Paper Citation Record · LEDGER

Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning

As of 8 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 0 inbound Pith citation observations for arXiv:2607.15702.

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

pith.paper-citation-record.v1
2607.15702 v2

Coverage vector

measured 11 of 11 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T22:37:46.809625Z

measured 11 of 11 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

11 of 11 outbound references displayed

verified exact2
verified fuzzy0
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c9cf0bf1-1f50-4030-91a7-dfd2b0873275 · outbound

This paper cites Estimates on the generalization error of physics-informed neural networks for approximating pdes.

Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning Estimates on the generalization error of physics-informed neural networks for approximating pdes

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T22:37:45.651422Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7334cd6c-12e1-478d-a4f0-940f05c5fd18 · outbound

This paper cites The deep ritz method: A deep learning-based numerical algorithm for solving variational problems.

Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning The deep ritz method: A deep learning-based numerical algorithm for solving variational problems

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T22:37:45.708572Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9477c7e7-4c07-422a-86c7-29aca69a9ce6 · outbound

This paper cites Variational Physics-Informed Neural Networks For Solving Partial Differential Equations.

Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T22:37:45.825741Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ff8aa929-150e-46ee-a7ab-d377325e50f8 · outbound

This paper cites Physics informed neural networks for elliptic equations with oscillatory differential operators.

Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning Physics informed neural networks for elliptic equations with oscillatory differential operators

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T22:37:45.915354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cad780d9-3e85-4d7d-9809-3f4242f047c6 · outbound

This paper cites Correctors for the homogenization of monotone operators.

Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning Correctors for the homogenization of monotone operators

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T22:37:46.001268Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0d0385a0-610d-4b51-88d3-96d4cadc4db0 · outbound

This paper cites Correctors for some nonlinear monotone operators.

Reference 6

Resolution: verified exact; doi, observed 2026-08-01T22:38:19.015436Z

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 03b4f5f4-1fda-40a5-8c70-b16721b48f57 · outbound

This paper cites Quantitative Estimates on Periodic Homogenization of Nonlinear Elliptic Operators.

Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning Quantitative Estimates on Periodic Homogenization of Nonlinear Elliptic Operators

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T22:37:46.298870Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7bd53aae-4f93-4267-a129-56b7a2e6b60f · outbound

This paper cites Primal-dual gap estimators for a posteriori error analysis of nonsmooth minimization problems.

Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning Primal-dual gap estimators for a posteriori error analysis of nonsmooth minimization problems

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T22:37:46.456439Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 208f89bb-b1b0-4da0-904e-fdc6487d1d21 · outbound

This paper cites A priori error estimate of deep mixed residual method for elliptic PDEs.

Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning A priori error estimate of deep mixed residual method for elliptic PDEs

Reference 9

Resolution: verified exact; doi, observed 2026-08-01T22:38:18.810273Z

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 2b2b50fd-26d5-4fab-9576-4cc62ea60316 · outbound

This paper cites Bersetche and Juan Pablo Borthagaray.

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T22:37:46.714369Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58cb26ba-286e-41be-bb78-468cac8ad695 · outbound

This paper cites First Order System Least Squares Neural Networks.

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T22:37:46.809625Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.