Paper Citation Record · LEDGER

Equality is Far Weaker than Constant-Cost Communication

As of 12 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 2 inbound Pith citation observations for arXiv:2507.11162.

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

pith.paper-citation-record.v1
2507.11162 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:36:23.129782Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-03T23:13:46.227475Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T19:30:07.057835Z

Reference resolution

23 of 23 outbound references displayed

verified exact5
verified fuzzy3
unresolved13
parse uncertain0
malformed identifier2
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation dea0b4cd-3543-4144-88f7-b829fdcd41f0 · outbound

This paper cites A discrepancy lower bound for information complexity.

Equality is Far Weaker than Constant-Cost Communication A discrepancy lower bound for information complexity

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T17:36:21.014300Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f796c4f0-5a24-460d-9441-ce479ced36b3 · outbound

This paper cites Equality alone does not simulate randomness.

Equality is Far Weaker than Constant-Cost Communication Equality alone does not simulate randomness

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T17:36:21.104292Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c5374fed-423e-4be1-b097-bd2cdc8fbaaa · outbound

This paper cites A lower bound on the trace norm of boolean matrices and its applications.

Equality is Far Weaker than Constant-Cost Communication A lower bound on the trace norm of boolean matrices and its applications

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T17:36:21.167841Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7310c35-a324-43e7-a1b2-cd2a11a7ab16 · outbound

This paper cites Separation of the factorization norm and randomized communication complexity.

Equality is Far Weaker than Constant-Cost Communication Separation of the factorization norm and randomized communication complexity

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T17:36:21.234157Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 79e09753-99d4-471f-9a02-cb865829272a · outbound

This paper cites Boolean functions with small approximate spectral norm.Discrete Analysis, 2024.doi:10.19086/da.122971.

Equality is Far Weaker than Constant-Cost Communication Boolean functions with small approximate spectral norm.Discrete Analysis, 2024.doi:10.19086/da.122971

Reference 5

Resolution: verified exact; doi, observed 2026-08-06T17:36:24.155677Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 69343d1f-f0b3-451e-93c1-4c6bb1959045 · outbound

This paper cites Sketching distances in monotone graph classes.

Equality is Far Weaker than Constant-Cost Communication Sketching distances in monotone graph classes

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T17:36:21.510443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec3ce024-f4e0-4f2e-8c93-1572044560b9 · outbound

This paper cites Constant-Cost Communication is not Reducible to k-Hamming Distance.

Equality is Far Weaker than Constant-Cost Communication Constant-Cost Communication is not Reducible to k-Hamming Distance

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T17:36:21.607785Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c58072b2-d90f-484c-9e0b-a077895f4f71 · outbound

This paper cites No Complete Problem for Constant-Cost Randomized Communication.

Equality is Far Weaker than Constant-Cost Communication No Complete Problem for Constant-Cost Randomized Communication

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T17:36:21.691751Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 350e3f66-cf6d-4983-9f1f-695b35d457e4 · outbound

This paper cites Dimension-free bounds and structural results in communication complexity.Israel Journal of Mathematics, 253(2):555– 616, 2023.doi:10.1007/s11856-022-2365-8.

Equality is Far Weaker than Constant-Cost Communication Dimension-free bounds and structural results in communication complexity.Israel Journal of Mathematics, 253(2):555– 616, 2023.doi:10.1007/s11856-022-2365-8

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-06T17:36:21.822931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0ff1250a-d5c4-491e-91f2-f5574a8cb68b · outbound

This paper cites Universal communication, universal graphs, and graph labeling.

Equality is Far Weaker than Constant-Cost Communication Universal communication, universal graphs, and graph labeling

Reference 10

Resolution: verified exact; doi, observed 2026-08-06T17:36:23.928923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 850180f5-bece-4b08-a182-c9676fce0996 · outbound

This paper cites Better boosting of communication oracles, or not.

Equality is Far Weaker than Constant-Cost Communication Better boosting of communication oracles, or not

Reference 11

Resolution: verified exact; doi, observed 2026-08-06T17:36:23.738798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4f9a9d46-7e73-4422-97d5-23a16343ac0e · outbound

This paper cites Randomized communication and implicit graph representations.

Equality is Far Weaker than Constant-Cost Communication Randomized communication and implicit graph representations

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T17:36:22.091278Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f71a3117-805f-4820-9eb1-ddd79774765f · outbound

This paper cites Randomized communication and implicit representa- tions for matrices and graphs of small sign-rank.

Equality is Far Weaker than Constant-Cost Communication Randomized communication and implicit representa- tions for matrices and graphs of small sign-rank

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T17:36:22.214048Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d9eee8b-979c-4bb7-9891-445beeb20c3e · outbound

This paper cites Guest column: Structure in communication complexity and constant-cost complexity classes.ACM SIGACT News, 55(1):67–93, 2024.doi:10.1145/ 3654780.3654788.

Equality is Far Weaker than Constant-Cost Communication Guest column: Structure in communication complexity and constant-cost complexity classes.ACM SIGACT News, 55(1):67–93, 2024.doi:10.1145/ 3654780.3654788

Reference 14

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T17:36:24.553266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 48ecab83-687b-4de2-b4c4-6f2aca1b303f · outbound

This paper cites Cambridge University Press, 1996.

Equality is Far Weaker than Constant-Cost Communication Cambridge University Press, 1996

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:36:24.967331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b030f9fb-2cdb-4a20-9659-ab72db10e999 · outbound

This paper cites The communication complexity of threshold gates.Combinatorics, Paul Erdos is Eighty, 1(301-315):6, 1993.

Equality is Far Weaker than Constant-Cost Communication The communication complexity of threshold gates.Combinatorics, Paul Erdos is Eighty, 1(301-315):6, 1993

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:36:24.856039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 5eea49be-6436-43ca-af62-789853852676 · outbound

This paper cites The strength of equality oracles in communication.

Equality is Far Weaker than Constant-Cost Communication The strength of equality oracles in communication

Reference 17

Resolution: malformed identifier; no resolver link, observed 2026-08-06T17:36:22.538860Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95791df5-1c77-4259-87c6-4024eb5b1995 · outbound

This paper cites Cambridge University Press, 2020.

Equality is Far Weaker than Constant-Cost Communication Cambridge University Press, 2020

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:36:24.726076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 83795de6-6e15-4a36-96bf-d5729160ac14 · outbound

This paper cites Boolean functions with small spectral norm, revisited.Mathematical Proceedings of the Cambridge Philosophical Society, 167(2):335–344, 2019.doi:10.1017/S030500411800035X.

Equality is Far Weaker than Constant-Cost Communication Boolean functions with small spectral norm, revisited.Mathematical Proceedings of the Cambridge Philosophical Society, 167(2):335–344, 2019.doi:10.1017/S030500411800035X

Reference 19

Resolution: verified exact; doi, observed 2026-08-06T17:36:23.553816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 7e7d5e6d-d443-41cb-b9de-43766822643d · outbound

This paper cites The communication complexity of approximat- ing matrix rank.

Equality is Far Weaker than Constant-Cost Communication The communication complexity of approximat- ing matrix rank

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T17:36:22.844760Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fa475bb2-6189-45d9-a1d8-90604304940a · outbound

This paper cites The discrepancy of greater-than.

Equality is Far Weaker than Constant-Cost Communication The discrepancy of greater-than

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-06T17:36:22.942054Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2bddbff7-26e0-48ce-8377-438797d43a88 · outbound

This paper cites Factorization norms and Zarankiewicz problems.

Equality is Far Weaker than Constant-Cost Communication Factorization norms and Zarankiewicz problems

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:36:23.362825Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b4431674-0b8c-48bb-8924-cc6599fa7ec4 · outbound

This paper cites The communication complexity of addition.Combinatorica, 35(6):703–747, 2015.doi:10.1007/s00493-014-3078-3.

Equality is Far Weaker than Constant-Cost Communication The communication complexity of addition.Combinatorica, 35(6):703–747, 2015.doi:10.1007/s00493-014-3078-3

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T17:36:23.129782Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 6f89c6f4-fa8b-4606-a1d0-47e898ce1dfc · inbound

Communication complexity of point-line incidences over the reals cites this paper.

Communication complexity of point-line incidences over the reals Equality is Far Weaker than Constant-Cost Communication

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-07-04T19:30:07.061778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 75eb4cd2-58d2-4029-b080-c86c5e9c8a01 · inbound

Communication complexity of point-line incidences over the reals cites this paper.

Communication complexity of point-line incidences over the reals Equality is Far Weaker than Constant-Cost Communication

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-07-03T23:19:02.666426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.