Pith. sign in

Paper Citation Record · LEDGER

A deep shotgun method for solving high-dimensional parabolic partial differential equations

As of 17 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2506.15481.

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

pith.paper-citation-record.v1
2506.15481 v1

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:42:20.619679Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+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

20 of 20 outbound references displayed

  • verified exact1
  • verified fuzzy10
  • unresolved6
  • parse uncertain0
  • malformed identifier1
  • metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4a6231cd-047a-4e7d-872c-fc3a6889b627 · outbound

This paper cites Nucleic acids re- search 9(13), 3015–3027 (1981).

A deep shotgun method for solving high-dimensional parabolic partial differential equations Nucleic acids re- search 9(13), 3015–3027 (1981)

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:42:20.920477Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.546534Z digest=sha256:7a0c394564c421115cf9a050c5f41080065c82b708c73290e932dfec2edf82dd

Observation a698512f-bf94-4ea1-832e-b56d9a518ada · outbound

This paper cites SOC-MartNet: A Martingale Neural Network for the Hamilton-Jacobi-Bellman Equation without Explicit inf H in Stochastic Optimal Controls.

A deep shotgun method for solving high-dimensional parabolic partial differential equations SOC-MartNet: A Martingale Neural Network for the Hamilton-Jacobi-Bellman Equation without Explicit inf H in Stochastic Optimal Controls

Reference 2

Resolution
metadata mismatch
local_arxiv, observed 2026-08-15T19:42:20.783470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.550658Z digest=sha256:c96b57e6610b72cfbed982009954f566c663c45c30c414cf3ba48e091b4886e8

Observation bd230071-0eea-4286-8013-db3e669571b7 · outbound

This paper cites DeepMartNet -- A Martingale Based Deep Neural Network Learning Method for Dirichlet BVPs and Eigenvalue Problems of Elliptic PDEs in R^d.

A deep shotgun method for solving high-dimensional parabolic partial differential equations DeepMartNet -- A Martingale Based Deep Neural Network Learning Method for Dirichlet BVPs and Eigenvalue Problems of Elliptic PDEs in R^d

Reference 3

Resolution
metadata mismatch
local_arxiv, observed 2026-08-15T19:42:20.767995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.554945Z digest=sha256:8d10997d548bd1cbe1c4485de7cc34347394878e8efacb01f7dc96372814aa37

Observation 6f6c7234-c5ad-42e5-a959-169ec94baf80 · outbound

This paper cites Nature526(7571), 68 (2015).

A deep shotgun method for solving high-dimensional parabolic partial differential equations Nature526(7571), 68 (2015)

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:42:20.909938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.558967Z digest=sha256:3a68c979ad61e3485f42b2145198119010310c515d8da26a657ae030bf188daa

Observation ab6608ab-1d7a-45e4-acae-0658c1db1391 · outbound

This paper cites Proceedings of the National Academy of Sciences 115(34), 8505–8510 (2018).

A deep shotgun method for solving high-dimensional parabolic partial differential equations Proceedings of the National Academy of Sciences 115(34), 8505–8510 (2018)

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:42:20.899235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.563125Z digest=sha256:2fddf603cf562a9c17e0446e2a6b7cfd9c605585b550e64978c16e8deef3e7b6

Observation 116d39ed-5cac-4ddc-aff1-798f0a8a3a22 · outbound

This paper cites Probability, Uncertainty and Quantitative Risk 5(1), 5 (2020).

A deep shotgun method for solving high-dimensional parabolic partial differential equations Probability, Uncertainty and Quantitative Risk 5(1), 5 (2020)

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:42:20.888941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.566763Z digest=sha256:73611afb77bc1e06adb1aa53785771a02a4ae59859844f2e550add8e0a61d298

Observation 3bdac93e-c522-41d7-9aba-75875b71e135 · outbound

This paper cites Neural Networks 176, 106369 (2024).

A deep shotgun method for solving high-dimensional parabolic partial differential equations Neural Networks 176, 106369 (2024)

Reference 7

Resolution
malformed identifier
no resolver link, observed 2026-08-15T19:42:20.570449Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:42:20.570449Z digest=sha256:06ed71e104a16387400899add25ec5f0d2594e03886d81bc9acbe6b74a6881e7

Observation 5fc33af0-02aa-4afb-91c6-6a9d64874878 · outbound

This paper cites Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs.

A deep shotgun method for solving high-dimensional parabolic partial differential equations Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Reference 8

Resolution
unresolved
no resolver link, observed 2026-08-15T19:42:20.573847Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:42:20.573847Z digest=sha256:81a86e5036f4d242be51937253ad9a942cff6c86ae8abb880f3f27a94fa48af1

Observation faefb63e-758a-431d-a383-542b98c746cc · outbound

This paper cites SIAM Journal on Scientific Computing43(6), B1105– B1132 (2021).

A deep shotgun method for solving high-dimensional parabolic partial differential equations SIAM Journal on Scientific Computing43(6), B1105– B1132 (2021)

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:42:20.878036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.578172Z digest=sha256:07213fdc708e2f1b27e9b31193f6c16cc76f255a27e477e6c01585fd5dc19ef9

Observation b15feade-e2fc-475c-9ca8-193029dbe5fb · outbound

This paper cites Journal of Machine Learning 2(1), 31–64 (2023).

A deep shotgun method for solving high-dimensional parabolic partial differential equations Journal of Machine Learning 2(1), 31–64 (2023)

Reference 10

Resolution
verified exact
doi, observed 2026-08-15T19:42:20.651482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.581572Z digest=sha256:b3545ac7bb8bdbb0be5b5ef6c8548e495c95d248fc59502fd629304913f59ec7

Observation 55e7d789-3395-4c21-a37e-bc8b539d9664 · outbound

This paper cites Randomized Automatic Differentiation.

A deep shotgun method for solving high-dimensional parabolic partial differential equations Randomized Automatic Differentiation

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-15T19:42:20.585570Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:42:20.585570Z digest=sha256:ca748a03ab948e855b211d4b7ba4d6d84f05fe3a08c3ad103cc4b0eb1715ca87

Observation 4213c2ef-fe85-4b12-8a4b-0182835be201 · outbound

This paper cites Systems & control letters 14(1), 55–61 (1990).

A deep shotgun method for solving high-dimensional parabolic partial differential equations Systems & control letters 14(1), 55–61 (1990)

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-15T19:42:20.589507Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:42:20.589507Z digest=sha256:0e3ffc1d60d6241c021d166f777d2e03f8ee8e00a772f4682730e6dcb5e7b771

Observation 7d6a0100-ebd7-4d80-93db-5874b7164390 · outbound

This paper cites an unresolved cited work.

A deep shotgun method for solving high-dimensional parabolic partial differential equations Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:42:20.861062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.593344Z digest=sha256:4c09b22c4f49699e67526e57d69e7711e2f57cb924ee8453fc57ae8c8c989bc3

Observation 849c6a75-17c0-4d03-9818-f561a883656a · outbound

This paper cites In: Peter Carr Gedenkschrift: Research Advances in Mathematical Finance, pp.

A deep shotgun method for solving high-dimensional parabolic partial differential equations In: Peter Carr Gedenkschrift: Research Advances in Mathematical Finance, pp

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:42:20.850829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.596675Z digest=sha256:40405db2b7297f9434cea08b45f573d5a4f476bd3ccaea822ea72a4145033d6c

Observation 1be84821-1c04-4c32-8877-66e446776173 · outbound

This paper cites Journal of Computational physics 378, 686–707 (2019).

A deep shotgun method for solving high-dimensional parabolic partial differential equations Journal of Computational physics 378, 686–707 (2019)

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:42:20.839969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.600358Z digest=sha256:d706919adda77594a056679da90278cc4c60ba88a10578d3be39db9874230fef

Observation 89474f04-f067-412c-a868-1ab005890be0 · outbound

This paper cites Journal of Machine Learning Re- search 25(248), 1–40 (2024).

A deep shotgun method for solving high-dimensional parabolic partial differential equations Journal of Machine Learning Re- search 25(248), 1–40 (2024)

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:42:20.829385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.603853Z digest=sha256:70b1d52cd5f7e579e32e9685984ce88c834c4f72aeba2b933e3725cd738474f3

Observation 4d2fca08-5cc4-46db-85a9-5c480bdb9c59 · outbound

This paper cites Randomized Forward Mode of Automatic Differentiation For Optimization Algorithms.

A deep shotgun method for solving high-dimensional parabolic partial differential equations Randomized Forward Mode of Automatic Differentiation For Optimization Algorithms

Reference 17

Resolution
unresolved
no resolver link, observed 2026-08-15T19:42:20.608405Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:42:20.608405Z digest=sha256:359e4ff988744dfe667fa9694d9dbf36af5f673d7959ea995ef2c19acc2234b2

Observation 078be6d4-6d4e-4257-947d-781b52d104e4 · outbound

This paper cites Journal of computational physics 375, 1339–1364 (2018).

A deep shotgun method for solving high-dimensional parabolic partial differential equations Journal of computational physics 375, 1339–1364 (2018)

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:42:20.817280Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.612409Z digest=sha256:5b2377d40c66a22ed204d223910384806a1cc043d61df41d4e8d9af338ce1ba3

Observation cb8088e9-a058-4201-a02e-d83d37703cdc · outbound

This paper cites an unresolved cited work.

A deep shotgun method for solving high-dimensional parabolic partial differential equations Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:42:20.806586Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.616019Z digest=sha256:8863c690f332cfb32f13eab8384f90e4311833e3cda010ceb6b77b10f0a35d78

Observation 166b4de6-2844-4453-8d5c-e3afe73e8504 · outbound

This paper cites Journal of Computational Physics 470, 111557 (2022).

A deep shotgun method for solving high-dimensional parabolic partial differential equations Journal of Computational Physics 470, 111557 (2022)

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:42:20.794878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:42:20.619679Z digest=sha256:d02f725dc64e3d457ed0a93dd1a2b2896856d6d267db7614d48d3695389c3b57

Pith citing papers

No inbound Pith citation observations are available.