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Paper Citation Record · LEDGER

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes

As of 8 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 3 inbound Pith citation observations for arXiv:2507.13148.

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

pith.paper-citation-record.v1
2507.13148 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:40:07.725670Z

measured 15 of 15 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 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T03:21:02.649418Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-02T00:56:24.328498Z

Reference resolution

12 of 12 outbound references displayed

  • verified exact3
  • verified fuzzy0
  • unresolved8
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 89968ff3-2fed-4e70-b7f0-451e73c98ebf · outbound

This paper cites Fine properties of branch point singularities: stationary two-valued graphs and stable minimal hypersurfaces near points of density $< 3$.

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes Fine properties of branch point singularities: stationary two-valued graphs and stable minimal hypersurfaces near points of density $< 3$

Reference 3

Resolution
unresolved
no resolver link, observed 2026-08-06T16:40:07.394061Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T16:40:07.394061Z digest=sha256:e519ad7a3f9fa6a269422438dfbdf6cae08b56db80c46c0be43fc5f088cb6251

Observation 3a61fc05-c3bb-40d0-b4a4-29af80173e8a · outbound

This paper cites The fine structure of the singular set of area-minimizing integral currents II: rectifiability of flat singular points with singularity degree larger than $1$.

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes The fine structure of the singular set of area-minimizing integral currents II: rectifiability of flat singular points with singularity degree larger than $1$

Reference 5

Resolution
unresolved
no resolver link, observed 2026-08-06T16:40:06.924555Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T16:40:06.924555Z digest=sha256:34596e3834b8d844dc47174d4cfccb63ef008a8374e291569fa3a1192bb3d846

Observation 05eb5089-28d1-4287-a829-3840a1e76df1 · outbound

This paper cites Analysis of singularities of area-minimizing currents, Part II: a uniform height bound, estimates away from branch points of rapid decay, and uniqueness of tangent cones.

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes Analysis of singularities of area-minimizing currents, Part II: a uniform height bound, estimates away from branch points of rapid decay, and uniqueness of tangent cones

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-06T16:40:07.616777Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T16:40:07.616777Z digest=sha256:36022ad847f61c9cfecf733f7e026499a1f40cc7e3ad46bc6c19caa18076a864

Observation a5893fae-9499-413a-a987-3186665fe7b1 · outbound

This paper cites Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents.

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents

Reference 12

Resolution
verified exact
local_arxiv, observed 2026-08-06T16:40:07.949578Z

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.

source=pdf_text observed=2026-08-06T16:40:07.725670Z digest=sha256:e1aae680e4b88a804559d11431351acd7c3961cd792c885c5ab637cf89f97c7e

Observation ae3b2b74-0da7-47c9-a640-1cb347c559b7 · outbound

This paper cites A Bernstein theorem for two-valued minimal graphs in dimension four.

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes A Bernstein theorem for two-valued minimal graphs in dimension four

Reference 1977

Resolution
unresolved
no resolver link, observed 2026-08-06T16:40:07.031354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T16:40:07.031354Z digest=sha256:f7151503c6cc17a7a352891024948023552e313a37ebb64df937416ab8fa92bc

Observation eca6b55f-d4ce-47fd-a196-742b871ce2b6 · outbound

This paper cites Stable prescribed-mean-curvature integral varifolds of codimension 1: regularity and compactness.

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes Stable prescribed-mean-curvature integral varifolds of codimension 1: regularity and compactness

Reference 1978

Resolution
unresolved
no resolver link, observed 2026-08-06T16:40:06.423347Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T16:40:06.423347Z digest=sha256:a5dd45ae7de01914b7bdb85e48764be63d3bf24fddc1b9ef8c81dc61dad26ea2

Observation 24c03f96-ac5f-4985-a989-d2df03a19c1a · outbound

This paper cites The Fine Structure of the Singular Set of Area-Minimizing Integral Currents III: Frequency 1 Flat Singular Points and $\mathcal{H}^{m-2}$-a.e. Uniqueness of Tangent Cones.

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes The Fine Structure of the Singular Set of Area-Minimizing Integral Currents III: Frequency 1 Flat Singular Points and $\mathcal{H}^{m-2}$-a.e. Uniqueness of Tangent Cones

Reference 1988

Resolution
unresolved
no resolver link, observed 2026-08-06T16:40:06.554033Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T16:40:06.554033Z digest=sha256:51a26069604776f21a7edaed45e02a0be2271dd782689f5823c505266af6ff5d

Observation 876ac9e4-08f8-4446-aece-7f15c7fdd95b · outbound

This paper cites The fine structure of the singular set of area-minimizing integral currents I: the singularity degree of flat singular points.

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes The fine structure of the singular set of area-minimizing integral currents I: the singularity degree of flat singular points

Reference 2016

Resolution
verified exact
local_arxiv, observed 2026-08-06T16:40:08.436055Z

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.

source=pdf_text observed=2026-08-06T16:40:06.815995Z digest=sha256:d7648be0fc381fdc6741fcfd00b3b67525ac209269ac894c6ed405762b7f857c

Observation adcf7fc6-ca45-4627-a0e8-7e269b80d0ea · outbound

This paper cites Dimension of the singular set for $2$-valued stationary Lipschitz graphs.

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes Dimension of the singular set for $2$-valued stationary Lipschitz graphs

Reference 2020

Resolution
unresolved
no resolver link, observed 2026-08-06T16:40:07.145155Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T16:40:07.145155Z digest=sha256:c676f457fa83caffab7bd69bc72054609629bff7dcc306d5027bb84159402452

Observation 4e146821-e631-40b4-8150-698922ca514d · outbound

This paper cites Analysis of singularities of area minimizing currents, Part I: planar frequency, branch points of rapid decay, and weak locally uniform approximation.

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes Analysis of singularities of area minimizing currents, Part I: planar frequency, branch points of rapid decay, and weak locally uniform approximation

Reference 2021

Resolution
unresolved
no resolver link, observed 2026-08-06T16:40:07.520110Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T16:40:07.520110Z digest=sha256:cb3b371c41c071b52b196c6727d1bb2f065a6477551a282606bb56e6d31fbca2

Observation 3278b659-b5d4-4791-bf62-7a0259cc42e3 · outbound

This paper cites Fine Structure of Singularities in Area-Minimizing Currents Mod$(q)$.

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes Fine Structure of Singularities in Area-Minimizing Currents Mod$(q)$

Reference 2023

Resolution
verified exact
local_arxiv, observed 2026-08-06T16:40:08.772480Z

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.

source=pdf_text observed=2026-08-06T16:40:06.695225Z digest=sha256:3efc1ea18cc00dc6bf40f0f1c9cd95bbf38df921c32d4d98835c61b161a27b40

Observation 4da36c7d-6b6b-40a0-a6b8-b49ea75ef3bf · outbound

This paper cites Constant frequency and the higher regularity of branch sets.

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes Constant frequency and the higher regularity of branch sets

Reference 2025

Resolution
metadata mismatch
local_arxiv, observed 2026-08-06T16:40:08.196107Z

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.

source=pdf_text observed=2026-08-06T16:40:07.275419Z digest=sha256:9970be623dd545ec61d69c7581d70f9ed3369a0d19672925f4ff0a209f5ba173

Pith citing papers

Observation ba125455-9c2f-446a-87f3-5d2585319009 · inbound

An Optimal Regularity Theory for Immersed Stable Minimal Hypersurfaces with Small Singular Set cites this paper.

An Optimal Regularity Theory for Immersed Stable Minimal Hypersurfaces with Small Singular Set On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes

Reference 5

Resolution
verified exact
arxiv_id, observed 2026-05-11T18:26:13.308410Z

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.

source=arxiv_source observed=2026-05-08T15:53:24.968784Z digest=sha256:05c0d18ff57f28fb9ca4c8965e381e84fe20a51586ece8546a4c346bec45ca83

Observation d3c92c83-d2b5-49f1-a6e9-c113b9481e87 · inbound

A Branch Set Stratification for Stationary Varifolds with Epsilon-Regularity cites this paper.

A Branch Set Stratification for Stationary Varifolds with Epsilon-Regularity On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes

Reference 1

Resolution
verified exact
arxiv_id, observed 2026-07-02T00:56:24.330515Z

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.

source=pdf_text observed=2026-06-28T13:13:24.478141Z digest=sha256:2c6f6a9394acb9119c01003ca299d9871de0661a39bc4c46600864c6d13f729d

Observation dd778d2e-0dcd-41e2-8349-d52c5a1173a6 · inbound

Regularity of branched stable minimal immersed hypersurfaces cites this paper.

Regularity of branched stable minimal immersed hypersurfaces On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes

Reference 3

Resolution
unresolved
no resolver link, observed 2026-08-03T03:21:02.649418Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-03T03:21:02.649418Z digest=sha256:af6b1ed541a11abfc190f1eb7d260c70152409c6dc18ca1db973492a525adb6f