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Paper Citation Record · LEDGER

On Extremal Properties of k-CNF: Capturing Threshold Functions

As of 17 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:2412.20493.

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

pith.paper-citation-record.v1
2412.20493 v1

Coverage vector

measured 15 of 15 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:31:19.579039Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+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

15 of 15 outbound references displayed

  • verified exact1
  • verified fuzzy12
  • unresolved2
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2c188ae0-2a56-45e3-8004-5caf9d69c9a8 · outbound

This paper cites 26 Nikhil Vyas and Ryan Williams.

On Extremal Properties of k-CNF: Capturing Threshold Functions 26 Nikhil Vyas and Ryan Williams

Reference 1977

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:31:19.657179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:31:19.576066Z digest=sha256:6dc5a57010fd1a8b766053ccc584e7ba562c07b46470342b86dc307bb7fa5d44

Observation 7fc1aaee-2e65-4cc7-8e7d-d28ae1226ead · outbound

This paper cites The composition complexity of majority.

On Extremal Properties of k-CNF: Capturing Threshold Functions The composition complexity of majority

Reference 1984

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:31:19.709094Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:31:19.558568Z digest=sha256:47cb652288bc42f4cefe0a44bf6d94b7e1bc3d544384e6174f8856441c099cbb

Observation 4371d701-77af-4258-b529-5e5d6f556751 · outbound

This paper cites Super strong ETH is true for PPSZ with small resolution width.

On Extremal Properties of k-CNF: Capturing Threshold Functions Super strong ETH is true for PPSZ with small resolution width

Reference 1994

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:31:19.695162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:31:19.562108Z digest=sha256:6edcd2c44e843c940cd31daefdf4e7112b636f8f39cd404f070707445d2635a6

Observation 0560e80e-4e2d-407b-aeb6-119822054f14 · outbound

This paper cites Marques Silva and Inês Lynce.

On Extremal Properties of k-CNF: Capturing Threshold Functions Marques Silva and Inês Lynce

Reference 1995

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:31:19.681806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:31:19.565651Z digest=sha256:959ab9a31d3ff2194b87cb4285ef05d46c6f6eec2540841762fba98a667e69ff

Observation 889bef08-5d7f-42be-ba55-b7f435582d79 · outbound

This paper cites A variant of the vc-dimension with applications to depth-3 circuits.

On Extremal Properties of k-CNF: Capturing Threshold Functions A variant of the vc-dimension with applications to depth-3 circuits

Reference 2006

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:31:19.765731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:31:19.530827Z digest=sha256:75b655d5c9efd93195f498369f91a0a99e8277cd2042db36ba08119155b05d5f

Observation 8df28111-937e-460d-baf5-5418a78caf84 · outbound

This paper cites Towards an optimal cnf encoding of boolean cardinality constraints.

On Extremal Properties of k-CNF: Capturing Threshold Functions Towards an optimal cnf encoding of boolean cardinality constraints

Reference 2007

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:31:19.669464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:31:19.568978Z digest=sha256:a0579057c28d2f5e871f251c7ec5d23d6f08e5ea4ff752ec9b0545328362a982

Observation 642c2ebc-84d8-4485-8b60-4082a7dc6343 · outbound

This paper cites The existence of designs.

On Extremal Properties of k-CNF: Capturing Threshold Functions The existence of designs

Reference 2011

Resolution
unresolved
no resolver link, observed 2026-08-10T23:31:19.550525Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T23:31:19.550525Z digest=sha256:4fc7f1c4a75d4041c573bd1c2f7439ae2f6ea59c9d13673d57470e59e59f0c34

Observation 37dac377-d6aa-4809-a91e-4f39ad346b4f · outbound

This paper cites Klawe, Wolfgang J.

On Extremal Properties of k-CNF: Capturing Threshold Functions Klawe, Wolfgang J

Reference 2014

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:31:19.721042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:31:19.554956Z digest=sha256:9ff1d24628eac7265dfc6898419e173057afc775a3e0046855e657180c13a49a

Observation 7ca7ab44-264d-476a-b84b-f45d9bc75b6d · outbound

This paper cites Depth-three circuits for inner product and majority functions.

On Extremal Properties of k-CNF: Capturing Threshold Functions Depth-three circuits for inner product and majority functions

Reference 2016

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:31:19.789329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:31:19.520091Z digest=sha256:fa78fb180907bcb2eec65baebb54ed3efbd8ae3244c3f5e9a5ebfcd44f83762a

Observation b3bd52fb-3f30-49b5-8c9f-bd3f650e485c · outbound

This paper cites 27 Guy Wolfovitz.

On Extremal Properties of k-CNF: Capturing Threshold Functions 27 Guy Wolfovitz

Reference 2019

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:31:19.645175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:31:19.579039Z digest=sha256:813defa6fad9a1e465aefd0bbd2c03195c334bd67e417e2e5318141c19df580e

Observation 8e0b2a77-9a76-4a90-bb76-1414ca5323fb · outbound

This paper cites Maximizing the number of maximal independent sets of a fixed size.

On Extremal Properties of k-CNF: Capturing Threshold Functions Maximizing the number of maximal independent sets of a fixed size

Reference 2020

Resolution
verified exact
local_arxiv, observed 2026-08-10T23:31:19.616707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:31:19.572405Z digest=sha256:251a48ddefae3ff46dd5700434e24d996a06d93487518cbd91e31e3d878844fc

Observation 86edd99b-e402-4d12-ac92-bed48d169e0b · outbound

This paper cites Saks, and Navid Tale- banfard.

On Extremal Properties of k-CNF: Capturing Threshold Functions Saks, and Navid Tale- banfard

Reference 2021

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:31:19.742812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:31:19.540517Z digest=sha256:0cbf8f76c8864b161870b77d1a5c968338ea955d853c9acc0f7529cd8dec6922

Observation cc67c5e1-45fe-44bc-bad1-c2c8d253ae40 · outbound

This paper cites Kulikov, and R.

On Extremal Properties of k-CNF: Capturing Threshold Functions Kulikov, and R

Reference 2022

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:31:19.754111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:31:19.535922Z digest=sha256:777cb165d6216517871e639f60aadb352a039611402bd1026fd552ba2bcf393d

Observation b14fbc0d-3b7a-414d-90d2-8775aa23611e · outbound

This paper cites an unresolved cited work.

On Extremal Properties of k-CNF: Capturing Threshold Functions Unresolved cited work

Reference 2023

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:31:19.778161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:31:19.526130Z digest=sha256:292ff998a68ab969d0ba2a4d7b30551d82789220aacc85d6f0cbe85197c5c6c1

Observation fc076ff4-34c0-4d08-9cbd-9a5deb8f4ef5 · outbound

This paper cites Fasterk-sat algorithms using biased-ppsz.

On Extremal Properties of k-CNF: Capturing Threshold Functions Fasterk-sat algorithms using biased-ppsz

Reference 2024

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:31:19.731929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:31:19.545757Z digest=sha256:8eea6c41788c0daf4bc3eeede091633cb5c31692e3141fe75049d3560beac100

Pith citing papers

No inbound Pith citation observations are available.