Paper Citation Record · LEDGER

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication

As of 21 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2507.12124.

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

pith.paper-citation-record.v1
2507.12124 v1

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:11:31.666266Z

measured 40 of 40 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

40 of 40 outbound references displayed

verified exact10
verified fuzzy4
unresolved23
parse uncertain0
malformed identifier0
metadata mismatch3

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c3c47b1f-51e0-4873-bdd4-0e0330b2fdef · outbound

This paper cites Razborov, and Avi Wigderson.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Razborov, and Avi Wigderson

Reference 1

Resolution: verified exact; doi, observed 2026-08-06T17:11:32.535525Z

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 6a810765-b337-4026-8f9d-faee1d08f9ff · outbound

This paper cites Lower bounds for k-dnf resolution on random 3-cnfs.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Lower bounds for k-dnf resolution on random 3-cnfs

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:29.826982Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b47d596-ed65-4308-bf35-f12be56630c9 · outbound

This paper cites Razborov.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Razborov

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:11:34.289003Z

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 dd6b9b6e-856c-4feb-b465-b6cdcefee6cc · outbound

This paper cites Karp, Toniann Pitassi, and Michael E.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Karp, Toniann Pitassi, and Michael E

Reference 4

Resolution: verified exact; doi, observed 2026-08-06T17:11:32.465580Z

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 3a0a6e8c-c597-439a-bdce-84f6f3d179fb · outbound

This paper cites Lower bounds for lov[a-acute]sz--schrijver systems and beyond follow from multiparty communication complexity.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Lower bounds for lov[a-acute]sz--schrijver systems and beyond follow from multiparty communication complexity

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:30.312847Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f3c6634-c7e0-4961-8ac3-e41daeb0c524 · outbound

This paper cites Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:30.503371Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bae64d65-685f-4ef3-a6e1-04b88c90e5b0 · outbound

This paper cites Many hard examples for resolution.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Many hard examples for resolution

Reference 7

Resolution: verified exact; raw_fallback, observed 2026-08-06T17:11:34.091940Z

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 dfeedae5-f26f-4085-aa1a-ecb47093b7e3 · outbound

This paper cites de Rezende, Jakob Nordstr \" o m, and Marc Vinyals.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication de Rezende, Jakob Nordstr \" o m, and Marc Vinyals

Reference 9

Resolution: verified exact; doi, observed 2026-08-06T17:11:32.391958Z

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 6925eadd-74d4-4e81-ac63-2cfe49c8a34e · outbound

This paper cites Complexity theoretic limitations on learning dnf's.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Complexity theoretic limitations on learning dnf's

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:11:34.213650Z

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 7c09e041-226b-4816-879c-52bb6ca0e833 · outbound

This paper cites On the Modularity of Hypernetworks.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication On the Modularity of Hypernetworks

Reference 11

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T17:11:33.789074Z

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 5b3cf6d3-73ad-454e-bd9c-ca8d0cc47a40 · outbound

This paper cites Random ( n) -CNFs are Hard for Cutting Planes.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Random ( n) -CNFs are Hard for Cutting Planes

Reference 12

Resolution: verified exact; doi, observed 2026-08-06T17:11:32.337601Z

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 146d72ac-f481-4f90-b4cf-ce760bbdb3be · outbound

This paper cites Quantum communication advantage in tfnp.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Quantum communication advantage in tfnp

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.289790Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 232ac06b-a8a3-422f-bf2c-6197a7fcfa12 · outbound

This paper cites Monotone circuit lower bounds from resolution.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Monotone circuit lower bounds from resolution

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.322928Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9d6b19ea-961e-4e71-b6e5-fbce1b452560 · outbound

This paper cites an unresolved cited work.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.375785Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b097e1bd-cb68-4aec-b657-88616e88504c · outbound

This paper cites Extension complexity of independent set polytopes.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Extension complexity of independent set polytopes

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.382211Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 782ba537-bfdd-4da6-afd1-e25e4de28079 · outbound

This paper cites Adventures in monotone complexity and TFNP.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Adventures in monotone complexity and TFNP

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.388468Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c0817972-525d-428b-8456-be60689a76d6 · outbound

This paper cites Rectangles are nonnegative juntas.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Rectangles are nonnegative juntas

Reference 18

Resolution: verified exact; doi, observed 2026-08-06T17:11:32.196433Z

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 d2084f1b-e217-45c4-914e-9aab5a11d15d · outbound

This paper cites Supercritical tradeoffs for monotone circuits.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Supercritical tradeoffs for monotone circuits

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.403781Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fffc3b1b-c223-45c1-9763-598709961f31 · outbound

This paper cites Hardness condensation by restriction.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Hardness condensation by restriction

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.414868Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2577db6d-ed04-483d-9dab-b5e3f01f807d · outbound

This paper cites Communication lower bounds via critical block sensitivity.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Communication lower bounds via critical block sensitivity

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.431588Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5374d4d4-3c6b-4aad-ad18-1c58b3491e40 · outbound

This paper cites Query-to-communication lifting for BPP.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Query-to-communication lifting for BPP

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.440259Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4044ffab-7dc0-45d1-8687-caf387fc50a8 · outbound

This paper cites Linear lower bound on degrees of positivstellensatz calculus proofs for the parity.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Linear lower bound on degrees of positivstellensatz calculus proofs for the parity

Reference 24

Resolution: verified exact; doi, observed 2026-08-06T17:11:32.117846Z

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 0f9d2e90-bd3c-4a68-bea4-b2559b2977d9 · outbound

This paper cites On the virtue of succinct proofs: amplifying communication complexity hardness to time-space trade-offs in proof complexity.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication On the virtue of succinct proofs: amplifying communication complexity hardness to time-space trade-offs in proof complexity

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.454527Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc3305f7-93b2-4aed-97b8-bfee0a931679 · outbound

This paper cites Random formulas, monotone circuits, and interpolation.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Random formulas, monotone circuits, and interpolation

Reference 26

Resolution: verified exact; doi, observed 2026-08-06T17:11:32.079689Z

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 bcd4a6d3-cb3e-4dd4-a78a-b287db46b6a1 · outbound

This paper cites Upper and lower bounds for tree-like cutting planes proofs.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Upper and lower bounds for tree-like cutting planes proofs

Reference 27

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T17:11:33.203595Z

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 466807ca-5e2c-48de-93da-17e17c5c9dc0 · outbound

This paper cites Proof complexity of natural formulas via communication arguments.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Proof complexity of natural formulas via communication arguments

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.482693Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0fae763-00e3-430f-8d50-78090f56f4da · outbound

This paper cites Resolution over linear equations modulo two.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Resolution over linear equations modulo two

Reference 29

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T17:11:33.084999Z

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 94502fc9-eac6-4374-bb5d-13321579a221 · outbound

This paper cites Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.501473Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 08ad0ab5-907d-44fa-99c3-ebdcb5f6c842 · outbound

This paper cites Monotone circuits for connectivity require super-logarithmic depth.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Monotone circuits for connectivity require super-logarithmic depth

Reference 31

Resolution: verified exact; doi, observed 2026-08-06T17:11:31.980730Z

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 02463312-d4db-4df6-b93b-e9ed0920bc60 · outbound

This paper cites Lifting with sunflowers.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Lifting with sunflowers

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.534363Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 801785b7-1b19-4345-9550-599e4bf154a0 · outbound

This paper cites Search problems in the decision tree model.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Search problems in the decision tree model

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.544958Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5bfd6985-ee8d-4606-9287-01f3fb13f706 · outbound

This paper cites Analytic and algorithmic solution of random satisfiability problems.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Analytic and algorithmic solution of random satisfiability problems

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.554851Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8bc1bda9-1e40-4384-bcb4-7d1775936321 · outbound

This paper cites Lifting nullstellensatz to monotone span programs over any field.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Lifting nullstellensatz to monotone span programs over any field

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.565333Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e94e204c-e33b-4bad-8460-198f74fd37c1 · outbound

This paper cites Lower bounds for resolution and cutting plane proofs and monotone computations.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Lower bounds for resolution and cutting plane proofs and monotone computations

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.577038Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b050e51-c532-4441-85fa-4deacff54374 · outbound

This paper cites Razborov.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Razborov

Reference 37

Resolution: verified exact; doi, observed 2026-08-06T17:11:31.830085Z

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 765dd5d1-6f43-4e66-ac49-84aa35026f53 · outbound

This paper cites an unresolved cited work.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.604827Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation feefe13f-93e8-4222-9805-a5c92289e9f4 · outbound

This paper cites (semi)algebraic proofs over \( \) 1 variables.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication (semi)algebraic proofs over \( \) 1 variables

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.617696Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7531ca09-2fb2-49b7-b5d2-c2c2847dc419 · outbound

This paper cites A lower bound for k-dnf resolution on random CNF formulas via expansion.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication A lower bound for k-dnf resolution on random CNF formulas via expansion

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:11:34.178725Z

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 0db557fd-8a14-4f07-ba72-e6b87a4daed6 · outbound

This paper cites Communication Complexity of Set-Intersection Problems and Its Applications.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Communication Complexity of Set-Intersection Problems and Its Applications

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:11:34.124147Z

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 a84f4752-d96b-4f2b-ae42-7a1f435007ae · outbound

This paper cites Communication lower bounds for collision problems via density increment arguments.

Searching for Falsified Clause in Random (log n)-CNFs is Hard for Randomized Communication Communication lower bounds for collision problems via density increment arguments

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-06T17:11:31.666266Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.