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Paper Citation Record · LEDGER

Multiscale modeling of materials and neural operators

As of 11 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2605.08466.

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

pith.paper-citation-record.v1
2605.08466 v1

Coverage vector

measured 50 of 50 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-12T00:52:15.702086Z

measured 50 of 50 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

50 of 50 outbound references displayed

  • verified exact1
  • verified fuzzy29
  • unresolved20
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 91c8e128-cc26-47ee-9af5-64e136bdf7d6 · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 1

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unresolved
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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.

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Observation 005cedb6-eed6-4803-946e-06280c2cd4d2 · outbound

This paper cites Bensoussan, J.

Multiscale modeling of materials and neural operators Bensoussan, J

Reference 2

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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.

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Observation 321e5f35-5f31-440b-88a2-b97288351585 · outbound

This paper cites Berdichevskii and L.

Multiscale modeling of materials and neural operators Berdichevskii and L

Reference 3

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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.

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Observation 9db54139-fedf-4cb4-96a2-77699afe741a · outbound

This paper cites Bhattacharya, B.

Multiscale modeling of materials and neural operators Bhattacharya, B

Reference 4

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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.

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Observation 1ec91ad6-16ae-4732-8de6-33fde69fbcb9 · outbound

This paper cites Bhattacharya, N.

Multiscale modeling of materials and neural operators Bhattacharya, N

Reference 5

Resolution
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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.

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Observation 4783fcea-f508-4f49-8726-202b789613cc · outbound

This paper cites Bhattacharya, B.

Multiscale modeling of materials and neural operators Bhattacharya, B

Reference 6

Resolution
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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.

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Observation 56ee134c-d248-45ca-aff5-e179e4b6028f · outbound

This paper cites Bonatti and D.

Multiscale modeling of materials and neural operators Bonatti and D

Reference 7

Resolution
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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.

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Observation b3105a18-98a8-4497-9ab3-b613d0ba7627 · outbound

This paper cites Bulatov and W.

Multiscale modeling of materials and neural operators Bulatov and W

Reference 8

Resolution
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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.

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Observation 886483c3-2e9e-4280-9af6-7a83eba100c2 · outbound

This paper cites Car and M.

Multiscale modeling of materials and neural operators Car and M

Reference 9

Resolution
verified fuzzy
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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.

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Observation 667caa47-7c6f-41d7-a2fc-07c7dd0c6b16 · outbound

This paper cites Chang and D.

Multiscale modeling of materials and neural operators Chang and D

Reference 10

Resolution
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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.

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Observation dac20e99-69c7-4bab-ba43-5fff8615f8cc · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 11

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

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Observation f6fbd599-2431-4141-bc90-15f7580153a4 · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 12

Resolution
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raw_fallback, observed 2026-05-14T09:43:27.155883Z

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.

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Observation f0d817ca-0679-4ce9-a7f9-22c8e1147d18 · outbound

This paper cites E.Principles of multiscale modeling.

Multiscale modeling of materials and neural operators E.Principles of multiscale modeling

Reference 13

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

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Observation ec2233a6-2e9d-4dee-a0a4-d9b56da36830 · outbound

This paper cites Fish.Multiscale Methods: Bridging the Scales in Science and Engineering.

Multiscale modeling of materials and neural operators Fish.Multiscale Methods: Bridging the Scales in Science and Engineering

Reference 14

Resolution
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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.

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Observation 781198ca-0af1-4640-9a86-506b6e1b9e96 · outbound

This paper cites Ghavamian and A.

Multiscale modeling of materials and neural operators Ghavamian and A

Reference 15

Resolution
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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.

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Observation 2b7cac63-4d9d-4de6-8490-4d6db4d2aedc · outbound

This paper cites Ghosh and P.

Multiscale modeling of materials and neural operators Ghosh and P

Reference 16

Resolution
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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.

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Observation fe4d38c2-fe57-4226-9a54-aa5ba4e9c321 · outbound

This paper cites Ghosh and P.

Multiscale modeling of materials and neural operators Ghosh and P

Reference 17

Resolution
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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.

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Observation da4a2705-7522-40f3-91a6-e58fa40b03dc · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 18

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

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Observation b8baae84-577e-4f88-b80c-496978c22d11 · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 19

Resolution
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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

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Observation 5ae3b37b-2e67-4eff-9884-a7131ddc7799 · outbound

This paper cites Karimi and K.

Multiscale modeling of materials and neural operators Karimi and K

Reference 20

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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.

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Observation a5a79971-e37a-42cc-93b2-193c9a5dab56 · outbound

This paper cites arXiv preprint arXiv:2412.10354 , year =.

Multiscale modeling of materials and neural operators arXiv preprint arXiv:2412.10354 , year =

Reference 21

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arxiv_id, observed 2026-05-12T08:41:23.838271Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

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Observation e57c947b-61f1-4460-b90c-0f7deb6946eb · outbound

This paper cites Kovachki, Z.

Multiscale modeling of materials and neural operators Kovachki, Z

Reference 22

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

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Observation 66275460-182e-490b-abe2-a3124927ccb5 · outbound

This paper cites Kovachki, B.

Multiscale modeling of materials and neural operators Kovachki, B

Reference 23

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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.

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Observation 8726a655-a28f-42a8-b915-73093caacca5 · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 24

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

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Observation 99e67cd1-a17a-4854-8216-98b0a61ef984 · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 25

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

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Observation d4699833-6c41-42b3-85bf-ee4baf962375 · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 26

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raw_fallback, observed 2026-05-14T09:43:27.083469Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

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Observation aa094f28-a1d7-42f9-8eff-9505baa62f70 · outbound

This paper cites Lefik, D.

Multiscale modeling of materials and neural operators Lefik, D

Reference 27

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

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Observation 408e3b54-8cba-4c1c-95f9-7ee3118f33b5 · outbound

This paper cites Lehmann, F.

Multiscale modeling of materials and neural operators Lehmann, F

Reference 28

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

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Observation 0ac75099-5579-48c0-b743-e54ba0daca9e · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 29

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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.

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Observation 70e4711c-1f08-4124-bbcb-cc1b59b0a819 · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 30

Resolution
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raw_fallback, observed 2026-05-14T09:43:27.039552Z

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.

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Observation 8f5963e2-0780-4b36-aff1-a992d88edd5e · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 31

Resolution
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raw_fallback, observed 2026-05-14T09:43:27.046888Z

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.

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Observation f89b82b6-70e2-474a-a52a-ad1a5d8b9213 · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 32

Resolution
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raw_fallback, observed 2026-05-14T09:43:27.043240Z

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.

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Observation 6210fcbe-3151-44b6-a786-2c5589fa63b5 · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 33

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raw_fallback, observed 2026-05-14T09:43:27.210932Z

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.

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Observation fd214ff6-9050-4e49-bdc3-8dced4233196 · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 34

Resolution
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raw_fallback, observed 2026-05-14T09:43:27.091293Z

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.

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Observation 11ca4bc1-f723-4582-96b8-a10c7d198146 · outbound

This paper cites Liu-Schiaffini, J.

Multiscale modeling of materials and neural operators Liu-Schiaffini, J

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-05-14T09:43:27.068064Z

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.

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Observation 70d18266-f2f7-4bec-a55e-1864724ae615 · outbound

This paper cites Maresca and E.

Multiscale modeling of materials and neural operators Maresca and E

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-05-14T09:43:27.071690Z

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=2026-05-12T00:52:15.702086Z digest=sha256:d27d7d261ebb6edc0a33af023542d0f7a8edbadb7ef51650bc867f6d2afa87c6

Observation 0238c374-dbe4-49b3-8aaa-ec18d734a32e · outbound

This paper cites Mozaffar, R.

Multiscale modeling of materials and neural operators Mozaffar, R

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-05-14T09:43:27.079209Z

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=2026-05-12T00:52:15.702086Z digest=sha256:fe8ea545aba1be609a5f6ce8c5587801adc807096886a928e2cccdfd1d8351bd

Observation 76de8e1f-e58f-46f6-a882-2a8ab1557841 · outbound

This paper cites Pavliotis and A.

Multiscale modeling of materials and neural operators Pavliotis and A

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-05-14T09:43:27.172193Z

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=2026-05-12T00:52:15.702086Z digest=sha256:a0ae0c209afb7d045880718fe1c2cbe1354c90c63b921e776e1e85f46459511e

Observation 1691b902-9ddf-4779-b6a4-7e6fb3a14056 · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-05-14T09:43:27.051531Z

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=2026-05-12T00:52:15.702086Z digest=sha256:dd927177dddea5490888b188cb5572bac9766f0cf6ed34170cae609b8f75f8df

Observation 48fe8a0c-fd1d-4b42-8659-eb152b5822e4 · outbound

This paper cites Phillips.Crystals, defects and microstructures: Modeling across scales.

Multiscale modeling of materials and neural operators Phillips.Crystals, defects and microstructures: Modeling across scales

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-05-14T09:43:27.058222Z

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=2026-05-12T00:52:15.702086Z digest=sha256:be68d8f4d37fb8f37a31812539dd9757bc824d82011436a5b4334317c171c36d

Observation eac34a72-aeab-49a9-9a42-66b5cf303ca8 · outbound

This paper cites Radhakrishnan.

Multiscale modeling of materials and neural operators Radhakrishnan

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-05-14T09:43:27.031816Z

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=2026-05-12T00:52:15.702086Z digest=sha256:662d45f771af90582064c57d75fd74f60411f5e7a62a733501e6e9d08ee3e8bc

Observation aaadad32-5c05-46b4-af02-ce56933d8c5e · outbound

This paper cites Raissi, P.

Multiscale modeling of materials and neural operators Raissi, P

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-05-14T09:43:27.035727Z

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=2026-05-12T00:52:15.702086Z digest=sha256:83b2c17028f5a2ce1c80cb1455d3b80f47b80a1231ceafa9293b1291556b5733

Observation 531e3599-4b0e-4e33-b9a4-cfd2576f4d9a · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 43

Resolution
unresolved
raw_fallback, observed 2026-05-14T09:43:27.064521Z

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=2026-05-12T00:52:15.702086Z digest=sha256:e2ebcb8a8c0555f47ff695cae1bbdddd491e88879035f2bb229f1fbb8da3fc6e

Observation 65831ca8-5608-4353-8d96-b4a2712cde3a · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-05-14T09:43:27.061036Z

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=2026-05-12T00:52:15.702086Z digest=sha256:f99ea3933a6c0448bda18dd603e7ecbdb71f03d7bcc877f1f0a4d8ba1cc82d63

Observation c65e79e6-56f9-4031-a5e7-b72768ac0abb · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-05-14T09:43:27.114890Z

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=2026-05-12T00:52:15.702086Z digest=sha256:30f98b0aec3bc2cad814d3294de09fad1f130f808ee5c1185dcad1d7abafb562

Observation d2ea5ea9-0a4b-4b13-a6c5-2cfdb6905ba6 · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 46

Resolution
unresolved
raw_fallback, observed 2026-05-14T09:43:27.103121Z

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=2026-05-12T00:52:15.702086Z digest=sha256:58ee1e9d8f0b7b08915c704af66653e22abc3a2d684a33a4b24a5fb5c59f4fc0

Observation 47ec51e6-a818-4da3-a553-6660104aba9e · outbound

This paper cites Van Der Giessen, P.

Multiscale modeling of materials and neural operators Van Der Giessen, P

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-05-14T09:43:27.107217Z

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=2026-05-12T00:52:15.702086Z digest=sha256:321ca02210c39e246d8f00503b08fd0fd2b0c4bb3ae3ec64b4f698e75b0d6ea4

Observation ab7b902f-c903-4775-ac44-1c974fec36e0 · outbound

This paper cites Woodward, D.

Multiscale modeling of materials and neural operators Woodward, D

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-05-14T09:43:27.111212Z

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=2026-05-12T00:52:15.702086Z digest=sha256:77e75395a02508142b14459568df9dc70d88805e4d1557e63a337ee461430f84

Observation 8315e968-b005-45fa-8167-150e1a89f9ef · outbound

This paper cites an unresolved cited work.

Multiscale modeling of materials and neural operators Unresolved cited work

Reference 49

Resolution
unresolved
raw_fallback, observed 2026-05-14T09:43:27.099246Z

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=2026-05-12T00:52:15.702086Z digest=sha256:3c1d3f7c55fa05db5fc2077624c1fba4291ae48136f63b8a4daceb20a17b9c37

Observation 185f3a43-515c-47b6-8159-8c5ac31a0102 · outbound

This paper cites Zhang and K.

Multiscale modeling of materials and neural operators Zhang and K

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-05-14T09:43:27.095146Z

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=2026-05-12T00:52:15.702086Z digest=sha256:e5af32b3a847e655158939c058af5944274619945fd46fe6e79384a3e760ffbf

Pith citing papers

No inbound Pith citation observations are available.