Paper Citation Record · LEDGER

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density

As of 8 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2507.16087.

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

pith.paper-citation-record.v1
2507.16087 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:25:38.186502Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

28 of 28 outbound references displayed

verified exact2
verified fuzzy20
unresolved6
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 38cce24c-c4c8-4090-995a-1874ec1f85c8 · outbound

This paper cites A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.546727Z

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 b9d22dd7-ed75-43c2-bfdb-a7ad380dfa61 · outbound

This paper cites A universal matrix-free split preconditioner for the fixed-point iterative solution of non-symmetric linear systems.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density A universal matrix-free split preconditioner for the fixed-point iterative solution of non-symmetric linear systems

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-06T15:25:38.865760Z

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 cbb5586d-fff9-4d60-8edf-c79189ae65ee · outbound

This paper cites Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.538405Z

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 8b0074e0-3714-4a8c-9e3b-4530be6f71c5 · outbound

This paper cites Waveholtz: Iterative solution of the helmholtz equation via the wave equation.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Waveholtz: Iterative solution of the helmholtz equation via the wave equation

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.529742Z

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 cdeec256-023c-44b0-9d63-709582c1f400 · outbound

This paper cites Advances in iterative methods and preconditioners for the Helmholtz equation.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Advances in iterative methods and preconditioners for the Helmholtz equation

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.521225Z

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 af704507-94c7-4be3-bcac-6e37c112069a · outbound

This paper cites An improved two-grid preconditioner for the solution of three-dimensional Helmholtz problems in heterogeneous media.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density An improved two-grid preconditioner for the solution of three-dimensional Helmholtz problems in heterogeneous media

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.511574Z

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 9064a8d4-f536-4909-a6d4-2699087658ca · outbound

This paper cites an unresolved cited work.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:25:39.502182Z

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 716b0eb0-260f-473f-b88b-cadec5e6ca9e · outbound

This paper cites A helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density A helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.490874Z

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 950c1445-16ab-4bbc-abfd-98c5ab2b6b55 · outbound

This paper cites A learned born series for highly-scattering media.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density A learned born series for highly-scattering media

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.481054Z

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 c1eef45f-73bd-4553-85e0-58a3682d6f1e · outbound

This paper cites A Neural Multigrid Solver for Helmholtz Equations with High Wavenumber and Heterogeneous Media.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density A Neural Multigrid Solver for Helmholtz Equations with High Wavenumber and Heterogeneous Media

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T15:25:36.085708Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f60512c6-6719-480c-8def-29350f038740 · outbound

This paper cites Solving 2-d helmholtz equation in the rectangular, circular, and elliptical domains using neural networks.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Solving 2-d helmholtz equation in the rectangular, circular, and elliptical domains using neural networks

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.471178Z

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 8dc006d8-2622-4944-87e3-7141ea149b1c · outbound

This paper cites Non-invasive transcranial ultrasound therapy based on a 3d ct scan: protocol validation and in vitro results.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Non-invasive transcranial ultrasound therapy based on a 3d ct scan: protocol validation and in vitro results

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.460394Z

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 298bee8d-48ab-4a41-a800-d3ad91e36fb4 · outbound

This paper cites Homotopy scattering series for seismic forward modelling with variable density and velocity.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Homotopy scattering series for seismic forward modelling with variable density and velocity

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.448374Z

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 01b0edd0-4b22-431b-ae28-52068e26b9ef · outbound

This paper cites Efficient Helmholtz equation solver for frequency domain waveform inversion based on the decomposition into one-way wave equations.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Efficient Helmholtz equation solver for frequency domain waveform inversion based on the decomposition into one-way wave equations

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.438676Z

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 852b2ef9-e339-4db9-bd63-6fc3bee89a4b · outbound

This paper cites Iterative solution of the Lippmann–Schwinger equation in strongly scattering acoustic media by randomized construction of preconditioners.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Iterative solution of the Lippmann–Schwinger equation in strongly scattering acoustic media by randomized construction of preconditioners

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.428690Z

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 b633ae46-fe50-453c-b283-a42d8018a3dc · outbound

This paper cites A k-space method for coupled first-order acoustic propagation equations.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density A k-space method for coupled first-order acoustic propagation equations

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.419108Z

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 04f324a7-d441-4ba9-b080-b52047067cc5 · outbound

This paper cites An overview of full-waveform inversion in exploration geophysics.Geophysics, 74(6):WCC1–WCC26, 2009.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density An overview of full-waveform inversion in exploration geophysics.Geophysics, 74(6):WCC1–WCC26, 2009

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T15:25:36.950914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0eeb960f-3922-4e34-a9ba-8d7233218573 · outbound

This paper cites Physics- informed machine learning.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Physics- informed machine learning

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T15:25:37.022739Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c357f4ba-4a19-4104-b46e-5ac9938f8c04 · outbound

This paper cites Sound scattering from a fluid sphere.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Sound scattering from a fluid sphere

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.397118Z

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 2de702eb-3a68-4f71-b29c-61cc0c9351d5 · outbound

This paper cites Sound scattering from two concentric fluid spheres.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Sound scattering from two concentric fluid spheres

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.388165Z

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 9cacb4a1-6687-4dc6-b028-5a0033919f38 · outbound

This paper cites Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.379102Z

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 37545f3e-010d-421e-a8d8-ca04ee3fe4b5 · outbound

This paper cites Computational frameworks for the fast Fourier transform.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Computational frameworks for the fast Fourier transform

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.369438Z

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 ff4adcf8-bd3f-49b3-ba52-0424f7e87ceb · outbound

This paper cites Vellekoop.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Vellekoop

Reference 23

Resolution: verified exact; raw_fallback, observed 2026-08-06T15:25:38.586666Z

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 dcfa6244-b56f-42ee-8023-ae23df6392a6 · outbound

This paper cites Ultrasonic neuromodulation by brain stimulation with transcranial ultrasound.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Ultrasonic neuromodulation by brain stimulation with transcranial ultrasound

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.359171Z

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 c818582e-1000-4101-b6e7-cdaa84ab2a4f · outbound

This paper cites Trans-spinal focused ultrasound stimulation selectively modulates descending motor pathway.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Trans-spinal focused ultrasound stimulation selectively modulates descending motor pathway

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.278014Z

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 6e755fab-8a27-453d-b970-eba677eb3e3d · outbound

This paper cites Three-dimensional frequency-domain full-waveform inversion with an iterative solver.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Three-dimensional frequency-domain full-waveform inversion with an iterative solver

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:25:39.120683Z

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 39c58068-25ed-4dbc-b1dd-8c899a8dba25 · outbound

This paper cites Neural Operator: Graph Kernel Network for Partial Differential Equations.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T15:25:38.032844Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9cc93f9b-65d5-4813-829e-fb988140ad1c · outbound

This paper cites Beyond regular grids: Fourier-based neural operators on arbitrary domains.

Iterative Born Solver for the Acoustic Helmholtz Equation with Heterogeneous Sound Speed and Density Beyond regular grids: Fourier-based neural operators on arbitrary domains

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T15:25:38.186502Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

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