Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T15:30:34.698290Z
Paper Citation Record · LEDGER
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity
As of 18 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2507.15775.
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 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-05-10T19:41:45.775046Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-10T22:35:51.528534Z
Reference resolution
31 of 31 outbound references displayed
- verified exact1
- verified fuzzy27
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 364c8a0d-9330-4a24-84ff-f894f4733548 · outbound
This paper cites PyTorch 2: Faster Machine Learning Through Dynamic Python Bytecode Transformation and Graph Compilation.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity PyTorch 2: Faster Machine Learning Through Dynamic Python Bytecode Transformation and Graph Compilation
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:40.756809Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 037ce965-4a01-448a-b95a-c758c8ede82e · outbound
This paper cites Active training of physics-informed neural networks to aggregate and inter- polate parametric solutions to the navier-stokes equations.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Active training of physics-informed neural networks to aggregate and inter- polate parametric solutions to the navier-stokes equations
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:40.631896Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation de084418-e7f8-42f7-bb8c-4786492f3666 · outbound
This paper cites What does a binary black hole merger look like? Classical and Quantum Gravity , 32(6):065002,.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity What does a binary black hole merger look like? Classical and Quantum Gravity , 32(6):065002,
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:40.455806Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c0f2500f-dd17-44d0-af15-ecf0830dd230 · outbound
This paper cites Physics-informed neural net- works for heat transfer problems.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Physics-informed neural net- works for heat transfer problems
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:40.181119Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 4e535fd2-e024-433a-ba81-56ce785e3a63 · outbound
This paper cites Superposed metric for spinning black hole binaries approaching merger.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Superposed metric for spinning black hole binaries approaching merger
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:39.899952Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7ed38246-4202-4a52-9ac2-d99eeba8afb9 · outbound
This paper cites Using physics-informed neural networks to compute quasinormal modes.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Using physics-informed neural networks to compute quasinormal modes
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:39.658293Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation badbecaf-5257-425e-865c-1bfe858e6ecc · outbound
This paper cites Solving the Regge-Wheeler and Teukolsky equations: supervised versus unsupervised physics-informed neural networks.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Solving the Regge-Wheeler and Teukolsky equations: supervised versus unsupervised physics-informed neural networks
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T15:30:31.948943Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 40b17ca7-3a2f-41ae-acbc-18404b856b59 · outbound
This paper cites δ-pinns: Physics-informed neural networks on complex geometries.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity δ-pinns: Physics-informed neural networks on complex geometries
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:39.391843Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 59c6dbd2-23db-47f8-a0a4-fa3987e584d6 · outbound
This paper cites Electromagnetic emission from supermassive binary black holes approaching merger.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Electromagnetic emission from supermassive binary black holes approaching merger
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:39.043772Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e3cf1781-4ae3-47fc-9c52-c237339f0baf · outbound
This paper cites Die grundlage der allgemeinen rela- tivit¨atstheorie.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Die grundlage der allgemeinen rela- tivit¨atstheorie
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:38.748308Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e2170e3c-495b-44b8-b6f6-d382ad068743 · outbound
This paper cites Physics-informed neural networks for solving reynolds-averaged navier–stokes equations.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Physics-informed neural networks for solving reynolds-averaged navier–stokes equations
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:38.520239Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 40b18800-aab3-4fc5-9e41-a17bcd9a6ec5 · outbound
This paper cites Null geodesics of the kerr exterior.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Null geodesics of the kerr exterior
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:38.138766Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 4a2a6b56-6d72-4888-9404-8ed0c70c1e99 · outbound
This paper cites A physics-informed deep learn- ing framework for inversion and surrogate modeling in solid mechanics.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity A physics-informed deep learn- ing framework for inversion and surrogate modeling in solid mechanics
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:38.025423Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 930a3e15-7365-48d4-bf6e-629d92f30d3f · outbound
This paper cites Taichi: a language for high-performance computation on spatially sparse data structures.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Taichi: a language for high-performance computation on spatially sparse data structures
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:37.830462Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a4823d5b-5163-4deb-9cee-9cb935b20c8f · outbound
This paper cites Gravitational lensing by spinning black holes in astrophysics, and in the movie interstellar.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Gravitational lensing by spinning black holes in astrophysics, and in the movie interstellar
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:37.668620Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d3ff79c8-e96d-43a9-be53-4f71e81bcf68 · outbound
This paper cites Kajiya and Brian P V on Herzen.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Kajiya and Brian P V on Herzen
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:37.484851Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c0621685-51cb-417a-a55b-99c07733b664 · outbound
This paper cites an unresolved cited work.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T15:30:37.302224Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation fabd259c-e8e6-4843-9f8f-f22d02cc52a6 · outbound
This paper cites Physics informed neural networks for electromagnetic analysis.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Physics informed neural networks for electromagnetic analysis
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:37.074870Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 049a450a-5400-479c-a522-2e3bc12b4563 · outbound
This paper cites Gravitationally lensed black hole emission tomography.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Gravitationally lensed black hole emission tomography
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:36.890481Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e2b18bc5-e4d6-4cdd-8380-f2119b09a030 · outbound
This paper cites Solving the teukolsky equation with physics-informed neural networks.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Solving the teukolsky equation with physics-informed neural networks
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:36.705705Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a88a3b30-b2f2-4edc-80f3-74ca7ead6520 · outbound
This paper cites Custom vulkan engine to render black holes in real time using ray-marching.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Custom vulkan engine to render black holes in real time using ray-marching
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:36.536774Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b57f30cd-f65a-430e-b6d5-c6621f99b28e · outbound
This paper cites ipole–semi- analytic scheme for relativistic polarized radiative transport.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity ipole–semi- analytic scheme for relativistic polarized radiative transport
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:36.327860Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 82f7defb-67b5-4e4e-8224-9cff08bd8ade · outbound
This paper cites Metric of a rotating, charged mass.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Metric of a rotating, charged mass
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:36.122001Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 1f83c935-4331-4292-a8d9-22230147b3b2 · outbound
This paper cites Quasinormal modes of ds and ads black holes: Feedforward neural net- work method.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Quasinormal modes of ds and ads black holes: Feedforward neural net- work method
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:35.962406Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d945c046-967d-48bc-9adf-909db46aae9a · outbound
This paper cites A Parameter Study of the Electromagnetic Signatures of an Analytical Mini-Disk Model for Supermassive Binary Black Hole Systems.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity A Parameter Study of the Electromagnetic Signatures of an Analytical Mini-Disk Model for Supermassive Binary Black Hole Systems
Reference 25
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T15:30:34.891572Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 66eb20c2-bfa9-4749-acb0-bece21dda618 · outbound
This paper cites Physics-informed neural networks: A deep learning frame- work for solving forward and inverse problems involving nonlinear partial differential equations.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Physics-informed neural networks: A deep learning frame- work for solving forward and inverse problems involving nonlinear partial differential equations
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:35.797870Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 2a8946a4-e8fd-4950-8b0d-9fa7e5a102c5 · outbound
This paper cites Seeing relativity-i: Ray tracing in a schwarzschild metric to explore the maximal analytic ex- tension of the metric and making a proper rendering of the stars.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Seeing relativity-i: Ray tracing in a schwarzschild metric to explore the maximal analytic ex- tension of the metric and making a proper rendering of the stars
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:35.601307Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7895d032-634d-4a13-9043-5bf068e13dd0 · outbound
This paper cites ¨Uber das gravitationsfeld eines massen- punktes nach der einsteinschen theorie.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity ¨Uber das gravitationsfeld eines massen- punktes nach der einsteinschen theorie
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:35.417495Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b69d9811-8b0f-4485-b06c-49eea8b3c7ff · outbound
This paper cites Fourier features let networks learn high frequency functions in low dimen- sional domains.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Fourier features let networks learn high frequency functions in low dimen- sional domains
Reference 29
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T15:30:34.545082Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2cac0e4e-75da-4299-896a-c9f6888ec0ee · outbound
This paper cites Single view refractive index tomography with neural fields.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity Single view refractive index tomography with neural fields
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:35.230372Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 40b08d95-0487-4406-984a-8a1ae0a74262 · outbound
This paper cites For the 3-black-hole scenario, this is equivalent to rendering a 63 minutes video in 30 FPS with Euler method.
Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity For the 3-black-hole scenario, this is equivalent to rendering a 63 minutes video in 30 FPS with Euler method
Reference 3090
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:30:35.032430Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Pith citing papers
Observation f1f03236-49a8-410b-9c37-8ccaf02f555d · inbound
Revisiting The Gravitational Mirroring In Presence of Compact Objects cites this paper.
Revisiting The Gravitational Mirroring In Presence of Compact Objects Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity
Reference 48
- Resolution
- verified exact
- arxiv_id, observed 2026-05-10T22:35:51.531489Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.