math.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Jamrom, The average number of real zeros of random polyn omials, Soviet Math

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:28.178900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.239273Z digest=sha256:6de0d36bcd2d1a9e74951d43f19df8cea2a229ad943571af2fe34e606e62aaf1

Observation ec103b3b-a016-4222-a217-96c64ae799cf · outbound

This paper cites Kac, On the average number of real roots of a random algeb raic equation, Bull.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Kac, On the average number of real roots of a random algeb raic equation, Bull

Reference 18

Resolution
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raw_fallback, observed 2026-08-14T15:07:28.140579Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.247999Z digest=sha256:2a8ddff30ed8c8b01ef602331d82bf05f94a08f3d42fcc6647e658cbf41ab63d

Observation 477bfcaf-4f98-48f9-a17d-68236f79a856 · outbound

This paper cites Littlewood and A.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Littlewood and A

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:28.080872Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.256139Z digest=sha256:834da25e425ea0155b627a80b5806bec567ea8ef68abdf8bcae51df35cd2be9e

Observation f46c14f8-845b-4868-9ab2-9dd480928298 · outbound

This paper cites Littlewood and A.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Littlewood and A

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:28.035962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.264179Z digest=sha256:f83681ffab075bda5b0a1e084f67a8f2d56daf79cd71fb6ad6b3cba1a83de77b

Observation 64767435-0020-4d2e-8a8d-f9b5c0b61d1b · outbound

This paper cites Littlewood and A.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Littlewood and A

Reference 21

Resolution
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raw_fallback, observed 2026-08-14T15:07:27.999056Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.273730Z digest=sha256:a9d770fff86ac6d8168136803ec4902ce0ffa197f5ed88300c1240ece1c913cc

Observation 488d6ebb-f3c2-49f6-b55e-b600e3d50adf · outbound

This paper cites Littlewood and A.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Littlewood and A

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:27.968450Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.286833Z digest=sha256:1f1fd51e392ff366201e26e5db4861b012a4af5efe531f97d2fc9d3910f748ad

Observation ec66fc5f-a02e-4593-a478-69b54316e788 · outbound

This paper cites Littlewood and A.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Littlewood and A

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:27.920128Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.294311Z digest=sha256:974a8c862b8a95d9729c563feb1bc841559013b9ad39914b1daa74505cf0925b

Observation f6ccf9ba-dd69-47ce-8088-df9260c70c89 · outbound

This paper cites Maslova, The variance of the number of real roots of rando m polynomials, Theor.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Maslova, The variance of the number of real roots of rando m polynomials, Theor

Reference 24

Resolution
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raw_fallback, observed 2026-08-14T15:07:27.885283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.300554Z digest=sha256:c9c63ea3e38d8b2225c436c1b31166a79bf35fce7ac8edd90792c504c05006d4

Observation 6ea4a2cc-ce30-442b-9657-3ce65208ed91 · outbound

This paper cites Random polynomials: central limit theorems for the real roots.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Random polynomials: central limit theorems for the real roots

Reference 25

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local_arxiv, observed 2026-08-14T15:07:27.470022Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.308903Z digest=sha256:a8fed893f7c3ea4a6fdb0eb22ab4e046f25148bbd15d80aad426986255b94314

Observation 31a9ab29-74bb-4d9d-865a-2eb396d13b7e · outbound

This paper cites Pritsker and A.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Pritsker and A

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:27.852294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.317131Z digest=sha256:4ebb1c706d1a7b8abea4e09fabb6ea837238e6a06f28e9aa34ec50024eeefb25

Observation 847d5164-0b7a-4c0c-87d2-01d2288cc4b5 · outbound

This paper cites Rice, Mathematical theory of random noise, Bell System Tec h J.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Rice, Mathematical theory of random noise, Bell System Tec h J

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:27.819676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.323024Z digest=sha256:bff6ab41c4d137afacceedc03612e697eafa125f446611ba6a946c3ac03a28a2

Observation 8718bf88-cffa-4627-9822-c07248d8f224 · outbound

This paper cites Shiffman and S.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Shiffman and S

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:27.785850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.330832Z digest=sha256:010eee7d59025aff5a2cc41d8ab0f3b7e8ed26ef12cb63975e1b2f6c44cffea4

Observation a2f163c3-8daf-47df-a8a7-900f71d85432 · outbound

This paper cites Simon, Orthogonal Polynomials on the Unit Circle.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Simon, Orthogonal Polynomials on the Unit Circle

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:27.741065Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.339613Z digest=sha256:f995057acfd698c1e1094f36033bfbb29e024fd7df42c92fbaa7d686f2ae2fc7

Observation e537b015-9452-4394-b9fc-bcf378e61c61 · outbound

This paper cites Stevens, The average and variance of the number of real z eros of random functions.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Stevens, The average and variance of the number of real z eros of random functions

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:27.686002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.346041Z digest=sha256:394552f4443c71bd4fdcd4c128685975f8063d848c31b1d20ba386e9df926b75

Observation ec4769cf-8736-447e-ad07-030591058032 · outbound

This paper cites Su and Q.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Su and Q

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:27.638864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.353079Z digest=sha256:8a2e790c716bdfe681f57c5088196cb1817034985f7ec2837c6387ea9b7d81e7

Observation 21d891dc-c3ba-4a24-9e9a-5ba0c4085c67 · outbound

This paper cites Wang, Bounds on the average number of real roots of a ran dom algebraic equation (Chinese), Chinese Ann.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Wang, Bounds on the average number of real roots of a ran dom algebraic equation (Chinese), Chinese Ann

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:27.598358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.359198Z digest=sha256:9a3f884ae9dc4457f8d97c0a93638cf75b5405d6b294a54bf3ff6546c60291a0

Observation 20f13e6a-d4c8-403d-abc4-e70fd77e364b · outbound

This paper cites Wilkins, An asymptotic expansion for the expected number of real zeros of a random polynomial, Proc.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Wilkins, An asymptotic expansion for the expected number of real zeros of a random polynomial, Proc

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:27.536647Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.367145Z digest=sha256:ce7f55c6e6d995720216842ad97203a5ff9fc37178a0676a4429ad891bc0fbdc

Observation c12271fd-ed15-4a1d-b61f-7c49a4851f43 · outbound

This paper cites Yeager, Zeros of random orthogonal polynomials with comple x Gaussian coefficients, Rocky Mout.

The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC Yeager, Zeros of random orthogonal polynomials with comple x Gaussian coefficients, Rocky Mout

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:07:27.505487Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:07:27.374519Z digest=sha256:46230832ef6d5b79704a45d2801b68ba1ddedde1f346dfcc928f8a67333e38a5

Pith citing papers

No inbound Pith citation observations are available.