Anisotropic isoperimetric double tilings of the plane | Paper Citation Record

Observation 46ebd59c-a7a3-4bc4-9470-5b18d4d51f04 · outbound

This paper cites The standard Lens cluster in $ R ^2$ uniquely minimizes relative perimeter.

Anisotropic isoperimetric double tilings of the plane The standard Lens cluster in $ R ^2$ uniquely minimizes relative perimeter

Reference 1

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Observation de2ae813-7463-4bdc-a7a3-b1f715e702d1 · outbound

This paper cites Connected components of sets of finite perimeter and applications to image processing.

Anisotropic isoperimetric double tilings of the plane Connected components of sets of finite perimeter and applications to image processing

Reference 2

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Observation 2de575df-46ae-4543-88dd-dac7f43141c6 · outbound

This paper cites Functions of bounded variation and free discontinuity problems.

Anisotropic isoperimetric double tilings of the plane Functions of bounded variation and free discontinuity problems

Reference 3

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Observation aec5192f-666c-4e17-919e-7c91e3b30842 · outbound

This paper cites an unresolved cited work.

Anisotropic isoperimetric double tilings of the plane Unresolved cited work

Reference 4

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Observation 3d984f68-4341-41f3-afaf-acd2b0114261 · outbound

This paper cites A stability inequality for planar lens partition.

Anisotropic isoperimetric double tilings of the plane A stability inequality for planar lens partition

Reference 5

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Observation 5f8e5ce2-4b63-481c-9f53-4105cfb4d9e8 · outbound

This paper cites The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$.

Anisotropic isoperimetric double tilings of the plane The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$

Reference 6

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Observation 964aa8c4-6707-4e3e-a122-d09cf7df3a44 · outbound

This paper cites Brothers and Frank Morgan.

Anisotropic isoperimetric double tilings of the plane Brothers and Frank Morgan

Reference 7

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Observation 7cba1a0b-4403-4c00-a114-409bb5217346 · outbound

This paper cites On the non-uniqueness of locally minimizing clusters via singular cones.

Anisotropic isoperimetric double tilings of the plane On the non-uniqueness of locally minimizing clusters via singular cones

Reference 8

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Observation 927c0094-3689-4199-9aec-b4c19969b8df · outbound

This paper cites Lattice tilings minimizing nonlocal perimeters.

Anisotropic isoperimetric double tilings of the plane Lattice tilings minimizing nonlocal perimeters

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-07-14T10:20:24.066217Z

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Observation e6148181-9770-4aba-aa59-49bbc9bf53b8 · outbound

This paper cites On the existence and regularity of fundamental domains with least boundary area.

Anisotropic isoperimetric double tilings of the plane On the existence and regularity of fundamental domains with least boundary area

Reference 10

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Observation e3dd0890-8143-4df4-96e5-dd72389c34a3 · outbound

This paper cites Sharp stability inequalities for planar double bubbles.

Anisotropic isoperimetric double tilings of the plane Sharp stability inequalities for planar double bubbles

Reference 11

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Observation 40f6d720-95dc-4088-8870-b8b57727b950 · outbound

This paper cites Minimal periodic foams with equal cells.

Anisotropic isoperimetric double tilings of the plane Minimal periodic foams with equal cells

Reference 12

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Observation 2d3bf439-5968-4209-b05e-6a3763b17b6f · outbound

This paper cites Periodic partitions with minimal perimeter.

Anisotropic isoperimetric double tilings of the plane Periodic partitions with minimal perimeter

Reference 13

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Observation ba2fa810-6051-4510-8743-926d7e6b8bb3 · outbound

This paper cites Proof of the planar double bubble conjecture using metacalibration methods.

Anisotropic isoperimetric double tilings of the plane Proof of the planar double bubble conjecture using metacalibration methods

Reference 14

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Observation f98b8b07-b058-47a8-8078-f651108dfcaf · outbound

This paper cites Connected perimeter of planar sets.

Anisotropic isoperimetric double tilings of the plane Connected perimeter of planar sets

Reference 15

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Observation 7a0459a4-3652-49e7-a866-1fdce86d3c34 · outbound

This paper cites The standard double soap bubble in R ^2 uniquely minimizes perimeter.

Anisotropic isoperimetric double tilings of the plane The standard double soap bubble in R ^2 uniquely minimizes perimeter

Reference 16

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Observation 2190ef56-a7a6-4df3-b850-75341ad8b373 · outbound

This paper cites A quantitative version of the isoperimetric inequality: the anisotropic case.

Anisotropic isoperimetric double tilings of the plane A quantitative version of the isoperimetric inequality: the anisotropic case

Reference 17

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Observation cad2d2d8-875c-44b9-bc8e-ea96bbb528ee · outbound

This paper cites The double-bubble problem on the square lattice.

Anisotropic isoperimetric double tilings of the plane The double-bubble problem on the square lattice

Reference 18

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Observation 2b2997c2-fdce-4c92-b451-49db8007b25b · outbound

This paper cites A characterization of $ _1$ double bubbles with general interface interaction.

Anisotropic isoperimetric double tilings of the plane A characterization of $ _1$ double bubbles with general interface interaction

Reference 19

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Observation 839f57ca-9070-4de0-9c7d-8c30c6c8b0ce · outbound

This paper cites The $ _1$ double-bubble problem in three dimensions.

Anisotropic isoperimetric double tilings of the plane The $ _1$ double-bubble problem in three dimensions

Reference 20

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Observation 9377d4f2-d7dd-44e1-b6db-cf20bb6bba06 · outbound

This paper cites Fortes, P.

Anisotropic isoperimetric double tilings of the plane Fortes, P

Reference 21

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Observation 15136d0b-9421-4043-95c2-a26febcd5534 · outbound

This paper cites Figalli, F.

Anisotropic isoperimetric double tilings of the plane Figalli, F

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 589a35cf-c2d4-4905-856b-680acfa1d6ef · outbound

This paper cites On the Steiner property for planar minimizing clusters.

Anisotropic isoperimetric double tilings of the plane On the Steiner property for planar minimizing clusters

Reference 23

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Observation e01c22f8-c075-4417-bf17-68d19d66be19 · outbound

This paper cites Symmetric double bubbles in the Grushin plane.

Anisotropic isoperimetric double tilings of the plane Symmetric double bubbles in the Grushin plane

Reference 24

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Observation 725baa54-782b-4469-8646-4a089e3366db · outbound

This paper cites Fortes and P.

Anisotropic isoperimetric double tilings of the plane Fortes and P

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 932c3430-9594-4ea0-95c8-5f1136b4c46a · outbound

This paper cites u cksichtigung der Anwendungsgebiete . Springer-Verlag, Berlin-G\.

Anisotropic isoperimetric double tilings of the plane u cksichtigung der Anwendungsgebiete . Springer-Verlag, Berlin-G\

Reference 26

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Observation 84276fd9-13e8-406e-a029-8866267ed26a · outbound

This paper cites Fejes T\' o th.

Anisotropic isoperimetric double tilings of the plane Fejes T\' o th

Reference 27

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 1e14e4c2-6793-4731-bced-4744ff512be1 · outbound

This paper cites Fejes T\' o th.

Anisotropic isoperimetric double tilings of the plane Fejes T\' o th

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 53ead539-3e97-495d-a5e6-81e3db9fa0ec · outbound

This paper cites Fejes T\' o th.

Anisotropic isoperimetric double tilings of the plane Fejes T\' o th

Reference 29

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 1e7d75e5-a326-4a17-8587-22f118b932a6 · outbound

This paper cites an unresolved cited work.

Anisotropic isoperimetric double tilings of the plane Unresolved cited work

Reference 30

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Observation 5f5402a0-a694-4451-9ace-3695e064cb18 · outbound

This paper cites an unresolved cited work.

Anisotropic isoperimetric double tilings of the plane Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 616d4d9f-e482-4639-8630-919b41e078f6 · outbound

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

Anisotropic isoperimetric double tilings of the plane Some theorems on the free energies of crystal surfaces

Reference 32

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 5dd3ad9f-cf66-4430-a0ff-d3765278087d · outbound

This paper cites The double bubble conjecture.

Anisotropic isoperimetric double tilings of the plane The double bubble conjecture

Reference 33

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation a44a7db7-efed-4581-bd61-f757b5616b77 · outbound

This paper cites Proof of the double bubble conjecture.

Anisotropic isoperimetric double tilings of the plane Proof of the double bubble conjecture

Reference 34

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 5f61a500-6c0f-4fe0-983b-03b4e876071f · outbound

This paper cites Double bubbles minimize.

Anisotropic isoperimetric double tilings of the plane Double bubbles minimize

Reference 35

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 9c0bcfdc-3ce8-446c-bbf1-00ee6b8fb6f8 · outbound

This paper cites Sets of finite perimeter and geometric variational problems , volume 135 of Cambridge Studies in Advanced Mathematics.

Anisotropic isoperimetric double tilings of the plane Sets of finite perimeter and geometric variational problems , volume 135 of Cambridge Studies in Advanced Mathematics

Reference 36

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 64e8fa76-a88c-4c6a-8256-b68548d76f22 · outbound

This paper cites Wulff clusters in R ^2.

Anisotropic isoperimetric double tilings of the plane Wulff clusters in R ^2

Reference 37

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 3cd8b0a2-e1f1-4d2d-89b4-827621356d28 · outbound

This paper cites Multi-bubble isoperimetric problems.

Anisotropic isoperimetric double tilings of the plane Multi-bubble isoperimetric problems

Reference 38

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation e918b4ee-8987-4383-8cb2-e87bf8881da8 · outbound

This paper cites Unilateral tilings of the plane with squares of three sizes.

Anisotropic isoperimetric double tilings of the plane Unilateral tilings of the plane with squares of three sizes

Reference 39

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 49715b61-9a6a-4dac-99c3-06b60fc0d4f1 · outbound

This paper cites The G aussian double-bubble and multi-bubble conjectures.

Anisotropic isoperimetric double tilings of the plane The G aussian double-bubble and multi-bubble conjectures

Reference 40

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 0fad3345-16ea-4580-96a6-6d5a4fd2aa00 · outbound

This paper cites The Structure of Isoperimetric Bubbles on $\mathbb{R}^n$ and $\mathbb{S}^n$.

Anisotropic isoperimetric double tilings of the plane The Structure of Isoperimetric Bubbles on $\mathbb{R}^n$ and $\mathbb{S}^n$

Reference 41

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Observation 6cd3d109-f084-4f75-87f9-7bef578b49ae · outbound

This paper cites Spines of minimal length.

Anisotropic isoperimetric double tilings of the plane Spines of minimal length

Reference 42

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Observation f2e76fe1-e79f-4055-a3ce-1f4b17012373 · outbound

This paper cites The hexagonal honeycomb conjecture.

Anisotropic isoperimetric double tilings of the plane The hexagonal honeycomb conjecture

Reference 43

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation b7e1051f-4e6e-4d09-92f6-06b1ead8c071 · outbound

This paper cites Geometric measure theory.

Anisotropic isoperimetric double tilings of the plane Geometric measure theory

Reference 44

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation df0ba7dc-afa9-4a26-986b-acaf57c51186 · outbound

This paper cites The standard double bubble is the unique stable double bubble in R^2.

Anisotropic isoperimetric double tilings of the plane The standard double bubble is the unique stable double bubble in R^2

Reference 45

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 9c43cabb-7283-4e79-844c-e39629530eb7 · outbound

This paper cites A strong form of the quantitative Wulff inequality.

Anisotropic isoperimetric double tilings of the plane A strong form of the quantitative Wulff inequality

Reference 46

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 2cfd48a8-60ed-412f-8d80-66d25acca8c6 · outbound

This paper cites Lattice tilings with minimal perimeter and unequal volumes.

Anisotropic isoperimetric double tilings of the plane Lattice tilings with minimal perimeter and unequal volumes

Reference 47

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 0c7fca85-97fe-494a-b4fb-77a01018322e · outbound

This paper cites Periodic double tilings of the plane.

Anisotropic isoperimetric double tilings of the plane Periodic double tilings of the plane

Reference 48

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 46d146f6-6bb2-4d54-9369-5410ddeadb01 · outbound

This paper cites Minimizing clusters with prescribed asymptotic geometry.

Anisotropic isoperimetric double tilings of the plane Minimizing clusters with prescribed asymptotic geometry

Reference 49

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Observation e7cca9f1-ed98-4f60-b9a5-3c0a71f6bd44 · outbound

This paper cites Isoperimetric clusters in homogeneous spaces via concentration compactness.

Anisotropic isoperimetric double tilings of the plane Isoperimetric clusters in homogeneous spaces via concentration compactness

Reference 50

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation f3d1cd8c-05cb-458b-bf68-0967072a6ac6 · outbound

This paper cites Isoperimetric planar clusters with infinitely many regions.

Anisotropic isoperimetric double tilings of the plane Isoperimetric planar clusters with infinitely many regions

Reference 51

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 66315b3f-353a-468d-9db5-f2f05742cc6e · outbound

This paper cites Novaga, E.

Anisotropic isoperimetric double tilings of the plane Novaga, E

Reference 52

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 84542002-c556-4c09-bdd6-31263598d62e · outbound

This paper cites Existence of a non-standard isoperimetric triple partition.

Anisotropic isoperimetric double tilings of the plane Existence of a non-standard isoperimetric triple partition

Reference 53

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 56faa16c-ef6c-4df7-afcd-31860ec0bece · outbound

This paper cites Paolini and A.

Anisotropic isoperimetric double tilings of the plane Paolini and A

Reference 54

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation c27bb12d-6f4d-4b0d-8bae-8dbca19f73c8 · outbound

This paper cites Minimal clusters of four planar regions with the same area.

Anisotropic isoperimetric double tilings of the plane Minimal clusters of four planar regions with the same area

Reference 55

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 5501f172-7565-4929-9879-a6cf9a27cae5 · outbound

This paper cites Paolini and V.

Anisotropic isoperimetric double tilings of the plane Paolini and V

Reference 56

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation f743c018-42b7-4ca5-bf79-fe8849003b82 · outbound

This paper cites Reichardt.

Anisotropic isoperimetric double tilings of the plane Reichardt

Reference 57

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation e25b00ef-b435-43de-8224-89613fd55db6 · outbound

This paper cites Sullivan and Frank Morgan.

Anisotropic isoperimetric double tilings of the plane Sullivan and Frank Morgan

Reference 58

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 5505e575-1d39-41e6-85ab-3fc92bdd28b2 · outbound

This paper cites an unresolved cited work.

Anisotropic isoperimetric double tilings of the plane Unresolved cited work

Reference 59

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 7fc88a78-6674-4c8f-a2e4-204d0a6a0a50 · outbound

This paper cites On the division of space with minimum partitional area.

Anisotropic isoperimetric double tilings of the plane On the division of space with minimum partitional area

Reference 60

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation a64e59c9-7dca-4e0c-9d57-4f0f841991f4 · outbound

This paper cites Proof of the planar triple bubble conjecture.

Anisotropic isoperimetric double tilings of the plane Proof of the planar triple bubble conjecture

Reference 61

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

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Observation 696ff0bf-8088-47c2-a947-4786081c63a5 · outbound

This paper cites Weaire and R.

Anisotropic isoperimetric double tilings of the plane Weaire and R

Reference 62

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Observation 97e40ad1-e8cb-4bcc-aae8-5cb7b77c62e3 · outbound

This paper cites o sung der krystallfl \.

Anisotropic isoperimetric double tilings of the plane o sung der krystallfl \

Reference 63

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