Paper Citation Record · LEDGER

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES

As of 5 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2509.00957.

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

pith.paper-citation-record.v1
2509.00957 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T13:05:09.813319Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+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

25 of 25 outbound references displayed

verified exact5
verified fuzzy5
unresolved11
parse uncertain0
malformed identifier1
metadata mismatch3

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9cf632b6-6cc8-4d34-b22e-3c52b307cade · outbound

This paper cites an unresolved cited work.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:05:12.025619Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation f5d59486-6ee5-4432-af85-eaaecb9c04f6 · outbound

This paper cites Randomized Sparse Neural Galerkin Schemes for Solving Evolution Equations with Deep Networks.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Randomized Sparse Neural Galerkin Schemes for Solving Evolution Equations with Deep Networks

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-05T13:05:11.241159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation ef15ed7a-4b5e-4329-8439-090eeb51a0f6 · outbound

This paper cites Bradbury, R.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Bradbury, R

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:05:11.962694Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation adf7f008-4400-4e75-8e03-2d2bc994c196 · outbound

This paper cites Bruna, B.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Bruna, B

Reference 4

Resolution: malformed identifier; raw_fallback, observed 2026-08-05T13:05:11.153072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 7c536969-d790-4efc-8a0d-17971d39e4d1 · outbound

This paper cites an unresolved cited work.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Unresolved cited work

Reference 5

Resolution: verified exact; doi, observed 2026-08-05T13:05:10.150700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 7abcc7b4-bba5-44b1-91f1-95cdef76cefd · outbound

This paper cites an unresolved cited work.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:05:11.866743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation cc167310-0e5d-45aa-a02e-9412177919f4 · outbound

This paper cites an unresolved cited work.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:05:11.800508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation c3986e81-0b5b-4219-8390-ba1305a79d64 · outbound

This paper cites Dong and Z.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Dong and Z

Reference 8

Resolution: metadata mismatch; raw_fallback, observed 2026-08-05T13:05:10.989338Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation c9a42555-c57c-4ff0-8237-3ed24159d88f · outbound

This paper cites Dong and J.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Dong and J

Reference 9

Resolution: metadata mismatch; raw_fallback, observed 2026-08-05T13:05:10.823378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 0f9acb48-6bcc-40c7-a6bf-6aa0a68ec8ba · outbound

This paper cites Neural Control of Parametric Solutions for High-dimensional Evolution PDEs.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Neural Control of Parametric Solutions for High-dimensional Evolution PDEs

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-05T13:05:10.652423Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation ae5decdd-6d88-40ce-a974-44e2fa03dd8d · outbound

This paper cites an unresolved cited work.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:05:11.719345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation d02562b2-b180-4bbf-9a48-dc9a77de2ed3 · outbound

This paper cites Hardwick, S.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Hardwick, S

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-05T13:05:08.817058Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47fdb337-e68d-4043-a93b-068e15b2517f · outbound

This paper cites an unresolved cited work.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Unresolved cited work

Reference 13

Resolution: metadata mismatch; raw_fallback, observed 2026-08-05T13:05:10.558882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 1490eb5f-cb19-49de-9186-ce0ec7e7ccd5 · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Fourier Neural Operator for Parametric Partial Differential Equations

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-05T13:05:08.956018Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c238db22-d9aa-4f5b-9c05-33606fb4b094 · outbound

This paper cites an unresolved cited work.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-05T13:05:09.027906Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7046a37c-f43e-45eb-a581-acc26ed27ebb · outbound

This paper cites A Natural Primal-Dual Hybrid Gradient Method for Adversarial Neural Network Training on Solving Partial Differential Equations.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES A Natural Primal-Dual Hybrid Gradient Method for Adversarial Neural Network Training on Solving Partial Differential Equations

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-05T13:05:09.061753Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 76879354-7ac9-43c0-9113-7799f8195b96 · outbound

This paper cites an unresolved cited work.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-05T13:05:09.136413Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce736168-c6d8-4086-87fc-14bde0fcca22 · outbound

This paper cites Otto, The Geometry of Dissipative Evolution Equations: The Porous Medium Equation , Communications in Partial Differential Equations, 26 (2001), pp.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Otto, The Geometry of Dissipative Evolution Equations: The Porous Medium Equation , Communications in Partial Differential Equations, 26 (2001), pp

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:05:11.655208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 45ed23a0-11b8-4b44-a7ad-babe9bbe4668 · outbound

This paper cites Raissi, P.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Raissi, P

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:05:11.569769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 65564517-6bde-4c85-9be3-f6d9298facd0 · outbound

This paper cites Ruthotto, S.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Ruthotto, S

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:05:11.497350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 333da8f0-5724-4ca0-8346-3faea9325c31 · outbound

This paper cites an unresolved cited work.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Unresolved cited work

Reference 21

Resolution: verified exact; doi, observed 2026-08-05T13:05:10.013265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation b6798d65-900c-4dba-a440-c7a0394f197f · outbound

This paper cites Yu et al., The deep ritz method: a deep learning-based numerical algorithm for solving variational problems , Commu- nications in Mathematics and Statistics, 6 (2018), pp.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Yu et al., The deep ritz method: a deep learning-based numerical algorithm for solving variational problems , Commu- nications in Mathematics and Statistics, 6 (2018), pp

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:05:11.398317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 0befb4e8-278a-4d61-83fe-26ce3e8bd507 · outbound

This paper cites an unresolved cited work.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:05:11.319739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 6e599aa2-6742-4030-9d19-e556782ca118 · outbound

This paper cites Structured and Balanced Multi-Component and Multi-Layer Neural Networks.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES Structured and Balanced Multi-Component and Multi-Layer Neural Networks

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-05T13:05:10.291362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 5c08eaaf-109d-405b-863b-3f3db4deff7e · outbound

This paper cites TransNet: Transferable Neural Networks for Partial Differential Equations.

Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES TransNet: Transferable Neural Networks for Partial Differential Equations

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-05T13:05:09.813319Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.