Paper Citation Record · LEDGER

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions

As of 17 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:2607.13888.

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

pith.paper-citation-record.v1
2607.13888 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T03:33:19.940316Z

measured 14 of 14 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

14 of 14 outbound references displayed

verified exact4
verified fuzzy0
unresolved8
parse uncertain0
malformed identifier2
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fa311dff-94e1-4326-816f-df343415b1fa · outbound

This paper cites Optimal Spectral Approximation in the Overlaps for Generalized Finite Element Methods.

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions Optimal Spectral Approximation in the Overlaps for Generalized Finite Element Methods

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-02T03:33:24.609793Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 144602fe-12a7-4d29-bf7d-c175af4f4b86 · outbound

This paper cites Homogenization and two-scale convergence.

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions Homogenization and two-scale convergence

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T03:33:19.055503Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 260eb940-ed53-4b15-a7bc-fe598f2d2c8d · outbound

This paper cites Axler, P.

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions Axler, P

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T03:33:19.147914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5505041f-4869-4c59-9949-6b6bc3e5178c · outbound

This paper cites Special finite element methods for a class of second order elliptic problems with rough coefficients.

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions Special finite element methods for a class of second order elliptic problems with rough coefficients

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T03:33:19.220146Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e73e837-a9dd-4959-a87c-0112383913e9 · outbound

This paper cites Optimal local approximation spaces for generalized finite element methods with application to multiscale problems.

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions Optimal local approximation spaces for generalized finite element methods with application to multiscale problems

Reference 5

Resolution: malformed identifier; no resolver link, observed 2026-08-02T03:33:19.283921Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 053f5048-a831-4954-95fb-97b1dab73c86 · outbound

This paper cites Constraint energy minimizing generalized multiscale finite element method.

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions Constraint energy minimizing generalized multiscale finite element method

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T03:33:19.331809Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 891d534a-2504-4c65-912c-c01882adb8ca · outbound

This paper cites an unresolved cited work.

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-02T03:33:19.422231Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5c686360-30a0-4d89-a72c-1dd04943c74e · outbound

This paper cites A super-localized generalized finite element method.

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions A super-localized generalized finite element method

Reference 8

Resolution: malformed identifier; no resolver link, observed 2026-08-02T03:33:19.544556Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 63018d20-0b85-43f4-a707-2087c8815c8e · outbound

This paper cites Super-localization of elliptic multiscale problems.

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions Super-localization of elliptic multiscale problems

Reference 9

Resolution: verified exact; doi, observed 2026-08-02T03:33:25.750043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3379f246-ce19-445e-aa61-6c8e674ac5c2 · outbound

This paper cites Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients.

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients

Reference 10

Resolution: verified exact; doi, observed 2026-08-02T03:33:25.576423Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5d48f0d1-f930-42fb-bbeb-85dca15fc1d2 · outbound

This paper cites A multiscale finite element method for elliptic problems in composite materials and porous media.

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions A multiscale finite element method for elliptic problems in composite materials and porous media

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T03:33:19.736686Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation da5b8a4d-64b1-43b0-8a05-874c2c3ce8bf · outbound

This paper cites Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients.

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T03:33:19.811666Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b220cbed-77f3-46ac-a436-78beb18f3d04 · outbound

This paper cites A unified framework for multiscale spectral generalized FEMs and low-rank approximations to multiscale PDEs.

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions A unified framework for multiscale spectral generalized FEMs and low-rank approximations to multiscale PDEs

Reference 13

Resolution: verified exact; doi, observed 2026-08-02T03:33:25.358747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 68766f36-09bd-4632-9cb8-3b60eb751491 · outbound

This paper cites Localization of elliptic multiscale problems.

An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions Localization of elliptic multiscale problems

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T03:33:19.940316Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.