Paper Citation Record · LEDGER

Communication Complexity is NP-hard

As of 9 August 2026, this Paper Citation Record lists 3 of 3 outbound references and 1 inbound Pith citation observation for arXiv:2507.10426.

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

pith.paper-citation-record.v1
2507.10426 v1

Coverage vector

measured 3 of 3 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:49:07.054642Z

measured 4 of 4 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-08T15:24:32.298912Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-08T15:24:32.382105Z

Reference resolution

3 of 3 outbound references displayed

verified exact0
verified fuzzy3
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b2ef6d1b-b94d-4aac-84e2-c01692fe96b1 · outbound

This paper cites Minimal NFA problems are hard.

Communication Complexity is NP-hard Minimal NFA problems are hard

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:49:07.740589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 898a8410-2b75-47eb-b7eb-e161b7f8b820 · outbound

This paper cites On the complexity of communication complexity.

Communication Complexity is NP-hard On the complexity of communication complexity

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:49:07.509293Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1822fcf0-d5b4-4a58-bf32-38d10428f578 · outbound

This paper cites Some complexity questions related to distributive computing.

Communication Complexity is NP-hard Some complexity questions related to distributive computing

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:49:07.301686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

Observation d12b3ec8-a24f-4395-8ee8-2a4b3f61da20 · inbound

Computationally Efficient Collaborative Communication Via Regularity-Based Coarsening cites this paper.

Computationally Efficient Collaborative Communication Via Regularity-Based Coarsening Communication Complexity is NP-hard

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-08T15:24:32.385985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.