Paper Citation Record · LEDGER

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology

As of 8 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:2607.13356.

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

pith.paper-citation-record.v1
2607.13356 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T05:34:25.756623Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-31T06:43:17.016128Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

33 of 33 outbound references displayed

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unresolved33
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External citation measurements

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Outbound references

Observation a7a4b5d0-98cf-4229-84cd-2a1ea00861ed · outbound

This paper cites an unresolved cited work.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:20.683528Z

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Unavailable: canonical work link unavailable.

Observation 9517e628-4a62-4510-b7a5-5850c18a0595 · outbound

This paper cites an unresolved cited work.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:20.801343Z

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Observation 36c850aa-f576-472a-8cf9-afd41e9740e9 · outbound

This paper cites Extensions of Schoen-Simon-Yau and Schoen-Simon theorems via iteration \'a la De Giorgi.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Extensions of Schoen-Simon-Yau and Schoen-Simon theorems via iteration \'a la De Giorgi

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:20.921875Z

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Observation 2d73ef86-e643-4e81-961d-108996641e70 · outbound

This paper cites Two dimensional area minimizing integral currents are classical minimal surfaces.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Two dimensional area minimizing integral currents are classical minimal surfaces

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:21.098391Z

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Observation 124b82ba-dcb1-4ef7-9c8a-c3095f5396bc · outbound

This paper cites Frontiere orientate di misura minima Sem.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Frontiere orientate di misura minima Sem

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:21.268774Z

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Observation 13cb2841-66b4-42a2-b473-3ee61d449b59 · outbound

This paper cites Fine structure of the singular set of area minimizing hypersurfaces modulo $p$.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Fine structure of the singular set of area minimizing hypersurfaces modulo $p$

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:21.468177Z

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Observation 7704c88f-eb76-4b99-8877-2a321e0d138d · 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.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology 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 7

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:21.617696Z

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Observation 60fbc40b-d3a4-4e52-9caf-d68642d08bda · outbound

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

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology The fine structure of the singular set of area-minimizing integral currents I: the singularity degree of flat singular points

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:21.816894Z

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Observation a3690669-5042-423d-84e5-2c75663afc61 · 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 $1$.

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:22.023692Z

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Observation 18eb2965-1ccc-40e7-8c35-160a64b9bfff · outbound

This paper cites and Spadaro, E.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology and Spadaro, E

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:22.188358Z

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Observation 3b0302d7-591d-426b-9050-a01dfa625cd0 · outbound

This paper cites and Spadaro, E.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology and Spadaro, E

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:22.331119Z

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Observation 3971638b-9adb-438b-a607-fe6e8ebf0c83 · outbound

This paper cites and Spadaro, E.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology and Spadaro, E

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:22.504973Z

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Observation 432f5eca-5f9d-488f-9503-5e152775b9a0 · outbound

This paper cites and Spadaro, E.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology and Spadaro, E

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:22.649207Z

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Observation 76ccb255-ad40-4e39-8284-0f0bacc652ab · outbound

This paper cites Geometric measure theory.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Geometric measure theory

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:22.793625Z

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Observation 719e3943-25dc-4169-931c-b5eca1997b12 · outbound

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

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Constant frequency and the higher regularity of branch sets

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:22.938087Z

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Observation ca5df54e-90d5-4a0f-9b13-9be6cf1eef6c · outbound

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

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology A Branch Set Stratification for Stationary Varifolds with Epsilon-Regularity

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:23.120807Z

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Observation 34485364-3b9e-4e62-bbbd-5851d3163484 · 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.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Analysis of singularities of area minimizing currents, Part I: planar frequency, branch points of rapid decay, and weak locally uniform approximation

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:23.204306Z

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Observation a299cc4a-c488-4323-9aea-cbbb4a022351 · 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.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology 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 18

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:23.331237Z

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Observation 444d587b-74d4-4b46-b580-8df938fdb835 · outbound

This paper cites and Wickramasekera, N.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology and Wickramasekera, N

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:23.513603Z

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Observation 430b332d-f772-4a0d-874d-d3b358a2e055 · outbound

This paper cites and Wickramasekera, N.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology and Wickramasekera, N

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:23.651250Z

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Observation a3ed43dd-505a-4407-af84-c51915f9cba6 · outbound

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

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Fine properties of branch point singularities: stationary two-valued graphs and stable minimal hypersurfaces near points of density $< 3$

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:23.819908Z

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Observation cfab821f-c8e9-454e-b56f-bdf865df40cf · outbound

This paper cites Fine properties of branch point singularities: Dirichlet energy minimizing multi-valued functions.

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:23.956123Z

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Observation 74c9fe73-b4f5-4859-b1ca-3b364fc5990f · outbound

This paper cites and White, B.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology and White, B

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:24.093971Z

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Observation c3134583-c982-4a8f-a01b-520438d9a2cd · outbound

This paper cites Area minimising hypersurfaces mod $p$ do not admit immersed branch points.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Area minimising hypersurfaces mod $p$ do not admit immersed branch points

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:24.217080Z

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Observation 253402c7-b6b3-4ab4-8bdd-a6762d8e9f73 · outbound

This paper cites and Wickramasekera, N.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology and Wickramasekera, N

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:24.329442Z

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Observation 0c53a0c4-2d7e-4f80-b6a1-96b30f3080b2 · outbound

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

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology An Optimal Regularity Theory for Immersed Stable Minimal Hypersurfaces with Small Singular Set

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:24.473330Z

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Observation f1c036a9-1452-481f-b4c1-81154b377fff · outbound

This paper cites and Valtorta, D.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology and Valtorta, D

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:24.625244Z

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Observation 6c5f48d6-0869-49a9-8272-471b219840b5 · outbound

This paper cites and Simon L.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology and Simon L

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:24.776124Z

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Observation e0ec1eef-9398-4a67-ae76-e9a65cc2390d · outbound

This paper cites Lecture Notes on Geometric Measure Theory.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Lecture Notes on Geometric Measure Theory

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:24.965974Z

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Observation 6d0aae53-e422-44f3-b988-ca646dab2bd3 · outbound

This paper cites Cylindrical Tangent Cones and the singular set of minimal submanifolds.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Cylindrical Tangent Cones and the singular set of minimal submanifolds

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:25.190840Z

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Observation 00ba000c-0449-4891-af4d-18aac4e801c7 · outbound

This paper cites Rectifiability of the singular sets of multiplicity 1 minimal surfaces and energy minimizing maps.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Rectifiability of the singular sets of multiplicity 1 minimal surfaces and energy minimizing maps

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:25.370996Z

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Observation 44a9484f-6357-4340-acbe-009de0496d52 · outbound

This paper cites Tangent cones to 2-dimensional area-minimizing integral currents are unique.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology Tangent cones to 2-dimensional area-minimizing integral currents are unique

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:25.587726Z

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Observation 07dff262-2dcc-4b41-be63-4165f5d02c91 · outbound

This paper cites A general regularity theory for stable codimension 1 integral varifolds.

Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology A general regularity theory for stable codimension 1 integral varifolds

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-02T05:34:25.756623Z

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Pith citing papers

Observation df36f07e-1066-430b-a3ea-9e9f87f2025a · inbound

Area-minimizing submanifolds are not generically smooth, except for geodesics, minimal surfaces, and minimal hypersurfaces cites this paper.

Area-minimizing submanifolds are not generically smooth, except for geodesics, minimal surfaces, and minimal hypersurfaces Analysis of singularities of area-minimizing currents, Part III: branch points of planar frequency $\neq$ 2, higher order asymptotics, and the local topology

Reference 44

Resolution: unresolved; no resolver link, observed 2026-07-31T06:43:17.016128Z

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