Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T11:58:31.986831Z
Paper Citation Record · LEDGER
Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole
As of 8 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2506.00951.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
13 of 13 outbound references displayed
- verified exact4
- verified fuzzy7
- unresolved2
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation cfffe20a-5fbd-43d4-be0b-11eaecd81a87 · outbound
This paper cites Amorim, P.
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:58:35.484465Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation cfb5067a-e5a6-410e-9f33-ebf69eb65505 · outbound
This paper cites an unresolved cited work.
Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:58:35.242660Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation cc9489b7-d7e1-4f90-811c-418069793954 · outbound
This paper cites Solutions in the large for nonlinear hyperbolic systems of equations.Communications on Pure and Applied Mathematics, 18:697–715,.
Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole Solutions in the large for nonlinear hyperbolic systems of equations.Communications on Pure and Applied Mathematics, 18:697–715,
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:58:34.976263Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation f5724a36-1bb7-4746-bcfe-419a30f03633 · outbound
This paper cites A generalized riemann problem for quasi-one-dimensional gas flows.Advances in Applied Mathe- matics, 5(1):1–30, 1984.
Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole A generalized riemann problem for quasi-one-dimensional gas flows.Advances in Applied Mathe- matics, 5(1):1–30, 1984
Reference 4
- Resolution
- verified exact
- raw_fallback, observed 2026-08-07T11:58:32.857254Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation bbd528cd-d116-4465-b4f8-cac973710693 · outbound
This paper cites Jagtap, George Em Karniadakis, and Kenji Kawaguchi.
Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole Jagtap, George Em Karniadakis, and Kenji Kawaguchi
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:58:34.701639Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 9428026b-0918-4f45-8463-5eb30549559e · outbound
This paper cites Jagtap and George Em Karniadakis.
Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole Jagtap and George Em Karniadakis
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:58:34.461319Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7fd95688-f51c-44a3-aae8-1a37e85aec17 · outbound
This paper cites Jagtap, Ehsan Kharazmi, and George Em Karniadakis.
Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole Jagtap, Ehsan Kharazmi, and George Em Karniadakis
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:58:34.187199Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 023526d9-2ef9-401e-b7d4-4f18c0b9a12a · outbound
This paper cites LeFloch and Shuyang Xiang.
Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole LeFloch and Shuyang Xiang
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:58:33.973782Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 52e52f21-47ac-44dc-b3d8-182210f4d5b1 · outbound
This paper cites LeFloch and Shuyang Xiang.
Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole LeFloch and Shuyang Xiang
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:58:33.692232Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 5830a111-05db-4581-a674-883bb68dc818 · outbound
This paper cites an unresolved cited work.
Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:58:33.456251Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation e1ca6084-080b-4139-8db9-17da8e0cd407 · outbound
This paper cites Central schemes for conservation laws with application to shallow water equations.
Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole Central schemes for conservation laws with application to shallow water equations
Reference 11
- Resolution
- verified exact
- raw_fallback, observed 2026-08-07T11:58:32.620910Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d58d81d0-4b26-42dd-9dcd-45b5dccd51f9 · outbound
This paper cites Adaptive mesh refinement for hyperbolic systems based on third-order compact weno reconstruction.Journal of Scientific Computing, 66(2):692–724, 2016.
Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole Adaptive mesh refinement for hyperbolic systems based on third-order compact weno reconstruction.Journal of Scientific Computing, 66(2):692–724, 2016
Reference 12
- Resolution
- verified exact
- raw_fallback, observed 2026-08-07T11:58:32.357354Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c8f99569-6d8a-40d6-9589-6fd0d9536d42 · outbound
This paper cites an unresolved cited work.
Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole Unresolved cited work
Reference 1965
- Resolution
- verified exact
- raw_fallback, observed 2026-08-07T11:58:33.166246Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Pith citing papers
No inbound Pith citation observations are available.