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Paper Citation Record · LEDGER

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes

As of 18 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 2026-08-18T06:34:40.430872+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=sha256:8987d1ea7694f349c29879219fd08c2809563f539d4a6be4b176bb5d4a4a49c6

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=sha256:4b4c606db3eb60960655e7dc21a7e5d787de181efa4a2223278bc7fcb44f5a22

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=sha256:71a7f3790f86e1098cc8f0d07e91eb8ceca4670650574b2d516e24be1242c1da

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-06T16:40:07.725670Z digest=sha256:3f060a12f5d3ab2000168fc79cc315b4b88b6fcc9b3c7faa06121aa6f107d7ab

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:bad58a3642fca7e73f0e7695cb1acebfd5dcee6f60af3f49cc8f5fad8577066d

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=sha256:33cce5be9ad791b4609b830e98e843f72efba9a6f936a92e3a6efc3c3c390620

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=sha256:93bf5f0089ed92587b8064494ba8f07c13dd452c31d2651c9987b5b34981766e

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-06T16:40:06.815995Z digest=sha256:2b998b28eb4ad8c3fcacf8f54bd8c3e1658ebb66ba2aa939fe2d8dc829e5f245

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=sha256:289cdc7502dfe33647379111197f1925ebfea441e37d41764950183ce3b4f0c9

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=sha256:91b2222bdafedbca7963917c0f75b2824c20a61f9d5182e7041df425a599f3d8

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-06T16:40:06.695225Z digest=sha256:6684391ed95929dfa63e015094b8671cd0293e1eff272064c5d7c529d3498bcd

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-06T16:40:07.275419Z digest=sha256:000b39470255a7b96a5871d5e8e7e27de4b97c1d836794d4f123ec6a2228d1a6

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 2026-08-18T06:34:40.430872+00:00.

source=arxiv_source observed=2026-05-08T15:53:24.968784Z digest=sha256:98c376901e7d7c5eef9a372d3bd6fd168fbaf946fbb6bd91419de7ff05e9b9a2

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-06-28T13:13:24.478141Z digest=sha256:7ad813f3f2544cb5847c2f20fb36ae4017fe31bf788924a75b332b229d0ab669

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:a12f67ba1d29a7117a8882b47ac5d380a7a644ec46dde35abb656ff654945ce2