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.

pith.paper-citation-record.v1
2507.15775 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:30:34.698290Z

measured 32 of 32 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-10T19:41:45.775046Z

measured 0 of 1 external citation measurements

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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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 2026-08-17T06:30:58.91139+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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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 2026-08-17T06:30:58.91139+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 2026-08-17T06:30:58.91139+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

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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

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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 2026-08-17T06:30:58.91139+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 2026-08-17T06:30:58.91139+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 2026-08-17T06:30:58.91139+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 2026-08-17T06:30:58.91139+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 2026-08-17T06:30:58.91139+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 2026-08-17T06:30:58.91139+00:00.