Paper Citation Record · LEDGER

Ulam Median is NP-hard for Four Permutations

As of 21 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:2608.05544.

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

pith.paper-citation-record.v1
2608.05544 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T11:16:57.727490Z

measured 14 of 14 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

14 of 14 outbound references displayed

verified exact6
verified fuzzy2
unresolved2
parse uncertain0
malformed identifier3
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0deec1d7-9a43-4723-adde-00993bb11ddc · outbound

This paper cites Procaccia, editors.

Ulam Median is NP-hard for Four Permutations Procaccia, editors

Reference 1

Resolution: verified exact; doi, observed 2026-08-08T11:16:58.138218Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 21c87464-c578-4f47-b160-6a759a6c334a · outbound

This paper cites 2 [ODL+20] Samuel E.

Ulam Median is NP-hard for Four Permutations 2 [ODL+20] Samuel E

Reference 11

Resolution: verified exact; doi, observed 2026-08-08T11:16:57.764233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 130b4167-e0a3-4962-b1b4-55e97a466198 · outbound

This paper cites Median strings.Pattern Recognit.

Ulam Median is NP-hard for Four Permutations Median strings.Pattern Recognit

Reference 1959

Resolution: unresolved; no resolver link, observed 2026-08-08T11:16:57.698093Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a93d022-9a12-4aad-8cdb-b138d4036fcb · outbound

This paper cites 2 [JKY25] Ragesh Jaiswal, Amit Kumar, and Jatin Yadav.

Ulam Median is NP-hard for Four Permutations 2 [JKY25] Ragesh Jaiswal, Amit Kumar, and Jatin Yadav

Reference 1997

Resolution: unresolved; no resolver link, observed 2026-08-08T11:16:57.656136Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fa87688f-2650-4e72-a3da-1cbee8060a27 · outbound

This paper cites Rácz, Siena Ang, Djordje Jevdjic, Sergey Yekhanin, Luis Ceze, and Karin Strauss.

Ulam Median is NP-hard for Four Permutations Rácz, Siena Ang, Djordje Jevdjic, Sergey Yekhanin, Luis Ceze, and Karin Strauss

Reference 2000

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T11:16:58.123118Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 780e1d23-8ee8-43fc-b394-71e344865d99 · outbound

This paper cites Approximating the median under the ulam metric.

Ulam Median is NP-hard for Four Permutations Approximating the median under the ulam metric

Reference 2003

Resolution: verified exact; doi, observed 2026-08-08T11:16:57.833611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0b1711fc-c706-4bd5-b484-58cdba2fb74a · outbound

This paper cites 2 [Gus97] Dan Gusfield.Algorithms on Strings, Trees, and Sequences - Computer Science and Com- putational Biology.

Ulam Median is NP-hard for Four Permutations 2 [Gus97] Dan Gusfield.Algorithms on Strings, Trees, and Sequences - Computer Science and Com- putational Biology

Reference 2013

Resolution: verified exact; doi, observed 2026-08-08T11:16:57.791985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2b30f9ef-e6a2-4c59-b076-74ca75ff8bf4 · outbound

This paper cites 2 [YL78] H.

Ulam Median is NP-hard for Four Permutations 2 [YL78] H

Reference 2017

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T11:16:58.106536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d257ebae-c4a2-4615-80a4-4b5ca769011b · outbound

This paper cites The Complexity of Kemeny Aggregation with Three Rankings.

Ulam Median is NP-hard for Four Permutations The Complexity of Kemeny Aggregation with Three Rankings

Reference 2019

Resolution: malformed identifier; local_arxiv, observed 2026-08-08T11:16:57.875658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b0b8da09-702c-4af0-b29b-7fe7190df002 · outbound

This paper cites 2021.12,doi:10.4230/LIPICS.FSTTCS.2021.12.

Ulam Median is NP-hard for Four Permutations 2021.12,doi:10.4230/LIPICS.FSTTCS.2021.12

Reference 2021

Resolution: malformed identifier; no resolver link, observed 2026-08-08T11:16:57.496716Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c93d3277-4826-4ed6-afd1-6f30ae131ba3 · outbound

This paper cites 2 [CDN26] Amir Carmel, Debarati Das, and Tien-Long Nguyen.

Ulam Median is NP-hard for Four Permutations 2 [CDN26] Amir Carmel, Debarati Das, and Tien-Long Nguyen

Reference 2022

Resolution: malformed identifier; no resolver link, observed 2026-08-08T11:16:57.455998Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c8b1582-a627-4a3b-9ea3-83d1d7c0614b · outbound

This paper cites 2, 3 [CDKS22] Diptarka Chakraborty, Syamantak Das, Arindam Khan, and Aditya Subramanian.

Ulam Median is NP-hard for Four Permutations 2, 3 [CDKS22] Diptarka Chakraborty, Syamantak Das, Arindam Khan, and Aditya Subramanian

Reference 2023

Resolution: verified exact; doi, observed 2026-08-08T11:16:57.817788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0f37b062-15f3-418f-a5e7-ba68c07eca37 · outbound

This paper cites URL:https:// drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.111,doi:10.4230/ LIPIcs.ESA.2025.111.

Ulam Median is NP-hard for Four Permutations URL:https:// drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.111,doi:10.4230/ LIPIcs.ESA.2025.111

Reference 2025

Resolution: metadata mismatch; raw_fallback, observed 2026-08-08T11:16:58.015337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c3349c21-1a1d-4e23-b0ea-a948d371c0a6 · outbound

This paper cites Kemeny Rank Aggregation is NP-Hard for Three Voters.

Ulam Median is NP-hard for Four Permutations Kemeny Rank Aggregation is NP-Hard for Three Voters

Reference 2026

Resolution: verified exact; local_arxiv, observed 2026-08-08T11:16:57.854748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

No inbound Pith citation observations are available.