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Paper Citation Record · LEDGER

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves

As of 17 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 0 inbound Pith citation observations for arXiv:2501.13477.

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

pith.paper-citation-record.v1
2501.13477 v1

Coverage vector

measured 48 of 48 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T16:17:10.269464Z

measured 48 of 48 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

48 of 48 outbound references displayed

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External citation measurements

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Outbound references

Observation 86f69463-8cb4-4db9-b979-cd311a258d1b · outbound

This paper cites Constant mean curvature tori in terms of elliptic functions.Journal für die reine und angewandte Mathematik, 374:169–192, 1987.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Constant mean curvature tori in terms of elliptic functions.Journal für die reine und angewandte Mathematik, 374:169–192, 1987

Reference 1

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Observation 9cd6545e-7b1d-4e20-a89e-e9a12dc31437 · outbound

This paper cites Integrable dynamics in projective geometry via dimers and triple crossing diagram maps on the cylinder.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Integrable dynamics in projective geometry via dimers and triple crossing diagram maps on the cylinder

Reference 2

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Observation 39c9ffa1-125c-4a9f-91ce-6e78d4a91ff1 · outbound

This paper cites Cross-ratio dynamics on ideal polygons.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Cross-ratio dynamics on ideal polygons

Reference 3

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Observation 8c830f2e-d492-42cb-a103-16372b5ef9b9 · outbound

This paper cites Area-constrained planar elastica.Phys.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Area-constrained planar elastica.Phys

Reference 4

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Observation 2c89c87c-8b76-4818-a21f-372390fcfa59 · outbound

This paper cites Discrete elastic rods.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Discrete elastic rods

Reference 5

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Observation 7227adaf-26a6-4ef8-bfb4-a5596f0a5986 · outbound

This paper cites Vorlesungen über Differentialgeometrie III.Springer Grundlehren XXIX, 1929.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Vorlesungen über Differentialgeometrie III.Springer Grundlehren XXIX, 1929

Reference 6

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Observation 00a4e8ba-7761-494c-b126-a43ab3d3516d · outbound

This paper cites Isothermic tori with one family of planar curvature lines and area constrained hyperbolic elastica.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Isothermic tori with one family of planar curvature lines and area constrained hyperbolic elastica

Reference 7

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Observation 0dfff5c3-cde4-471f-bbed-9ac533fe81bf · outbound

This paper cites Bobenko and Ulrich Pinkall.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Bobenko and Ulrich Pinkall

Reference 8

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Observation f1c8ed29-963e-4bd0-9230-c1e172544e36 · outbound

This paper cites Bobenko and Ulrich Pinkall.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Bobenko and Ulrich Pinkall

Reference 9

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Observation a710cc7f-3a37-479f-b0a2-79e3d581e834 · outbound

This paper cites Bobenko and Yuri B.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Bobenko and Yuri B

Reference 10

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Source-reported events for the cited work

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Observation 2d41f531-6645-4f25-81d1-536631e63e09 · outbound

This paper cites Bobenko and Yuri B.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Bobenko and Yuri B

Reference 11

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Observation 2afe6fbe-1b83-4e1c-adee-fe197e08b611 · outbound

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Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Unresolved cited work

Reference 12

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Observation 2708258b-ada1-4ba9-8713-e5b7293d8205 · outbound

This paper cites Lund, Toke B.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Lund, Toke B

Reference 13

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Observation d0445cdf-1917-4287-8ce5-63b8ebbf166f · outbound

This paper cites Nørbjerg.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Nørbjerg

Reference 14

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Observation 2dfc39ce-c233-4237-bc47-5b50bc4d8fcf · outbound

This paper cites Burstall and Susana D.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Burstall and Susana D

Reference 15

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Observation af692949-2953-4de0-b632-c9735152238c · outbound

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Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Unresolved cited work

Reference 16

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Observation e264479e-cf08-474e-9331-4bfc89a6bac8 · outbound

This paper cites LMS Lecture Note Series.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves LMS Lecture Note Series

Reference 17

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Observation e17c5b7e-2873-4f9d-93ed-e12ba215039c · outbound

This paper cites Periodic discrete Darboux transforms.Differential Geometry and its Applications, 91:102065, 2023.doi:10.1016/j.difgeo.2023.102065.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Periodic discrete Darboux transforms.Differential Geometry and its Applications, 91:102065, 2023.doi:10.1016/j.difgeo.2023.102065

Reference 18

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Observation ca03a707-ebbf-4c17-a262-c656ca240897 · outbound

This paper cites Constrained elastic curves and surfaces with spherical curvature lines.Indiana University Mathematics Journal, (72(5):2059–2099), 2023.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Constrained elastic curves and surfaces with spherical curvature lines.Indiana University Mathematics Journal, (72(5):2059–2099), 2023

Reference 19

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Observation f70e3db6-a56f-4313-93d0-a906a9a5cd4b · outbound

This paper cites Discrete mKdV equation via Darboux transformation.Math- ematical Physics, Analysis and Geometry, 24, 09 2021.doi:10.1007/s11040-021-09398-y.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Discrete mKdV equation via Darboux transformation.Math- ematical Physics, Analysis and Geometry, 24, 09 2021.doi:10.1007/s11040-021-09398-y

Reference 20

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Observation 42dfd543-a6d6-45c9-97b2-71c9e2dbbc1d · outbound

This paper cites Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio prob- lematis isoperimetrici lattissimo sensu accepti.Marcum-Michaelem Bousquet, 1744.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio prob- lematis isoperimetrici lattissimo sensu accepti.Marcum-Michaelem Bousquet, 1744

Reference 21

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Observation 7962e4ef-ebbe-46d9-a5da-774bd3046b61 · outbound

This paper cites Goldstein and Dean M.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Goldstein and Dean M

Reference 22

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Observation c4f8677a-15c9-40cd-9cba-d5cbe1784b71 · outbound

This paper cites On the zeros of polynomials over division rings.Transactions of the American Mathematical Society, 116:218–226, 1965.doi:10.1090/S0002-9947-1965-0195853-2.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves On the zeros of polynomials over division rings.Transactions of the American Mathematical Society, 116:218–226, 1965.doi:10.1090/S0002-9947-1965-0195853-2

Reference 23

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Observation 0f736515-27c6-45eb-8ff5-337fb8f25f9b · outbound

This paper cites The design space of plane elastic curves.ACM Transactions on Graphics, 40(4), 2021.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves The design space of plane elastic curves.ACM Transactions on Graphics, 40(4), 2021

Reference 24

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Observation d5516ddc-6fff-400f-807d-921e02caf08f · outbound

This paper cites Constrained Willmore tori and elastic curves in 2-dimensional space forms.Comm.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Constrained Willmore tori and elastic curves in 2-dimensional space forms.Comm

Reference 25

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Observation 049aa13b-440c-4aca-add6-4936ce62e729 · outbound

This paper cites Periodic discrete conformal maps.J.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Periodic discrete conformal maps.J

Reference 26

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Observation 652d8ca9-9291-4009-9f31-d2e9c33e6b84 · outbound

This paper cites Discrete Hashimoto surfaces and a doubly discrete smoke-ring flow.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Discrete Hashimoto surfaces and a doubly discrete smoke-ring flow

Reference 27

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 689f49e8-3cdb-46b3-b1b2-aaa9fdeaf26c · outbound

This paper cites Discrete differential geometry of curves and surfaces.Kyushu University Lecture Note Series Vol.18, 2009.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Discrete differential geometry of curves and surfaces.Kyushu University Lecture Note Series Vol.18, 2009

Reference 28

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation a67713fd-825f-4f10-b221-32b7ed2b509c · outbound

This paper cites Discrete curves inCP1 and the Toda lattice.Studies in Applied Mathematics, 113(1):31–55, 2004.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Discrete curves inCP1 and the Toda lattice.Studies in Applied Mathematics, 113(1):31–55, 2004

Reference 29

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Observation 2e942f70-60a8-4a17-a600-a3822e7d358b · outbound

This paper cites Skew parallelogram nets and universal factorization.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Skew parallelogram nets and universal factorization

Reference 30

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local_arxiv, observed 2026-08-10T16:17:10.457083Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 94b637d7-0242-41c0-89b1-38ce03b86f54 · outbound

This paper cites Isothermic nets with spherical parameter lines from discrete holomorphic maps.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Isothermic nets with spherical parameter lines from discrete holomorphic maps

Reference 31

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 6c1f627f-2b40-439b-a5e6-64c0b431e815 · outbound

This paper cites Discrete mKdV and discrete sine- Gordon flows on discrete space curves.Journal of Physics A: Mathematical and Theoretical, 47(23):235202, may 2014.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Discrete mKdV and discrete sine- Gordon flows on discrete space curves.Journal of Physics A: Mathematical and Theoretical, 47(23):235202, may 2014

Reference 32

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 5bf5e375-a8cb-4036-9d44-11233dfe4f3e · outbound

This paper cites Polygon recutting as a cluster integrable system.Selecta Mathematica, 29(2):21, 2023.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Polygon recutting as a cluster integrable system.Selecta Mathematica, 29(2):21, 2023

Reference 33

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Observation 266b0f9e-7e75-4fdc-bb15-1558393460c1 · outbound

This paper cites Poisson geometry of the filament equation.Journal of Nonlinear Science, 1:71–93,.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Poisson geometry of the filament equation.Journal of Nonlinear Science, 1:71–93,

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:17:11.204504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T16:17:10.219214Z digest=sha256:91bf78d6b2f5474fb823a4cf797165b92cbc8ac669537a565b850e8da82ab092

Observation 0f7e28e5-53ba-40d3-ba46-63fd583be40c · outbound

This paper cites an unresolved cited work.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Unresolved cited work

Reference 35

Resolution
unresolved
no resolver link, observed 2026-08-10T16:17:10.226189Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T16:17:10.226189Z digest=sha256:ec356c6608147f1d906f4cebe11df051c482735cfebbde6ff6ca7d590a59f185

Observation 0449a1c8-0a04-46d1-adff-59d700317fbb · outbound

This paper cites Scharler, and Hans-Peter Schröcker.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Scharler, and Hans-Peter Schröcker

Reference 36

Resolution
unresolved
no resolver link, observed 2026-08-10T16:17:10.229695Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T16:17:10.229695Z digest=sha256:21a69d12df757b3f8eae6b7da662219981b106a645734d9297340b67dfe93b60

Observation e59c8d05-1ba0-4f3f-8c5c-a81151080e3b · outbound

This paper cites From Euler’s elastica to the mKdV hierarchy, through the Faber polynomials.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves From Euler’s elastica to the mKdV hierarchy, through the Faber polynomials

Reference 37

Resolution
verified exact
doi, observed 2026-08-10T16:17:10.382555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T16:17:10.233054Z digest=sha256:08c83663904fa59ec295a3bb4e3ff2cc796e08cb74603fed3fed00b4238cd554

Observation 97763187-54c4-4ee2-99cf-d88484a62a13 · outbound

This paper cites Equations in quaternions.The American Mathematical Monthly, 48(10):654–661, 1941.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Equations in quaternions.The American Mathematical Monthly, 48(10):654–661, 1941

Reference 38

Resolution
verified exact
raw_fallback, observed 2026-08-10T16:17:10.766187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T16:17:10.236439Z digest=sha256:bcd171566786623433a7ef4e47875b2c626e3badeead7aea88a43e6598e45e34

Observation 73e2d09b-d001-4cb6-aa2a-b7868458ce2d · outbound

This paper cites Compact Textbooks in Mathematics.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Compact Textbooks in Mathematics

Reference 39

Resolution
verified exact
doi, observed 2026-08-10T16:17:10.370696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T16:17:10.239688Z digest=sha256:ec3c745a66808591304ccf867e4318afc98e616311cf74dd74bf4a748363ea59

Observation 3bfeba17-5126-4fea-b4a9-8cebb7f52a57 · outbound

This paper cites A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow.Journal of Physics A: Mathematical and Theoretical, 40(42):12563,.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow.Journal of Physics A: Mathematical and Theoretical, 40(42):12563,

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:17:11.193733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T16:17:10.243255Z digest=sha256:7c5ec429836d95172eb72bb9e3bb6e602ab56cbbcb85945ecbf5e0e17efc8914

Observation 1d5c972c-0a36-478b-abda-2d2045f3eb8d · outbound

This paper cites Springer-Verlag, 1970.doi:10.1007/978-3-642-86411-7.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Springer-Verlag, 1970.doi:10.1007/978-3-642-86411-7

Reference 41

Resolution
verified exact
doi, observed 2026-08-10T16:17:10.346377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T16:17:10.250602Z digest=sha256:7281a6feb063cf637dd0b6c49fe247b1a73196a0853707e53377a0a0a1b74ba6

Observation 0e09e1d9-deeb-49a2-b7d4-48361f811b3e · outbound

This paper cites an unresolved cited work.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Unresolved cited work

Reference 42

Resolution
verified exact
doi, observed 2026-08-10T16:17:10.333046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T16:17:10.254188Z digest=sha256:0aaa3e6a370c5e095839c5c85fa5dc64946dd9a8cbc7095afd395168f89f09e5

Observation 2e8fbc39-291c-4be3-a7e0-ad77ae20a456 · outbound

This paper cites On skew parallelogram nets, PhD thesis in preparation.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves On skew parallelogram nets, PhD thesis in preparation

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:17:11.182481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T16:17:10.258196Z digest=sha256:2c0b9706699fc6a22ef20c08e8a9a23629d8a554c17f8b3676d76de8476538c5

Observation 746ed4ce-dca0-4de2-b4bc-46d1e6d052ea · outbound

This paper cites On the discrete bicycle transformation.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves On the discrete bicycle transformation

Reference 44

Resolution
verified exact
local_arxiv, observed 2026-08-10T16:17:10.320664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T16:17:10.261776Z digest=sha256:895e292cfad992aa166a59ee91993353c6fac3837447ac485d4d29881f06bc6e

Observation e890b598-253f-49e8-b472-eb53111e0223 · outbound

This paper cites Einfache elastische Kurven.Dissertation, TU Berlin, 1991.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Einfache elastische Kurven.Dissertation, TU Berlin, 1991

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:17:11.169924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T16:17:10.265870Z digest=sha256:6463452f5fdac586e27559953d2acff3fac796a9c4365b81e229a43f2741b29e

Observation e6c09177-efe9-41bf-999f-77be5d8285f8 · outbound

This paper cites Fairing of discrete planar curves by discrete Euler’s elasticae.JSIAM Letters, 11:73–76, 2019.doi:10.14495/jsiaml.11.73.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Fairing of discrete planar curves by discrete Euler’s elasticae.JSIAM Letters, 11:73–76, 2019.doi:10.14495/jsiaml.11.73

Reference 46

Resolution
verified exact
doi, observed 2026-08-10T16:17:10.303436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T16:17:10.269464Z digest=sha256:5d536bec0feefc9e4a87d3742407bf215ec38d96fb65494ce8e14e9db2ed4488

Observation ea7bddac-35bc-4126-a3e7-6cb2c07dedce · outbound

This paper cites an unresolved cited work.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Unresolved cited work

Reference 1991

Resolution
verified exact
doi, observed 2026-08-10T16:17:10.400871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T16:17:10.222723Z digest=sha256:46ee2bcceb13a925982578bd994c9636043729ffafa75e29888dd290bd89d767

Observation 35c8fdc7-1e0d-43fe-b647-c3db8597c83e · outbound

This paper cites an unresolved cited work.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Unresolved cited work

Reference 2007

Resolution
verified exact
doi, observed 2026-08-10T16:17:10.358959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T16:17:10.246763Z digest=sha256:86eb783a3d494e19452a97ebbf2132b22d4c2bfb9bb1cd763fff8bc8fa61b490

Pith citing papers

No inbound Pith citation observations are available.