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Paper Citation Record · LEDGER

Universality of physical neural networks with multivariate nonlinearity

As of 10 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 1 inbound Pith citation observation for arXiv:2509.05420.

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

pith.paper-citation-record.v1
2509.05420 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T05:17:09.864162Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-21T19:32:33.621988Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-21T19:34:20.126755Z

Reference resolution

32 of 32 outbound references displayed

  • verified exact0
  • verified fuzzy23
  • unresolved9
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a4206d12-76e8-442f-aa1a-227d692f49cf · outbound

This paper cites de Vries ,\ title title The growing energy footprint of artificial intelligence ,\ @noop journal journal Joule \ volume 7 ,\ pages 2191 ( year 2023 ) NoStop.

Universality of physical neural networks with multivariate nonlinearity de Vries ,\ title title The growing energy footprint of artificial intelligence ,\ @noop journal journal Joule \ volume 7 ,\ pages 2191 ( year 2023 ) NoStop

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.384360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.713440Z digest=sha256:022317a9255e9f2dc72e09acb315d42ba4cfb555e66d096e55177c06e3d1faa2

Observation 39086290-69d6-4ef5-add2-b3ecc033adc3 · outbound

This paper cites Marković , author A.

Universality of physical neural networks with multivariate nonlinearity Marković , author A

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.366896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.718676Z digest=sha256:7416549eb805279e4d5dd3bebae3d827c8019e4cb442bca539e967830da15437

Observation 9d68566d-c89e-47f6-a1db-bf90d2fa2c24 · outbound

This paper cites Wetzstein , author A.

Universality of physical neural networks with multivariate nonlinearity Wetzstein , author A

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.350437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.723488Z digest=sha256:697294a6d50028568bf95ee2e7b5a2363a1a2eecadf93efc812d4d4a2bd674bd

Observation e70570f3-4955-4f5b-a34a-9f96f5f19710 · outbound

This paper cites an unresolved cited work.

Universality of physical neural networks with multivariate nonlinearity Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:17:10.334141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.729287Z digest=sha256:83b80a5329a4bade813aa873d2fe792acc24474aef2deb24ea7ba95fb54cc2c4

Observation 7519c463-f5bc-4f73-b44d-f2d1cb208f84 · outbound

This paper cites Training of Physical Neural Networks.

Universality of physical neural networks with multivariate nonlinearity Training of Physical Neural Networks

Reference 5

Resolution
unresolved
no resolver link, observed 2026-08-05T05:17:09.734647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-05T05:17:09.734647Z digest=sha256:2130b086f3f91e68fa5c5f54295882ab3a2735cd67c1c6e18e1d40d21931280b

Observation 6f94d2a6-d07b-43a0-98e9-005fdbc1ac2e · outbound

This paper cites Psaltis \ and\ author N.

Universality of physical neural networks with multivariate nonlinearity Psaltis \ and\ author N

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.316996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.740489Z digest=sha256:6f2552c7ef5afc609f1a8e32d7bbe8f07846e8742abe46af366579e0cf8ee92e

Observation 674166d0-4fd1-4c8a-8454-a09ac013e0be · outbound

This paper cites Lin , author Y.

Universality of physical neural networks with multivariate nonlinearity Lin , author Y

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.302597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.746144Z digest=sha256:880c3e52d1e5166ab54a1988ca9e7bf02894bc636688d04531fceb06562953eb

Observation 237b5ccc-8e46-4422-86a4-c6b900c85cb2 · outbound

This paper cites an unresolved cited work.

Universality of physical neural networks with multivariate nonlinearity Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:17:10.288051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.750735Z digest=sha256:45fc0ffd295e18c8537097bc0e2bc25ff50cd0f92e6577da65a81a5d1249e1ed

Observation 19659fa7-3501-42f2-a762-5f9b39508a72 · outbound

This paper cites an unresolved cited work.

Universality of physical neural networks with multivariate nonlinearity Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:17:10.273619Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.755201Z digest=sha256:ad775fe3201883be99269586696318e71e8d413cc683e79998b85635a92ff9ca

Observation 7cdf5815-c7fd-4e5c-bc3c-715ee73e9983 · outbound

This paper cites Eliezer , author U.

Universality of physical neural networks with multivariate nonlinearity Eliezer , author U

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.259385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.759710Z digest=sha256:8a0c664a235f17ef3a4f52b7159fe3a1609fe55af0c6ca9f6347904bd3629e3a

Observation 6ef85fd8-ec63-4f9e-9db2-ea45fb0cf4da · outbound

This paper cites an unresolved cited work.

Universality of physical neural networks with multivariate nonlinearity Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:17:10.243798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.764424Z digest=sha256:2c4cca51070d5a3c9c86e1a0e4ccd25da6c6074736e2802556de5e2dc4a95622

Observation d0320576-74b5-46cc-8e25-102afa122bc3 · outbound

This paper cites Xia , author K.

Universality of physical neural networks with multivariate nonlinearity Xia , author K

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.229721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.768939Z digest=sha256:47b216cc3ad282872e3d24af130f078b32f9ed17cd37c93b85ed31fd162be35e

Observation 6c7fca51-0837-4f23-abc3-5f86b7b9ab90 · outbound

This paper cites Yildirim , author N.

Universality of physical neural networks with multivariate nonlinearity Yildirim , author N

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.215054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.774554Z digest=sha256:e9c2dff21d136dfe0dce06c65d1e0e6e11ce92389ebbe83e260e2482fae47e92

Observation a82dd7f6-83c7-4f56-b713-e396291e21ea · outbound

This paper cites Hornik , author M.

Universality of physical neural networks with multivariate nonlinearity Hornik , author M

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.200246Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.779542Z digest=sha256:12106f41baa263e80f7c72e6631e6a9123444da939e6ae5c9182b8d90d73ad23

Observation 0494aa59-6c4e-4815-8fb2-a89e3428ceb4 · outbound

This paper cites an unresolved cited work.

Universality of physical neural networks with multivariate nonlinearity Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:17:10.185169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.784398Z digest=sha256:6b79945595b4ceedda69c8f5673d213e0af4ef7b074887d2f284a955a82ea6e7

Observation 6a1c45d7-364e-4c5e-b14a-61f44282d38c · outbound

This paper cites Athale \ and\ author D.

Universality of physical neural networks with multivariate nonlinearity Athale \ and\ author D

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.169489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.788977Z digest=sha256:578eb6ede6bcb697407f6c1710a0e8f7ac00973778aca4f0686286476834c92b

Observation 0609e594-fd67-4a18-adb2-4ab6a10b7f16 · outbound

This paper cites Silva , author F.

Universality of physical neural networks with multivariate nonlinearity Silva , author F

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.153973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.793796Z digest=sha256:09489a8a2f62d5c08eb3affb89907fec31a547d1104668f5639098af05d4c604

Observation 7142d9ec-030d-4a55-b556-e27e999db67c · outbound

This paper cites Cordaro , author H.

Universality of physical neural networks with multivariate nonlinearity Cordaro , author H

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.139693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.798503Z digest=sha256:11d82027dfc4a0b44237741a7184da1b6120750bf0d46eacc30cd300027a561d

Observation e2101b93-e0f5-4afa-9f23-8d87f3c151a4 · outbound

This paper cites Zangeneh-Nejad , author D.

Universality of physical neural networks with multivariate nonlinearity Zangeneh-Nejad , author D

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.124858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.803032Z digest=sha256:df711e012a58b6e25b00407c3d751ac4ce1a28c37bef8829c59eb67a4528a64d

Observation 7eeb3a88-b8cc-4ad9-abd5-e546e2d7c9aa · outbound

This paper cites Mohammadi Estakhri , author B.

Universality of physical neural networks with multivariate nonlinearity Mohammadi Estakhri , author B

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.111070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.807365Z digest=sha256:ab825a8ba341cc526ce8c823209a7cf4aa891514b70118bf359323836f737af2

Observation 9c5aaff8-f0c0-4fd6-815c-acfc20adaf3d · outbound

This paper cites Cordaro , author B.

Universality of physical neural networks with multivariate nonlinearity Cordaro , author B

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.095681Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.812273Z digest=sha256:e20ccb99fe6f2a827d302096e0e2a05701f4aa4ec9d667952342c2febe1eb442

Observation a4ae7287-07f1-482f-8505-d96c88350a79 · outbound

This paper cites Yang , author L.

Universality of physical neural networks with multivariate nonlinearity Yang , author L

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.080786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.816796Z digest=sha256:ee68e8fc3b46bb4bee5e7da2c5080f416d04c09fd41cd909ecbe0a6610c2903b

Observation 53828583-20de-455e-ba0a-0869eed59704 · outbound

This paper cites Nikkhah , author A.

Universality of physical neural networks with multivariate nonlinearity Nikkhah , author A

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.064844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.821697Z digest=sha256:2a60c5cb8d38c5e93e1ab11c677c66b5adb95e969c3817cc2d88bac1d07abc94

Observation 251cf99b-194a-412e-be31-dfcd61a48fb5 · outbound

This paper cites an unresolved cited work.

Universality of physical neural networks with multivariate nonlinearity Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:17:10.048467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.826677Z digest=sha256:bd50884f5876aa5d7dc628739f34d57d993f818b261951daba0192c20ed033a2

Observation c72a08b2-1e6c-4ce2-8333-cc3f912e5372 · outbound

This paper cites Shen , author N.

Universality of physical neural networks with multivariate nonlinearity Shen , author N

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.032895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.831329Z digest=sha256:87af9a848e796fdc6496faa6d95004fe719bc042c9151aa578019a62a729edde

Observation cb19861b-2792-4285-b703-728740acf3c8 · outbound

This paper cites Pai , author Z.

Universality of physical neural networks with multivariate nonlinearity Pai , author Z

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.017378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.836125Z digest=sha256:fa244e2c030108058880dbbc6e4f9cac318ccb02a8208c0136580f8bb748ad33

Observation d86106c7-bb20-4dad-961e-0c061342f64b · outbound

This paper cites Hua , author E.

Universality of physical neural networks with multivariate nonlinearity Hua , author E

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:10.000388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.840501Z digest=sha256:97bf030833188f4262a7be2a19ec5d966c80e5956b3853836c70581535bd8e56

Observation 8aee66f0-690d-433f-9b01-7e9a2a74996b · outbound

This paper cites Yu , author Z.

Universality of physical neural networks with multivariate nonlinearity Yu , author Z

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:09.984150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.845026Z digest=sha256:51e0dd413c265f9d10f3811fe3308eb8d6afe4d9a6dda2c879a1a43dcbf09c4c

Observation 0fc1ebb3-32eb-43c1-934c-9cab98c34854 · outbound

This paper cites Bandyopadhyay , author A.

Universality of physical neural networks with multivariate nonlinearity Bandyopadhyay , author A

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:09.968486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.849824Z digest=sha256:f0debfa7621a3c946d16b8fbe5c180b3cab1bb1032049c126c82c7431e9b0e17

Observation ff868291-068f-4985-9b88-6285b97a37ab · outbound

This paper cites LeCun , author L.

Universality of physical neural networks with multivariate nonlinearity LeCun , author L

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:17:09.952467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.854434Z digest=sha256:53a92ea443beb0130f7324c67518e4084202b17189de5fc394afc8f0672302bf

Observation 3331ff13-aa27-44f3-9085-8ef1bc1dca07 · outbound

This paper cites Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms.

Universality of physical neural networks with multivariate nonlinearity Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms

Reference 31

Resolution
unresolved
no resolver link, observed 2026-08-05T05:17:09.859247Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-05T05:17:09.859247Z digest=sha256:80881f738d7ebcaf2b77214a91c5a9d44977cff1afe1d43a06cfed04b12bbab0

Observation a8927473-3525-418b-872e-3c6e20f35346 · outbound

This paper cites an unresolved cited work.

Universality of physical neural networks with multivariate nonlinearity Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:17:09.936080Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-05T05:17:09.864162Z digest=sha256:d5b2a91eaef507feb41241167326ee1f24dedf29e7e7a3e252390471540e9cad

Pith citing papers

Observation fba75295-2740-465c-a530-458b79bf4071 · inbound

Tutorial: A practical guide to the alignment of defocused spatial light modulators for fast diffractive neural networks cites this paper.

Tutorial: A practical guide to the alignment of defocused spatial light modulators for fast diffractive neural networks Universality of physical neural networks with multivariate nonlinearity

Reference 19

Resolution
verified exact
arxiv_id, observed 2026-05-21T19:34:20.129142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-21T19:32:33.621988Z digest=sha256:b45951869905b4bf673f7b46194e93425c468a166f38be8630fe434dfab94680