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Paper Citation Record · LEDGER

Linear equations and chromatic thresholds in $B_h$ sets

As of 12 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2606.30767.

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

pith.paper-citation-record.v1
2606.30767 v2

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-03T22:24:35.160412Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

22 of 22 outbound references displayed

  • verified exact3
  • verified fuzzy8
  • unresolved11
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a13146f5-594c-40f8-905c-3f4b3b5d4613 · outbound

This paper cites an unresolved cited work.

Linear equations and chromatic thresholds in $B_h$ sets Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-07-05T00:30:28.902391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:3eae11ea9255fb31636eea38ae5444b9a3963fd91b3fb8e1e365949e56ecf58c

Observation 37ff6a80-46d9-44cc-a98a-dddaed3cce59 · outbound

This paper cites 5, 497–511.

Linear equations and chromatic thresholds in $B_h$ sets 5, 497–511

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-07-05T00:30:28.914715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:9c50d323157decfae340deb0b855f1f5c70823bf929da634760fd23c7646e291

Observation 8b0e6716-f60c-48b1-9824-31c4527e147b · outbound

This paper cites an unresolved cited work.

Linear equations and chromatic thresholds in $B_h$ sets Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-07-05T00:30:28.918823Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:8cff10b832a321f5bfe70a849b8a6137ed43bdb5727fa9c8c0ab7bd6df0419c9

Observation 2e9418b2-b087-4de8-b885-004703457525 · outbound

This paper cites an unresolved cited work.

Linear equations and chromatic thresholds in $B_h$ sets Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-07-05T00:30:28.922242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:c8a3b902f51a22801aaf1e5cc0454358a3d8c251af23a80323335a4192750981

Observation c631d4c9-30b4-4c5e-87da-ff2acfed90bf · outbound

This paper cites Erdős and M.

Linear equations and chromatic thresholds in $B_h$ sets Erdős and M

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-07-05T00:30:28.930173Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:dac57ea4d307b5710f7c05024fbd24f0135594d6aa807fa2c139a22bf67de5d9

Observation c26908d8-bbfc-4f22-ab5b-6dc7d583ecca · outbound

This paper cites Erdős and P.

Linear equations and chromatic thresholds in $B_h$ sets Erdős and P

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-07-05T00:30:28.921287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:fb3029d713258b969a5778fb6f7b7231d503883678a75ab64ae383527f34995c

Observation 284355b4-0c2f-4f48-a677-e3bca668db6c · outbound

This paper cites an unresolved cited work.

Linear equations and chromatic thresholds in $B_h$ sets Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-07-05T00:30:28.907049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:ee12a14150acc0fedcf37a456fc02ad08a646cd4feb05d6810f0379d3fdf4117

Observation d97f4293-19f2-4987-ab82-1920cb5404ea · outbound

This paper cites 84, Springer-Verlag, New York, (1990).

Linear equations and chromatic thresholds in $B_h$ sets 84, Springer-Verlag, New York, (1990)

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-07-05T00:30:28.904799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:493186dd874cb0abaa43861db0115c0f96c2a20f7fe5cf45320c6d57c633a61a

Observation d3779f84-dc8b-474c-ae20-b3de2d6a2fca · outbound

This paper cites Number Theory44(1993), no.

Linear equations and chromatic thresholds in $B_h$ sets Number Theory44(1993), no

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-07-05T00:30:28.908840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:75cfbb44390f716eab7044bab1d58d5637d5332f400cb1ae01d1c3074198a3ea

Observation 88d006aa-ba70-424b-ac07-c1bd98c3fd4d · outbound

This paper cites arXiv:2601.18738.

Linear equations and chromatic thresholds in $B_h$ sets arXiv:2601.18738

Reference 10

Resolution
verified exact
arxiv_id, observed 2026-07-03T22:29:00.012008Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:2daf56a0fa60c2d47ebb995c0222eea3e8f2bbf6753bd768dce55221fff5ace6

Observation 66923e39-2311-43b9-b234-ef9e86f1ad71 · outbound

This paper cites an unresolved cited work.

Linear equations and chromatic thresholds in $B_h$ sets Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-07-05T00:30:28.912238Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:4279d5e2525b94c9efefcbb3c21a5cd9c5bdc9c6bc51377c82e7523ad8566db4

Observation 6a311cff-14e2-4ea7-ad51-e76679a9501f · outbound

This paper cites an unresolved cited work.

Linear equations and chromatic thresholds in $B_h$ sets Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-07-05T00:30:28.913964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:9ed35751ef48fc82be36050d108881974cc55f51cc42a0a0616e29943eaf8e1c

Observation aa52008b-2213-4964-bdd5-61800633b42f · outbound

This paper cites Chromatic thresholds for linear equations and recurrence.

Linear equations and chromatic thresholds in $B_h$ sets Chromatic thresholds for linear equations and recurrence

Reference 13

Resolution
verified exact
local_arxiv, observed 2026-07-03T22:29:00.014446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:eb4a2cf98892a6673a43732e50d46bfa8b90d2fb39784a022108e352753d71a1

Observation 84ba0cec-af6b-4479-98f7-dd1d74504a08 · outbound

This paper cites an unresolved cited work.

Linear equations and chromatic thresholds in $B_h$ sets Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-07-05T00:30:28.915695Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:3dab8696af5591d2cff8b8d23c150634f5493a21ddbdcd6cc0c12350150b05d4

Observation 7b0b457b-0acd-4f0c-b7a6-02bfec13bacc · outbound

This paper cites an unresolved cited work.

Linear equations and chromatic thresholds in $B_h$ sets Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-07-05T00:30:28.928383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:27596ae63bb5489e151f737b183a9b64c628e24c28d62ccbaee0e75202f592e7

Observation e6f451fe-e7b6-4361-bf32-b114903056df · outbound

This paper cites an unresolved cited work.

Linear equations and chromatic thresholds in $B_h$ sets Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-07-05T00:30:28.926567Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:c977716e5d181e71dbc99210fcb18d3e8a78e91d5947f2f24276eac4b2ffcfb5

Observation f68be64d-7c26-4418-95d9-d0c6818884da · outbound

This paper cites an unresolved cited work.

Linear equations and chromatic thresholds in $B_h$ sets Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-07-05T00:30:28.931807Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:2e1fd4f090e298c476bf2afb62d614780900a87a920c7a9e7f382bb18b81f753

Observation c0aa9786-43de-41bc-b2ae-188cac546a57 · outbound

This paper cites Ruzsa,Solving a linear equation in a set of integers.

Linear equations and chromatic thresholds in $B_h$ sets Ruzsa,Solving a linear equation in a set of integers

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-07-05T00:30:28.910739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:d702bb125fd18d55a839a959ae4b937d7c4287abaedf3a538c2c23037fc5a71e

Observation 28ff95e0-945a-4886-ae47-f1dbe559198f · outbound

This paper cites an unresolved cited work.

Linear equations and chromatic thresholds in $B_h$ sets Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-07-05T00:30:28.912636Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:24502bdb5d566fa91e3e3286a726fff3c8b36841fe06a0b89ec6140681b40c17

Observation 42293041-8d08-4205-b0b3-f96b63afbaae · outbound

This paper cites Coloring sparse random Cayley graphs.

Linear equations and chromatic thresholds in $B_h$ sets Coloring sparse random Cayley graphs

Reference 20

Resolution
verified exact
local_arxiv, observed 2026-07-03T22:29:00.017173Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:fe05b47ff7ef3a1e4ebd490ea8b8d44950ed3de21a12b2b1e94b4b6f95a2e09b

Observation e976a876-966e-4053-be09-0a5f3a10e8ee · outbound

This paper cites Varnavides,On certain sets of positive density, J.

Linear equations and chromatic thresholds in $B_h$ sets Varnavides,On certain sets of positive density, J

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-07-05T00:30:28.923050Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-07-03T22:24:35.160412Z digest=sha256:abef785c80a79bff5f5f2d47644717928d3215958e335fabe7fd7e190b315d28

Observation c9d613d5-f6fa-4204-a0d2-9680dfd726b4 · outbound

This paper cites Combin.32(2011), no.

Linear equations and chromatic thresholds in $B_h$ sets Combin.32(2011), no

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-07-05T00:30:28.924684Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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Pith citing papers

No inbound Pith citation observations are available.