Paper Citation Record · LEDGER

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions

As of 21 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 1 inbound Pith citation observation for arXiv:2506.15869.

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

pith.paper-citation-record.v1
2506.15869 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:37:08.996180Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T03:35:39.360114Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

32 of 32 outbound references displayed

verified exact0
verified fuzzy28
unresolved4
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fb830f65-2c15-4411-88b8-dcea8940f6d3 · outbound

This paper cites Andrews: Singularities in crystalline curvature flows.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Andrews: Singularities in crystalline curvature flows

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.394932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b426115e-5abe-4d01-a643-da7832d612e4 · outbound

This paper cites Bellettini: On facet breaking for crystalline mean curvature flow in 3D.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Bellettini: On facet breaking for crystalline mean curvature flow in 3D

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.381767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 951ecb47-16c4-44cc-942f-1ec13cbda409 · outbound

This paper cites Bellettini, L.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Bellettini, L

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.369512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7226382f-308c-4213-a62e-2f6cfcc42249 · outbound

This paper cites Bellettini, M.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Bellettini, M

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.358162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a212efde-a525-4673-a9f2-bc711f7c9e9d · outbound

This paper cites Bellettini, M.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Bellettini, M

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.346858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d6b518fa-2cbd-4b49-85d2-3c69d25e252b · outbound

This paper cites Benois, T.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Benois, T

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.335084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1c7333dd-95e8-461e-83ef-79dedc11503e · outbound

This paper cites Bierstone, P.D.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Bierstone, P.D

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.324607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 07efbe34-cee3-4b20-9ed7-a2b137e8fec3 · outbound

This paper cites Cahn: Stability, microstructural evolution, grain growth, and coarsening in a two-dimensional two-phase microstructure.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Cahn: Stability, microstructural evolution, grain growth, and coarsening in a two-dimensional two-phase microstructure

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.313397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 767daaa9-7730-47f3-b5b9-62ff1f748f45 · outbound

This paper cites Cahn, C.A.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Cahn, C.A

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.300855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation cf50d960-4f1c-49f8-b365-dc6a7193add7 · outbound

This paper cites Cahn, J.E.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Cahn, J.E

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.289414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1705eb78-66b5-4328-b695-79352f1d2461 · outbound

This paper cites Carter, A.R.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Carter, A.R

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.277965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4a7c7fce-043c-406b-bb04-2567c681e51d · outbound

This paper cites Dziuk, E.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Dziuk, E

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.265634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2b33bc91-ece2-472c-9181-3585d23e264a · outbound

This paper cites Epshteyn, Ch.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Epshteyn, Ch

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.254053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7b656e47-8044-4277-a8aa-7e5b2f63fe3c · outbound

This paper cites Fonseca, N.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Fonseca, N

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.242635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 104b9348-5391-46d9-9303-a75d23a0132c · outbound

This paper cites Garcke, B.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Garcke, B

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.232354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d453ecb6-7a00-4816-bc1e-9c38df4f2aed · outbound

This paper cites Falconer: The Geometry of Fractal Sets.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Falconer: The Geometry of Fractal Sets

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.220319Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 38abffd4-5189-48f8-862f-d301839afc12 · outbound

This paper cites an unresolved cited work.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:37:09.207822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a27f4ef0-26ab-4223-96e0-1ff610a3a331 · outbound

This paper cites an unresolved cited work.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:37:09.196304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6d06d715-8f72-47c6-99f1-47061c3b0174 · outbound

This paper cites an unresolved cited work.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:37:09.184093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 36be2766-4226-46ad-88f0-92a1cb326d17 · outbound

This paper cites an unresolved cited work.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:37:09.172688Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5bedfaf8-0261-4c4a-88d1-057d25038836 · outbound

This paper cites Herring: Some theorems on the free energies of crystal surfaces.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Herring: Some theorems on the free energies of crystal surfaces

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.162193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f9637907-10af-45fa-8030-b4014f5a1e91 · outbound

This paper cites Herring: Surface tension as a motivation for sintering.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Herring: Surface tension as a motivation for sintering

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.150912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 590a69ab-85d7-4a3b-b745-623ac480dfd2 · outbound

This paper cites Hironaka: Subanalytic sets.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Hironaka: Subanalytic sets

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.140192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8c3c2a2d-06e3-4ae7-94da-8b636d9357dd · outbound

This paper cites Ishii, H.M.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Ishii, H.M

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.129346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2949005f-fb00-4fa5-bfe3-b38ffebb1f3d · outbound

This paper cites Kinderlehrer, C.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Kinderlehrer, C

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.117740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ef91b3d1-7f43-4f7a-bfb5-01e7cb6b6c73 · outbound

This paper cites Lojasiewicz: On semi-analytic and subanalytic geometry.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Lojasiewicz: On semi-analytic and subanalytic geometry

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.105396Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b742d3ea-3228-480e-b834-2040a7577ab9 · outbound

This paper cites Mantegazza: Smooth geometric evolutions of hypersurfaces.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Mantegazza: Smooth geometric evolutions of hypersurfaces

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.092856Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f426a705-1593-4928-b06b-2a3a3e1e53d3 · outbound

This paper cites Mantegazza, A.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Mantegazza, A

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.080823Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 79c5283b-ec1b-4694-be78-194a5818cc93 · outbound

This paper cites Mantegazza, M.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Mantegazza, M

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.069416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a10d1581-795d-4565-9408-550b825d1335 · outbound

This paper cites Mullins: Two-dimensional motion of idealized grain boundaries.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Mullins: Two-dimensional motion of idealized grain boundaries

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.057816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 04bc2019-929d-499a-b9a8-acd25abcd99e · outbound

This paper cites Taylor: Crystalline variational problems.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Taylor: Crystalline variational problems

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.044339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation cfa29ad2-18e0-44b8-8964-f93451b4d60a · outbound

This paper cites Taylor: Overview no.

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions Taylor: Overview no

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:37:09.031444Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

Observation 6d4d592d-c02b-49a9-9db5-563b46fc7235 · inbound

One thousand and one higher-order geometric flows of networks cites this paper.

One thousand and one higher-order geometric flows of networks Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T03:35:39.360114Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.