Paper Citation Record · LEDGER

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds

As of 19 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 1 inbound Pith citation observation for arXiv:2606.24043.

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

pith.paper-citation-record.v1
2606.24043 v1

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-25T23:52:01.522445Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-02T06:25:52.460966Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-02T06:26:43.614869Z

Reference resolution

22 of 22 outbound references displayed

verified exact1
verified fuzzy0
unresolved21
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External citation measurements

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Outbound references

Observation a1e917a2-b378-483e-a008-4fe058ae56e1 · outbound

This paper cites Functions of Bounded Variation and Free Discontinuity Problems.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds Functions of Bounded Variation and Free Discontinuity Problems

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation 2f9026ea-b8ea-4cb9-b650-d6f62ef4c830 · outbound

This paper cites Characterization of pointwise H \" o lder regularity.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds Characterization of pointwise H \" o lder regularity

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation 21d475a2-f566-4a53-a53a-72323e71fe52 · outbound

This paper cites A notion of nonlocal curvature.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds A notion of nonlocal curvature

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation 4fcd21fe-39a6-4d60-b2eb-8156300f15bf · outbound

This paper cites Ciraolo, A.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds Ciraolo, A

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation e85f7481-2e0a-4524-9db7-b9b04a919498 · outbound

This paper cites A nonlocal approximation of the area in codimension two.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds A nonlocal approximation of the area in codimension two

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation b635b551-b430-42b7-807e-36b127648fed · outbound

This paper cites Curves and surfaces with constant nonlocal mean curvature: Meeting alexandrov and delaunay.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds Curves and surfaces with constant nonlocal mean curvature: Meeting alexandrov and delaunay

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation 666ec47e-17a3-4da5-b739-55461622daad · outbound

This paper cites A notion of s-fractional mass for 1-currents in higher codimension.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds A notion of s-fractional mass for 1-currents in higher codimension

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation 9388b0e5-8971-4e3b-80bf-af23b0776e52 · outbound

This paper cites Nonlocal curvature flows.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds Nonlocal curvature flows

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation c2db75ad-dbec-49b8-bef4-2299a52cbf06 · outbound

This paper cites Nonlocal minimal surfaces.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds Nonlocal minimal surfaces

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation af36659b-f7f9-4cad-b055-f1268be63696 · outbound

This paper cites Uniform estimates and limiting arguments for nonlocal minimal surfaces.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds Uniform estimates and limiting arguments for nonlocal minimal surfaces

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation 76d71728-2b23-4aad-b3f9-b52e35b5b58e · outbound

This paper cites Boundary behaviour of nonlocal minimal surfaces.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds Boundary behaviour of nonlocal minimal surfaces

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation 7a605e43-673f-48f2-9b37-8801f2868230 · outbound

This paper cites Nonlocal minimal graphs in the plane are generically sticky.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds Nonlocal minimal graphs in the plane are generically sticky

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation 507a7097-baf1-42da-bf78-71a3549ce404 · outbound

This paper cites Nonlocal minimal surfaces: Interior regularity, quantitative estimates and boundary stickiness.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds Nonlocal minimal surfaces: Interior regularity, quantitative estimates and boundary stickiness

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation 29aa3436-bdbc-4886-9a56-c8b904d26d33 · outbound

This paper cites Geometric Measure Theory.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds Geometric Measure Theory

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation ffda7bee-a01d-4d01-b699-785df652b844 · outbound

This paper cites Differential Topology.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds Differential Topology

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation b1927a35-aa36-44f8-b7cd-c9f74657cc48 · outbound

This paper cites The incomplete gamma functions.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds The incomplete gamma functions

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation 2b3296ba-bc30-47b2-a958-bc99358678e8 · outbound

This paper cites Essai sur la g\'eom\'etrie \`a n dimensions.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds Essai sur la g\'eom\'etrie \`a n dimensions

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation 2abb3102-fbb0-42d5-81a4-5aa33c6929ed · outbound

This paper cites A definition of fractional k -dimensional measure: bridging the gap between fractional length and fractional area.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds A definition of fractional k -dimensional measure: bridging the gap between fractional length and fractional area

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation 4ac992e2-ec58-4b81-aba8-1368d5d80e78 · outbound

This paper cites On the nonlocal curvatures of open surfaces.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds On the nonlocal curvatures of open surfaces

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Observation 24d99633-2706-4720-b8f0-4523a642641c · outbound

This paper cites Geometric Multivector Analysis: From Grassmann to Dirac.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds Geometric Multivector Analysis: From Grassmann to Dirac

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Unavailable: canonical work link unavailable.

Observation a4b4d1f9-0073-4187-95c1-095bb639e7a2 · outbound

This paper cites A fractional notion of length and an associated nonlocal curvature.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds A fractional notion of length and an associated nonlocal curvature

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-07-04T17:09:59.530720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5c491949-467f-4cde-b851-ddbe34f26364 · outbound

This paper cites A fractional notion of length and an associated nonlocal curvature.

First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds A fractional notion of length and an associated nonlocal curvature

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-25T23:52:01.522445Z

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Pith citing papers

Observation c081ddf6-ccff-4cd8-a1d3-4ebed1a499b8 · inbound

Another look at a notion of fractional mass in codimension two cites this paper.

Another look at a notion of fractional mass in codimension two First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds

Reference 50

Resolution: verified exact; local_arxiv, observed 2026-07-02T06:26:43.616376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.