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Paper Citation Record · LEDGER

Robust Shattering Arguments

As of 14 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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  • verified fuzzy0
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External citation measurements

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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:fad8ccca6c4dbfaec65e1f92e84b7c53a4a3259d836ba90b8f7f1e249aa3fa1e

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:aa71c5e174b94e655b864f17c8ce19749e7387183622151d771bcecbe7873192

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:ad3348910a08072c954b8b6f1062ef66f4631c511bdead43320e9647dcb586c7

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=sha256:93f9d447f05864921cbdfcf77109ec4cb6cc14872220789cd6158587238c5558

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=sha256:1e2ab2e8899fd606cd02c163e61781193a4caaa050d70c4f5294819ef7d6930a

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=sha256:76ce4f3bdf58b498dac974d77b2eccb366031b5dd4c2e1430b5de7f2dca2ca82

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=sha256:2efa93fec361ca85f6d432b4806ad6d47a642bc735dd34685c84e49948f1bd1c

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=sha256:52b7cd036ee02a9c932f3bdc56032339909269251762cf589898e3e82450c46f

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:c67576ba0d54b3b1ec0461d5e2a9e121d9f80b4ba036967918a62b47eccb14cd

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:cf0c9923b05e543b42a9e910214f85b784567334a9407cd3d9795c567ccf224b

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:e07fecb49fdf9a7a7bfe2d06264bb09dabb78079776bf45a5906aa0b4af41b2d

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=sha256:76764749fe61de85afdfc234c405e2c5b8f827a2b604aeab237763cf0986893e

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=sha256:7758753e8bb35732b6b559335e07bdef5f822da2bf75a66823a7f0ef2a514b2d

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=sha256:8128042d16d2eb9481ed61788a3caa26f49287954700af510e9323a60abcdac1

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=sha256:24d5804e155286005605221786a3a4400cfdc15ffa5e2469ee0f2215f076ff96

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=sha256:8fe2833540f08e9645a1fc43b215a10c9f9d0ef40d41e2a08e2ee3822f001540

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:c596f06f88707aab30a1de2412cfd465547f0d237aeaf7753e282ae61ae7dff2

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-reported events for the cited work

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:7b0d34e3adc8111ee83f2bf3e2a11bbf70bd3be7f850a7e5b917b6244fb8fcb0

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=sha256:137eab02917fe982d2fa099728078c3a9acc0d680e3398812968d0e4cd815015

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=sha256:2dcb65dfd48d9e1f253c1035719aff8a2f25d86e7b7b4ebd438d9465eb20d686

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:fb8ebe9ab89c7402e4466d1fb34f97337514076a390dd9197830b6087063dbee

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:f8fa4fb2739408d8161309ee050386551653de02331acc4857307e8ad7af5e71

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

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source=pdf_text observed=2026-06-29T02:34:12.606759Z digest=sha256:0c4b38b33690b6590e82ed5de5cc746b45931d2fe19cd00f7d0557c86eb138a4

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=sha256:6c3ec224c04e2bc451e84e5b185d77ef9c50e366b7cc4cc2685579be8f7fd8aa

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:c53df0113e627b29bd7112c935f46f52b3fe94f6616ed6a797b4b7222a59deac

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=sha256:37c241796790c3467eda4c780b906debc6905dacaa62aa986db371bd14229f59

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=sha256:3aec6c7e52207f1acad397067c18d877842c21d9370fba5839122be39967e8c4

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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source=pdf_text observed=2026-07-13T04:56:33.944199Z digest=sha256:3cf1a02009c0f37880277ebe31b3a7bdb6150e31e46315f86ee579856a520011