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Paper Citation Record · LEDGER

Quality control in sublinear time: a case study via random graphs

As of 21 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 2 inbound Pith citation observations for arXiv:2508.16531.

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

pith.paper-citation-record.v1
2508.16531 v2

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T17:36:56.149986Z

measured 16 of 16 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:06:59.633890Z

measured 1 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T02:28:24.338817Z

Reference resolution

14 of 14 outbound references displayed

  • verified exact0
  • verified fuzzy10
  • unresolved3
  • parse uncertain0
  • malformed identifier1
  • metadata mismatch0

External citation measurements

0
pith, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 3604c38f-7258-44bc-a8d8-a3a6dfb89940 · outbound

This paper cites an unresolved cited work.

Quality control in sublinear time: a case study via random graphs Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-05T17:36:58.566818Z

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.

source=pdf_text observed=2026-08-05T17:36:55.042377Z digest=sha256:fb53bad0d0547fef386cd065205ea818dc244c2f2acd61dc27605e25d863ff49

Observation d4e12d89-7a62-416a-86a5-700dfe8ed6a2 · outbound

This paper cites The algorithm performs adjacency list, adjacency matrix, and degree queries.

Quality control in sublinear time: a case study via random graphs The algorithm performs adjacency list, adjacency matrix, and degree queries

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T17:36:58.397714Z

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.

source=pdf_text observed=2026-08-05T17:36:55.109615Z digest=sha256:b1651d422134f6f001b07dde440dc3492da70ad7d955736b7ecfd10dbb4baeeb

Observation 4576f226-7d77-405e-9d6f-62afaec637a6 · outbound

This paper cites If Algorithm A rejects, then reject.

Quality control in sublinear time: a case study via random graphs If Algorithm A rejects, then reject

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T17:36:58.255696Z

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.

source=pdf_text observed=2026-08-05T17:36:55.193684Z digest=sha256:ebc4af1971803f79718d25ee8afbfe612129871f3f723f0cbd7f0f16de8e2a76

Observation eacf722b-21dc-4f6b-8c6b-18ea698c402c · outbound

This paper cites If Algorithm B rejects, then reject.

Quality control in sublinear time: a case study via random graphs If Algorithm B rejects, then reject

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T17:36:58.098049Z

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.

source=pdf_text observed=2026-08-05T17:36:55.297791Z digest=sha256:62e271dafa1d5f0b32b9c7ec60a01bd3fd2a5762c5b90362704ef0ef4ada9f88

Observation 89a1feb1-a847-4617-a3c0-cc5c7a360110 · outbound

This paper cites If the output btis< t, then reject.

Quality control in sublinear time: a case study via random graphs If the output btis< t, then reject

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T17:36:57.936132Z

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.

source=pdf_text observed=2026-08-05T17:36:55.390328Z digest=sha256:e384c4ba70e84b5b6cbfb508c7f01c7e7dfa0d5c29b9747f25a4202d4bdd2fc9

Observation a3f13783-56a5-4510-8101-59d819f0a724 · outbound

This paper cites If the output btis>(1 + ε 2 ) n 3 p3, then reject.

Quality control in sublinear time: a case study via random graphs If the output btis>(1 + ε 2 ) n 3 p3, then reject

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T17:36:57.778364Z

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.

source=pdf_text observed=2026-08-05T17:36:55.471943Z digest=sha256:7396a24e4c8ec9e3f5e5d8a20c115baa88d51a638c5a3a52b17d444638f55c71

Observation 2c748914-9e71-4af6-af51-8e3c817c6e46 · outbound

This paper cites robust quasirandomness.

Quality control in sublinear time: a case study via random graphs robust quasirandomness

Reference 7

Resolution
malformed identifier
raw_fallback, observed 2026-08-05T17:36:57.651794Z

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.

source=pdf_text observed=2026-08-05T17:36:55.541667Z digest=sha256:a11bf11c10052ee0166bc758163887b856989f010b5d481cdf85162f9b7b5f77

Observation 75124f31-2639-4a30-9b87-92835f38f12b · outbound

This paper cites To see this, observe that such a circuit can only depend on at mostk d input variables/coordinates.

Quality control in sublinear time: a case study via random graphs To see this, observe that such a circuit can only depend on at mostk d input variables/coordinates

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T17:36:57.448797Z

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.

source=pdf_text observed=2026-08-05T17:36:55.613632Z digest=sha256:eff74abc177de701113f7da029a6b5a3b33df096a6b52b50896fc18522c25c34

Observation 8abbe268-cb20-4e5f-8e96-aaa78132944f · outbound

This paper cites Consider permutationsσ(x G) of theverticesof then-vertex input graphG.

Quality control in sublinear time: a case study via random graphs Consider permutationsσ(x G) of theverticesof then-vertex input graphG

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T17:36:57.273520Z

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.

source=pdf_text observed=2026-08-05T17:36:55.697633Z digest=sha256:4dc18694486499a3d8937985968ee9bb4654b465705ce5a4fa4d39031143e055

Observation 51932875-3109-4572-b230-3c49f0506cdc · outbound

This paper cites an unresolved cited work.

Quality control in sublinear time: a case study via random graphs Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-05T17:36:57.085640Z

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.

source=pdf_text observed=2026-08-05T17:36:55.791307Z digest=sha256:7d963344b88e0a354f8525bb114239380f52c3deb7bd51844cc17e22b8413e26

Observation 7970e241-ffc9-43c8-8174-608b7a7be3e7 · outbound

This paper cites Constructing an algorithm that is correct with high probability overD.

Quality control in sublinear time: a case study via random graphs Constructing an algorithm that is correct with high probability overD

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T17:36:56.914278Z

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.

source=pdf_text observed=2026-08-05T17:36:55.887762Z digest=sha256:75d01bf0b15c128680b66c50fa451237ad5a3bc6cd857551ead2ef215ccbe4c2

Observation d4c142fb-19e7-4a0f-a1ff-383b126db27e · outbound

This paper cites an unresolved cited work.

Quality control in sublinear time: a case study via random graphs Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-05T17:36:56.751474Z

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.

source=pdf_text observed=2026-08-05T17:36:55.947672Z digest=sha256:39402bdd64ec183079de90d88f8749bb86ee0ccccd0b1f411c2d0089a0537f95

Observation e7ce3ddd-4d10-4f15-9d3b-bc02fd8d5d93 · outbound

This paper cites Proof of Proposition C.1.First, by the correctness of algorithmsCandEfor quality control andρ-approximation, respectively, the algorithm always outputs a (1±ε)-approximation ofρ(x).

Quality control in sublinear time: a case study via random graphs Proof of Proposition C.1.First, by the correctness of algorithmsCandEfor quality control andρ-approximation, respectively, the algorithm always outputs a (1±ε)-approximation ofρ(x)

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T17:36:56.552652Z

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.

source=pdf_text observed=2026-08-05T17:36:56.054859Z digest=sha256:3e61d0830151a4f59564c7b9f27df748ceed7ce147dc6beb8487c7057abe55e5

Observation a7cb087d-5244-4cb7-941f-5c1243cceb2e · outbound

This paper cites Sincen 2 ≥2 2( k 2)+1np∆(H)/2 andn≥Cp −∆(H) , this is ≤E[X G]2 · 1 10 · 1 k2 · ε2 2k.

Quality control in sublinear time: a case study via random graphs Sincen 2 ≥2 2( k 2)+1np∆(H)/2 andn≥Cp −∆(H) , this is ≤E[X G]2 · 1 10 · 1 k2 · ε2 2k

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T17:36:56.382812Z

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.

source=pdf_text observed=2026-08-05T17:36:56.149986Z digest=sha256:49f08cd654a009aa2cf5a68a68b346b9d8e2da0aaddf2bf4e5b7106a13b01dcb

Pith citing papers

Observation d1e01075-8755-4fc1-822d-d306ae921e1d · inbound

Graph k-Coloring in Average Sublinear Time cites this paper.

Graph k-Coloring in Average Sublinear Time Quality control in sublinear time: a case study via random graphs

Reference 43

Resolution
verified exact
local_arxiv, observed 2026-08-01T13:04:33.554039Z

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.

source=arxiv_source observed=2026-08-01T13:00:57.942192Z digest=sha256:59c75e67229a164722b741d9ed39f6048b8cf57e277a60233696696ab90f4b1c

Observation dc203b69-d6d8-4632-93f6-66fbbda1f853 · inbound

Quality Control Algorithms for Pattern Counting cites this paper.

Quality Control Algorithms for Pattern Counting Quality control in sublinear time: a case study via random graphs

Reference 4

Resolution
unresolved
no resolver link, observed 2026-08-15T15:06:59.633890Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:06:59.633890Z digest=sha256:9504e5fc638125ee02362ca0bfbb52ad2cc5b6ecf52e17e34924bb031b035716