Paper Citation Record · LEDGER

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces

As of 18 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:2506.18869.

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

pith.paper-citation-record.v1
2506.18869 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:49:12.991397Z

measured 34 of 34 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:02:46.851082Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-10T23:02:47.365800Z

Reference resolution

33 of 33 outbound references displayed

verified exact2
verified fuzzy30
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e5492438-a811-4be9-b7c8-6486757cc1cb · outbound

This paper cites Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:49:13.064190Z

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.

Observation 5937b129-3712-45e7-9141-d468388b535d · outbound

This paper cites Acceleration by stepsize hedging: Silver stepsize schedule for smooth convex optimization.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Acceleration by stepsize hedging: Silver stepsize schedule for smooth convex optimization

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.561854Z

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.

Observation 892c8f23-6d59-450a-82e9-387dba227c56 · outbound

This paper cites Acceleration by stepsize hedging: Multi-step descent and the silver stepsize schedule.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Acceleration by stepsize hedging: Multi-step descent and the silver stepsize schedule

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.545634Z

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.

Observation 700aa59b-1952-4c94-8626-fe81c5e96396 · outbound

This paper cites Numerical methods for nonlinear partial differential equations , volume 47.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Numerical methods for nonlinear partial differential equations , volume 47

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.530841Z

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.

Observation 9c732987-fc3d-4b12-bf05-2c0db247ef69 · outbound

This paper cites Motion by mean curvature as the singular limit of ginzburg-landau dynamics.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Motion by mean curvature as the singular limit of ginzburg-landau dynamics

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.515661Z

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.

Observation d5a22fb6-aeb1-4f76-8e0d-5dc45fd8e96f · outbound

This paper cites Generalizing diffuse interface methods on graphs: nonsmooth potentials and hypergraphs.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Generalizing diffuse interface methods on graphs: nonsmooth potentials and hypergraphs

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.500580Z

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.

Observation 02603c8e-5cd0-4d59-99db-169354b646e9 · outbound

This paper cites Approssimazione variazionale di funzionali con curvatura.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Approssimazione variazionale di funzionali con curvatura

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.484869Z

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.

Observation 93e51062-7e36-465a-8ebe-ffadde4a67ea · outbound

This paper cites On the slowness of phase boundary motion in one space dimension.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces On the slowness of phase boundary motion in one space dimension

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.468428Z

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.

Observation 8d9be491-1bc8-4c8b-aaa6-6f92d1c0655a · outbound

This paper cites Graph MBO as a semi-discrete implicit Euler scheme for graph Allen-Cahn flow.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Graph MBO as a semi-discrete implicit Euler scheme for graph Allen-Cahn flow

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:49:13.040797Z

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.

Observation 329d6a36-e299-4f56-b186-8d4f2ab5d31b · outbound

This paper cites Classification and image processing with a semi-discrete scheme for fidelity forced allen--cahn on graphs.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Classification and image processing with a semi-discrete scheme for fidelity forced allen--cahn on graphs

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.451732Z

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.

Observation 32599b29-9c80-459c-acbb-7fe3069fec7b · outbound

This paper cites Metastable patterns in solutions of u_t= ^2u_ xx - f (u).

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Metastable patterns in solutions of u_t= ^2u_ xx - f (u)

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.436563Z

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.

Observation 1854d4ca-fd26-46b8-a8a4-424766c7f95f · outbound

This paper cites Phase field models for thin elastic structures with topological constraint.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Phase field models for thin elastic structures with topological constraint

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.419901Z

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.

Observation 944d1496-e04c-411e-9f93-b224cc17476d · outbound

This paper cites Angewandte Funktionalanalysis: Funktionalanalysis, Sobolev-R \"a ume und elliptische Differentialgleichungen.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Angewandte Funktionalanalysis: Funktionalanalysis, Sobolev-R \"a ume und elliptische Differentialgleichungen

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.404846Z

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.

Observation eeea8e60-0b70-489c-a6a6-9f98fbf9f5aa · outbound

This paper cites Uniform regularity and convergence of phase-fields for willmore’s energy.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Uniform regularity and convergence of phase-fields for willmore’s energy

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.388897Z

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.

Observation bcaa0bed-0842-4a52-a085-363221489ebb · outbound

This paper cites Threshold dynamics for networks with arbitrary surface tensions.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Threshold dynamics for networks with arbitrary surface tensions

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.372748Z

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.

Observation e3d1799e-3b14-4f7e-982b-5f59b59fc38d · outbound

This paper cites Slow-motion manifolds, dormant instability, and singular perturbations.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Slow-motion manifolds, dormant instability, and singular perturbations

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.357356Z

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.

Observation b41685de-66a4-4363-b5ef-2d73dbd63fa7 · outbound

This paper cites Traveling waves as limits of solutions on bounded domains.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Traveling waves as limits of solutions on bounded domains

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.342311Z

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.

Observation 329049d3-28c0-43a8-b25b-cf374ab10aba · outbound

This paper cites Convergence rates of the A llen-- C ahn equation to mean curvature flow: A short proof based on relative entropies.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Convergence rates of the A llen-- C ahn equation to mean curvature flow: A short proof based on relative entropies

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.325666Z

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.

Observation f40e89ef-8ddb-4981-9559-2051834416ca · outbound

This paper cites Global c^ 1, 1 -regularity for solutions of quasilinear variational inequalities.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Global c^ 1, 1 -regularity for solutions of quasilinear variational inequalities

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.308393Z

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.

Observation 1f457d1c-97ce-41e0-91f2-e97f959de562 · outbound

This paper cites Accelerated objective gap and gradient norm convergence for gradient descent via long steps.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Accelerated objective gap and gradient norm convergence for gradient descent via long steps

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.292089Z

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.

Observation 6158e2bf-97a6-44d3-b297-0f221ff46c4e · outbound

This paper cites Convergence of the A llen- C ahn equation to B rakke's motion by mean curvature.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Convergence of the A llen- C ahn equation to B rakke's motion by mean curvature

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.276113Z

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.

Observation 76af69eb-a90c-4c88-8620-fd0838c30746 · outbound

This paper cites Threshold dynamics type approximation schemes for propagating fronts.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Threshold dynamics type approximation schemes for propagating fronts

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.260369Z

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.

Observation 92328f36-4ddf-4f9a-98f1-bcbbb559b818 · outbound

This paper cites A generalization of the bence, merriman and osher algorithm for motion by mean curvature.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces A generalization of the bence, merriman and osher algorithm for motion by mean curvature

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.244416Z

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.

Observation 28055f8d-3466-4a13-b0d8-c2fe1da0eba5 · outbound

This paper cites An introduction to variational inequalities and their applications.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces An introduction to variational inequalities and their applications

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T18:49:12.945885Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7e985bf7-b953-4abd-a72a-4a622bfbc592 · outbound

This paper cites Convergence of the thresholding scheme for multi-phase mean-curvature flow.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Convergence of the thresholding scheme for multi-phase mean-curvature flow

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.216136Z

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.

Observation 053525f6-02eb-41e7-8a93-a96b12d2c426 · outbound

This paper cites The thresholding scheme for mean curvature flow and de G iorgi's ideas for minimizing movements.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces The thresholding scheme for mean curvature flow and de G iorgi's ideas for minimizing movements

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.199194Z

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.

Observation c4c1065c-d8f9-4c17-adc4-94d53e274a9b · outbound

This paper cites The regularity theory for the double obstacle problem.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces The regularity theory for the double obstacle problem

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.179804Z

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.

Observation 0c087ee0-4383-4312-b940-a32db54445e2 · outbound

This paper cites Convergence of the A llen- C ahn equation to multiphase mean curvature flow.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Convergence of the A llen- C ahn equation to multiphase mean curvature flow

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.163469Z

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.

Observation a7435a90-6f31-4830-ae07-14f40923d96c · outbound

This paper cites Un esempio di -convergenza.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Un esempio di -convergenza

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.148512Z

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.

Observation dab8e9d4-1ad6-4201-bde8-c1f402dc89aa · outbound

This paper cites The gradient theory of phase transitions and the minimal interface criterion.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces The gradient theory of phase transitions and the minimal interface criterion

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.132089Z

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.

Observation 0f2bb95d-0e48-4b7c-be59-7bb1354cb5cf · outbound

This paper cites o ger and Reiner Sch \.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces o ger and Reiner Sch \

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.114804Z

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.

Observation 2173559a-7dde-443c-b921-cd327befe6cb · outbound

This paper cites Osqp: an operator splitting solver for quadratic programs.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Osqp: an operator splitting solver for quadratic programs

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.097543Z

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.

Observation 04df6b6a-fe66-47b9-aa25-ea9c8802890b · outbound

This paper cites Stochastic gradient descent with noise of machine learning type part i: Discrete time analysis.

Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces Stochastic gradient descent with noise of machine learning type part i: Discrete time analysis

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:49:13.080822Z

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.

Pith citing papers

Observation 3145c192-76cd-4e52-a31e-7a680080a900 · inbound

Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs cites this paper.

Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs Convex-concave splitting for the Allen-Cahn equation leads to $\varepsilon^2$-slow movement of interfaces

Reference 2010

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:02:47.372080Z

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.