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Paper Citation Record · LEDGER

Robust Shattering Arguments

As of 15 August 2026, this Paper Citation Record lists 66 of 66 outbound references and 1 inbound Pith citation observation for arXiv:2606.27847.

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

pith.paper-citation-record.v1
2606.27847 v1

Coverage vector

measured 66 of 66 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-29T02:34:12.606759Z

measured 67 of 67 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-13T04:56:33.944199Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

66 of 66 outbound references displayed

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Outbound references

Observation db57cfaa-226f-4b6e-84fb-3f36b934d493 · outbound

This paper cites Halld´ orsson, and Alexandre Nolin.

Robust Shattering Arguments Halld´ orsson, and Alexandre Nolin

Reference 1

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Observation a5eec33d-9704-4d26-9d82-839271f752cf · outbound

This paper cites Ziegler.Proofs from THE BOOK.

Robust Shattering Arguments Ziegler.Proofs from THE BOOK

Reference 2

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Observation 1af7fdef-0cd7-47ff-8ff8-ee6d582cc8ae · outbound

This paper cites A parallel algorithmic version of the local lemma.Random Struct.

Robust Shattering Arguments A parallel algorithmic version of the local lemma.Random Struct

Reference 3

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Observation 279e3d1e-f9e5-4a45-9c82-022ef738b391 · outbound

This paper cites Almost global prob- lems in the LOCAL model.

Robust Shattering Arguments Almost global prob- lems in the LOCAL model

Reference 4

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Observation 065a0efd-de55-47c3-853e-d4eb413ae5c1 · outbound

This paper cites Korhonen, Tuomo Lempi¨ ainen, Dennis Olivetti, and Jukka Suomela.

Robust Shattering Arguments Korhonen, Tuomo Lempi¨ ainen, Dennis Olivetti, and Jukka Suomela

Reference 5

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Observation 1e7ce085-97e5-43f8-837a-520f5f36ed07 · outbound

This paper cites On the complexity of distributed splitting problems.

Robust Shattering Arguments On the complexity of distributed splitting problems

Reference 6

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Observation a79d6c4e-093c-426e-b30b-3c6903c644de · outbound

This paper cites Barenboim.

Robust Shattering Arguments Barenboim

Reference 7

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Observation ebab423d-cba4-4876-ad38-984845926645 · outbound

This paper cites Morgan & Claypool Publishers, 2013.

Robust Shattering Arguments Morgan & Claypool Publishers, 2013

Reference 8

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Observation ce6b197c-5fb4-4a64-9502-658213cd40fe · outbound

This paper cites Goldenberg.

Robust Shattering Arguments Goldenberg

Reference 9

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Observation 869608d0-566a-4120-aa4e-c10c273e2f1d · outbound

This paper cites The locality of distributed symmetry breaking.J.

Robust Shattering Arguments The locality of distributed symmetry breaking.J

Reference 10

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Observation 53f9ae4a-a80e-453a-83b0-38cc87a42534 · outbound

This paper cites Nearly-optimal distributed ruling sets for trees and high-girth graphs.

Robust Shattering Arguments Nearly-optimal distributed ruling sets for trees and high-girth graphs

Reference 11

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Observation cb44a1c2-09e4-456d-a320-bfd95a7350a7 · outbound

This paper cites An algorithmic approach to the Lov´ asz local lemma.

Robust Shattering Arguments An algorithmic approach to the Lov´ asz local lemma

Reference 12

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Observation e8db6aea-997f-46c8-a8a6-eba43680f491 · outbound

This paper cites The randomized local compu- tation complexity of the Lov´ asz local lemma.

Robust Shattering Arguments The randomized local compu- tation complexity of the Lov´ asz local lemma

Reference 13

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Observation 12f49e5c-4451-43ec-a2fe-8db39bb02282 · outbound

This paper cites On the locality of Hall’s theorem.

Robust Shattering Arguments On the locality of Hall’s theorem

Reference 14

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Observation 5ef5eff9-fdb8-4dac-9bd4-f5adaf66aa43 · outbound

This paper cites PhD thesis, University of Michigan, USA, 2019.

Robust Shattering Arguments PhD thesis, University of Michigan, USA, 2019

Reference 15

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Observation a6638b85-bccb-4cc0-a7e7-a6fa0d36f1ee · outbound

This paper cites Distributed edge coloring and a special case of the constructive Lov´ asz local lemma.ACM Trans.

Robust Shattering Arguments Distributed edge coloring and a special case of the constructive Lov´ asz local lemma.ACM Trans

Reference 16

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Observation 9677e11a-0b54-4c98-90b4-2aa46dc3fe43 · outbound

This paper cites An exponential separation between ran- domized and deterministic complexity in the LOCAL model.SIAM J.

Robust Shattering Arguments An exponential separation between ran- domized and deterministic complexity in the LOCAL model.SIAM J

Reference 17

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Observation 671f8397-d5b7-4192-8bde-1d61e646359f · outbound

This paper cites An optimal distributed (∆+1)-coloring algorithm? InProc.

Robust Shattering Arguments An optimal distributed (∆+1)-coloring algorithm? InProc

Reference 18

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Observation ce072554-2437-4c4b-8cfd-75572d4dd677 · outbound

This paper cites Distributed (∆ + 1)-coloring via ultrafast graph shattering.SIAM Journal on Computing, 49(3):497–539, 2020.

Robust Shattering Arguments Distributed (∆ + 1)-coloring via ultrafast graph shattering.SIAM Journal on Computing, 49(3):497–539, 2020

Reference 19

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Observation ce387ff6-f657-4078-966b-57a85f9df974 · outbound

This paper cites A time hierarchy theorem for the LOCAL model.SIAM J.

Robust Shattering Arguments A time hierarchy theorem for the LOCAL model.SIAM J

Reference 20

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Observation cfe030bc-178d-4c46-8200-f2bff455ee1f · outbound

This paper cites Distributed algorithms for the Lov´ asz local lemma and graph coloring.Distributed Comput., 30(4):261–280, 2017.

Robust Shattering Arguments Distributed algorithms for the Lov´ asz local lemma and graph coloring.Distributed Comput., 30(4):261–280, 2017

Reference 21

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Observation 25f41327-99a5-4806-bff8-1b1f3d5caa29 · outbound

This paper cites Component Stability in Low-Space Mas- sively Parallel Computation.

Robust Shattering Arguments Component Stability in Low-Space Mas- sively Parallel Computation

Reference 22

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Observation 580a99cd-b690-40a4-b7f8-8188fa463b7a · outbound

This paper cites Improved deterministic (∆+1) coloring in low-space MPC.

Robust Shattering Arguments Improved deterministic (∆+1) coloring in low-space MPC

Reference 23

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Observation 754e172f-0b69-4053-8680-56b52036266d · outbound

This paper cites Improved distributed algorithms for the lov´ asz local lemma and edge coloring.

Robust Shattering Arguments Improved distributed algorithms for the lov´ asz local lemma and edge coloring

Reference 24

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Observation 72e58f61-0cc0-457d-a89e-e0b3f9181f68 · outbound

This paper cites Problems and Results on 3-chromatic Hypergraphs and some Related Questions.Colloquia Mathematica Societatis J´ anos Bolyai, pages 609–627, 1974.

Robust Shattering Arguments Problems and Results on 3-chromatic Hypergraphs and some Related Questions.Colloquia Mathematica Societatis J´ anos Bolyai, pages 609–627, 1974

Reference 25

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Observation 786152fc-7158-4931-a7bb-3deed6c5f5be · outbound

This paper cites Sublogarithmic distributed algorithms for Lov´ asz local lemma, and the complexity hierarchy.

Robust Shattering Arguments Sublogarithmic distributed algorithms for Lov´ asz local lemma, and the complexity hierarchy

Reference 26

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Observation 485565bf-e1e2-457f-895e-1a7c0514f579 · outbound

This paper cites Halld´ orsson, and Alexandre Nolin.

Robust Shattering Arguments Halld´ orsson, and Alexandre Nolin

Reference 27

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Observation a975ab73-6685-44b9-867d-2c785b7f9753 · outbound

This paper cites Halld´ orsson, and Alexandre Nolin.

Robust Shattering Arguments Halld´ orsson, and Alexandre Nolin

Reference 28

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Observation ce2b0cc0-2fbe-46f8-8672-05bb79a9ffa4 · outbound

This paper cites Halld´ orsson, and Alexandre Nolin.

Robust Shattering Arguments Halld´ orsson, and Alexandre Nolin

Reference 29

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Observation 20ec8d65-5321-491e-b319-3239ad015f0e · outbound

This paper cites Local conflict coloring.

Robust Shattering Arguments Local conflict coloring

Reference 30

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Observation 6771f115-0da1-4a7d-9935-9c6f17a3aee5 · outbound

This paper cites A randomized distributed algorithm for the maximal in- dependent set problem in growth-bounded graphs.

Robust Shattering Arguments A randomized distributed algorithm for the maximal in- dependent set problem in growth-bounded graphs

Reference 31

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Observation 3c866e9b-6cf1-47cf-8166-53a42a6c469b · outbound

This paper cites An improved distributed algorithm for maximal independent set.

Robust Shattering Arguments An improved distributed algorithm for maximal independent set

Reference 32

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Observation 2f621077-bdf0-4c90-aada-786da1d6a541 · outbound

This paper cites Distributed maximal independent set using small messages.

Robust Shattering Arguments Distributed maximal independent set using small messages

Reference 33

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Observation 794875bd-d8f9-467c-afdb-ef6282714055 · outbound

This paper cites Local computation of maximal independent set.

Robust Shattering Arguments Local computation of maximal independent set

Reference 34

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Observation 74438edd-540f-43ac-b9e7-eb241eb5c3da · outbound

This paper cites Faster deterministic distributed MIS and approx- imate matching.

Robust Shattering Arguments Faster deterministic distributed MIS and approx- imate matching

Reference 35

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Observation 2d08cbd6-d6ca-4321-86ec-296f47868fcc · outbound

This paper cites Near-optimal network decomposition and ruling set, and improved mis.

Robust Shattering Arguments Near-optimal network decomposition and ruling set, and improved mis

Reference 36

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Observation 2f24b0cb-f670-41dc-a8b8-a2af183ea8fe · outbound

This paper cites Harris, and Fabian Kuhn.

Robust Shattering Arguments Harris, and Fabian Kuhn

Reference 37

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Observation 424b97a6-595c-4197-8074-5a44e507c150 · outbound

This paper cites Improved distributed delta-coloring.

Robust Shattering Arguments Improved distributed delta-coloring

Reference 38

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Observation b08cf6c1-a08f-4852-9340-d28228750025 · outbound

This paper cites Deterministic distributed vertex coloring: Simpler, faster, and without network decomposition.

Robust Shattering Arguments Deterministic distributed vertex coloring: Simpler, faster, and without network decomposition

Reference 39

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Observation 7b22f4c7-59b7-41ab-aee5-80eb0df023df · outbound

This paper cites On the complexity of local distributed graph problems.

Robust Shattering Arguments On the complexity of local distributed graph problems

Reference 40

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:dcd640f9b392683a1203628d7dd5c58ba0bcee3279e65f0b24fa535c0cab31e1

Observation 7aaec4df-50a4-4940-bba2-8be53963f29e · outbound

This paper cites Distributed degree splitting, edge coloring, and ori- entations.

Robust Shattering Arguments Distributed degree splitting, edge coloring, and ori- entations

Reference 41

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:a52ee2b0a3f4675f925517647cb2f3dfb7d2b7b1f5c6c62bad7a5cbbe08c8a8b

Observation 3cba9853-2c6b-45d5-886a-31cf9f1cb13c · outbound

This paper cites Sparsifying distributed algorithms with ramifications in massively parallel computation and centralized local computation.

Robust Shattering Arguments Sparsifying distributed algorithms with ramifications in massively parallel computation and centralized local computation

Reference 42

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:6a17abc8c0053d3adf94e197af04a99eb60677d5ef8faeb2f41bf1d524242d04

Observation 8c81a940-dad0-46c4-b41a-c91fe5d301a5 · outbound

This paper cites Halld´ orsson, Fabian Kuhn, Yannic Maus, and Alexandre Nolin.

Robust Shattering Arguments Halld´ orsson, Fabian Kuhn, Yannic Maus, and Alexandre Nolin

Reference 43

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:c0d951f7683eef0c95aeb4bf1494790a25170f57164aab96e564c2e026d16b76

Observation a9f529dd-3a01-4575-bb8e-ffe46b614c8e · outbound

This paper cites Halld´ orsson, Fabian Kuhn, Yannic Maus, and Tigran Tonoyan.

Robust Shattering Arguments Halld´ orsson, Fabian Kuhn, Yannic Maus, and Tigran Tonoyan

Reference 44

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:06eed17b7a9953b08efb0b58149bfd27b69ed1333985fc5b31469960472dc545

Observation 30b8e671-40f7-401b-af03-923ceee71164 · outbound

This paper cites Halld´ orsson, Fabian Kuhn, Alexandre Nolin, and Tigran Tonoyan.

Robust Shattering Arguments Halld´ orsson, Fabian Kuhn, Alexandre Nolin, and Tigran Tonoyan

Reference 45

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:e543888864398d2cff3a81f2bd9e324c9738ba95eb61c93909a1170d423aa263

Observation f54e9749-ba80-4fbf-bed6-6c0548a3e4c3 · outbound

This paper cites Halld´ orsson, Yannic Maus, and Alexandre Nolin.

Robust Shattering Arguments Halld´ orsson, Yannic Maus, and Alexandre Nolin

Reference 46

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:f98eca8eacec137c4b3031c07c231d332d47a786f77906f970aa5b4ef8c90b7b

Observation 692d9402-0eb1-4851-b919-6428a0fa2b0d · outbound

This paper cites Distributed Lov\'{a}sz Local Lemma under Bandwidth Limitations.

Robust Shattering Arguments Distributed Lov\'{a}sz Local Lemma under Bandwidth Limitations

Reference 47

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arxiv_id, observed 2026-07-01T18:05:58.937205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:14c2c513b78e8a4870a91fdf8fdcc5f4dd74a99452e18b8e2f3dc42569fdc372

Observation 907b94d1-3dbc-4f32-ab9c-30fc7eab9590 · outbound

This paper cites Halld´ orsson and Alexandre Nolin.

Robust Shattering Arguments Halld´ orsson and Alexandre Nolin

Reference 48

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:4bdf5a2d0083e86561125e69e74f45c0746f1b35087ee816eae850de022c31bf

Observation 4c66f9db-afcd-421b-b6f0-114a333e13ff · outbound

This paper cites Halld´ orsson, Alexandre Nolin, and Tigran Tonoyan.

Robust Shattering Arguments Halld´ orsson, Alexandre Nolin, and Tigran Tonoyan

Reference 49

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:da4e921ae742259d5382239fbdc5f75074209c1451bdf5de13e91be740b72705

Observation fcc0dfd3-b05f-46eb-b33e-12c3bef173ad · outbound

This paper cites A fast and simple randomized parallel algorithm for maximal matching.Inf.

Robust Shattering Arguments A fast and simple randomized parallel algorithm for maximal matching.Inf

Reference 50

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:64fccf7ec57632c62fb41c18c43b0be8790b8e379fa8f50333ff6b1929f64833

Observation 1317b5be-f853-4fbd-9bc7-4d3aca767a21 · outbound

This paper cites Feedback from nature: simple randomised dis- tributed algorithms for maximal independent set selection and greedy colouring.Distributed Comput., 29(5):377–393, 2016.

Robust Shattering Arguments Feedback from nature: simple randomised dis- tributed algorithms for maximal independent set selection and greedy colouring.Distributed Comput., 29(5):377–393, 2016

Reference 51

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:5e2a140b69e4cf68a3c14d6b6eed9a16cfc1bbb6c1a9f051b3a5aac19a616f20

Observation 817068ec-e037-4cb0-ac9a-5d8d39c06aa8 · outbound

This paper cites Simple distributed ∆ + 1-coloring of graphs.Inf.

Robust Shattering Arguments Simple distributed ∆ + 1-coloring of graphs.Inf

Reference 52

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:102971bd107a3b868f2e943b977142e0441d456af3bc273999bfff40525215d0

Observation 8d0bb0b2-33cb-4a7f-8dd3-d24584fbd4af · outbound

This paper cites Locality in distributed graph algorithms.SIAM Journal on computing, 21(1):193–201, 1992.

Robust Shattering Arguments Locality in distributed graph algorithms.SIAM Journal on computing, 21(1):193–201, 1992

Reference 53

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:3ecf59d4e049cdebc9dd70e4e08c6108cec8185a61d4ebb57f79e3239abf540d

Observation 139884a3-cf89-41fa-84ed-1d68c4f0733d · outbound

This paper cites Distributed graph coloring made easy.

Robust Shattering Arguments Distributed graph coloring made easy

Reference 54

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:9ee5a63dcf269235bb66acf3ce54a616875527a68a8f3a233925c1a7813eae73

Observation 4ccd4a4e-3cc5-4c1d-9147-fdf160fa2ef3 · outbound

This paper cites Distributed symmetry breaking on power graphs via sparsification.

Robust Shattering Arguments Distributed symmetry breaking on power graphs via sparsification

Reference 55

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:ac792c8c6c82c3123814862aae21b3f9e1fabf035ada86314f66f464a895ec94

Observation 2810dc90-9523-4a83-8a57-70b4e0c4dfdd · outbound

This paper cites Distributed symmetry breaking on power graphs via sparsification.Distributed Comput., 38(3):261–296, 2025.

Robust Shattering Arguments Distributed symmetry breaking on power graphs via sparsification.Distributed Comput., 38(3):261–296, 2025

Reference 56

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:a069992f31db2a78a40620d7efd135419898c8ce1f827398193cf364c6de6e3f

Observation 2637055a-faa5-47d7-9c52-573867284551 · outbound

This paper cites Efficient CONGEST algorithms for the Lov´ asz local lemma.

Robust Shattering Arguments Efficient CONGEST algorithms for the Lov´ asz local lemma

Reference 57

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:ef9058f2b5f581b4346ca70c5de85bb41f9c83efe2661073bde0a013114f04ea

Observation 355b7038-4f03-48e2-8d50-a81134af385f · outbound

This paper cites an unresolved cited work.

Robust Shattering Arguments Unresolved cited work

Reference 58

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:0909110114a9dae71d6d0c3917c104458e04f8b800231dc96bd5df20dbb02130

Observation 4e938004-6778-48f5-9409-1a4fed91fa73 · outbound

This paper cites Moser and G´ abor Tardos.

Robust Shattering Arguments Moser and G´ abor Tardos

Reference 59

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:70231c86961eb3bbc43cff9149abce39da8923c9504613377b9e29cdce6abee1

Observation 2b872a7c-4eb2-4a51-a227-32acf8d8a88c · outbound

This paper cites Conflict-free colourings of graphs and hypergraphs.Comb.

Robust Shattering Arguments Conflict-free colourings of graphs and hypergraphs.Comb

Reference 60

Resolution
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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:0b4ca2cf30f74c14a77a9e4c48a6297ff509303b1d19e269ee279b6ed6beebff

Observation 276b5816-c4f5-4cc8-9b43-e748e9b18481 · outbound

This paper cites Distributed coloring algorithms for triangle-free graphs.

Robust Shattering Arguments Distributed coloring algorithms for triangle-free graphs

Reference 61

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:bbf528bb87136391ead5f0283de8ca9a87b649bbfe605e23f17bb134948025f0

Observation 8d80dd7e-458f-41b5-bcb5-6515d4611721 · outbound

This paper cites Polylogarithmic-time deterministic network decom- position and distributed derandomization.

Robust Shattering Arguments Polylogarithmic-time deterministic network decom- position and distributed derandomization

Reference 62

Resolution
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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:7190a33e492d32784bb20de3093a652092936519cfa0612a634f77d59a2778a8

Observation 0dcd882b-058b-457c-ba7a-f807964de5c5 · outbound

This paper cites Fast local computation algo- rithms.

Robust Shattering Arguments Fast local computation algo- rithms

Reference 63

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:082ac7458a50f47027c505c413ecb0be977c5e2c44ec5fd98f2c6d77a31f7df9

Observation bd731659-49ce-4f60-8f04-de36b63ef4e7 · outbound

This paper cites Symmetry breaking depending on the chromatic number or the neighborhood growth.Theor.

Robust Shattering Arguments Symmetry breaking depending on the chromatic number or the neighborhood growth.Theor

Reference 64

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:1890346ce5648ab616b276e7840a023a6668cd8f2dbb46a5bcefae8e68653111

Observation 811a910c-01b5-4c00-8883-a3a9f5b3ef84 · outbound

This paper cites It is the element ofRnearest tovinG c[B], with ties broken with IDs.

Robust Shattering Arguments It is the element ofRnearest tovinG c[B], with ties broken with IDs

Reference 65

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:5448d83e7b7d15e96b35fb1298ce860172ee935e431aa27ebe1fd0905d881d83

Observation e90a0790-67dd-4a25-bada-67a2531f52dd · outbound

This paper cites Note that given a setsRandBthe cost of computing a cluster graph essentially scales with how far a node inBcan be from the nearest node inR.

Robust Shattering Arguments Note that given a setsRandBthe cost of computing a cluster graph essentially scales with how far a node inBcan be from the nearest node inR

Reference 66

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:48a1dd9c6a8ec91bcd88a6636d8786be23a886c8dd59118cb93c55e61e2675f1

Pith citing papers

Observation 6efcc15e-8ecd-4c24-a201-58a1e24af49a · inbound

Distributed Symmetry Breaking on Hyperbolic Random Graphs cites this paper.

Distributed Symmetry Breaking on Hyperbolic Random Graphs Robust Shattering Arguments

Reference 49

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no resolver link, observed 2026-07-13T04:56:33.944199Z

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source=pdf_text observed=2026-07-13T04:56:33.944199Z digest=sha256:eb10abb7d37385bc431755956c30c3052374938169cfa6c8a89e29e1a8bd58e4