Paper Citation Record · LEDGER

S$^2$GPT-PINNs: Sparse and Small models for PDEs

As of 22 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2506.15687.

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

pith.paper-citation-record.v1
2506.15687 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T14:23:52.163084Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+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

35 of 35 outbound references displayed

verified exact0
verified fuzzy11
unresolved23
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation aa0a0f37-dc12-48ef-879e-705934c81fe6 · outbound

This paper cites Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T14:23:49.081662Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 597cf95b-1a92-4018-b553-e37d6aecc283 · outbound

This paper cites Ainsworth and J.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Ainsworth and J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:23:56.343562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation dc075f14-fcbe-47b3-a029-357fa0c1a66a · outbound

This paper cites empirical interpolation.

S$^2$GPT-PINNs: Sparse and Small models for PDEs empirical interpolation

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:23:56.180711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3960ae8e-2983-48d6-81a7-1cfdf2e87071 · outbound

This paper cites Binev, A.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Binev, A

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:23:55.963611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5eba236a-7357-4e39-96c2-a1f38aad9569 · outbound

This paper cites Brown, B.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Brown, B

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:23:55.821521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c5378c6d-d94e-4785-9aac-155fa8fef609 · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:23:55.636726Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 04875530-6192-4076-b0ea-870617ebd008 · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:23:55.407259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 79f1a0c7-961b-44de-8d20-4ab45863f735 · outbound

This paper cites Chen and S.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Chen and S

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:23:55.256131Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0a3a67b7-82c1-4999-a1b6-63be492aa758 · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T14:23:49.991049Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9f5422c4-e6da-49b4-8a8f-fa76c0a9e555 · outbound

This paper cites DeVore, B.

S$^2$GPT-PINNs: Sparse and Small models for PDEs DeVore, B

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T14:23:50.143914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation daea3657-79df-40e2-b480-597f0613312a · outbound

This paper cites Dhariwal and A.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Dhariwal and A

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T14:23:50.259467Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 597727d8-8b32-426d-b980-4c1dd6f32a85 · outbound

This paper cites Fresca, L.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Fresca, L

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:23:55.037032Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation fcbe22a0-a706-4deb-bf7e-8753d53d6515 · outbound

This paper cites Fresca and A.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Fresca and A

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:23:54.869353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 47e06d6b-0f08-4c7b-ab8b-07eb6c5daa33 · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:23:54.674469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation bb03a5a6-6f94-48a0-925c-a110c3a12e37 · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:23:54.528988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1594860b-f4cf-4b93-b7ff-7bf5213f3435 · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T14:23:50.864262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6fc73fef-8485-4c19-bdc5-bf3be3df0d2e · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:23:54.357277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 402bd7e0-dc14-4485-9d0b-9568b3e3e3ab · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:23:54.183012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c213dac7-e2bd-4439-82f2-d8536cfda6bc · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:23:54.026550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 64a946c6-0c58-4aa2-a786-0e12016675dd · outbound

This paper cites Huang, Z.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Huang, Z

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:23:53.855664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0d61d01d-23a0-4729-9d23-0b28dd49df71 · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:23:53.702115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8c78c47d-199f-49d5-862e-0ec70dd45f5d · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:23:53.538748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 10819d8b-a29d-43c0-a809-4ce105a845df · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:23:53.399317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0a4d4b55-f8b8-459f-b737-f6538eb39758 · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:23:53.238534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8cdf2c60-a3d8-453f-b53d-490e94c854f8 · outbound

This paper cites Blending Is All You Need: Cheaper, Better Alternative to Trillion-Parameters LLM.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Blending Is All You Need: Cheaper, Better Alternative to Trillion-Parameters LLM

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T14:23:51.484850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78df61d9-714a-43f4-b9da-f300032c2220 · outbound

This paper cites Small Language Models: Survey, Measurements, and Insights.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Small Language Models: Survey, Measurements, and Insights

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-07T14:23:51.551308Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2310294c-a424-4a2c-975b-a7163c3ac4a8 · outbound

This paper cites Maday and O.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Maday and O

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:23:53.063062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9dc401b1-e27b-4165-b2ab-fbffa8b6202e · outbound

This paper cites Maday, O.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Maday, O

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:23:52.932066Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b69cb480-25b5-4ff8-a86d-450799b6f4ad · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:23:52.803974Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 93b48186-03d8-4b4a-bb0a-e1fffc133570 · outbound

This paper cites A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEs.

S$^2$GPT-PINNs: Sparse and Small models for PDEs A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEs

Reference 30

Resolution: metadata mismatch; local_arxiv, observed 2026-08-07T14:23:52.360309Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 615bcce8-d54e-4f47-b481-cbdcc46e4e37 · outbound

This paper cites Quarteroni, A.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Quarteroni, A

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-07T14:23:51.883280Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8904a60-616d-4afb-bdc2-7fdc23c53dcf · outbound

This paper cites Raissi, P.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Raissi, P

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-07T14:23:51.959582Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 64bd7638-c8f8-4413-b914-d80fbfff1749 · outbound

This paper cites It's Not Just Size That Matters: Small Language Models Are Also Few-Shot Learners.

S$^2$GPT-PINNs: Sparse and Small models for PDEs It's Not Just Size That Matters: Small Language Models Are Also Few-Shot Learners

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-07T14:23:52.026903Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8adfe50e-3c5d-48eb-8e7c-810044ec20bf · outbound

This paper cites an unresolved cited work.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:23:52.648707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ecd579a5-cd5b-456a-a1cd-8abb737115fa · outbound

This paper cites Vaswani, N.

S$^2$GPT-PINNs: Sparse and Small models for PDEs Vaswani, N

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:23:52.517077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

No inbound Pith citation observations are available.