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Paper Citation Record · LEDGER

Settling the no-$(k+1)$-in-line problem when $k$ is not small

As of 23 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 3 inbound Pith citation observations for arXiv:2502.00176.

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

pith.paper-citation-record.v1
2502.00176 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T20:12:02.064076Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:16:40.130553Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-07T21:34:09.297452Z

Reference resolution

28 of 28 outbound references displayed

  • verified exact0
  • verified fuzzy12
  • unresolved16
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 971c90ff-11af-4c15-8e66-08f52d9d55a4 · outbound

This paper cites Aichholzer, D.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Aichholzer, D

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T20:12:02.410385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.737779Z digest=sha256:abe3cdeef677418ae446633689b4499d5300e0d9cc6f2b5476596a74b2442f51

Observation ff8346c7-8f0e-4187-bd3d-6d0bee8f992d · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-09T20:12:02.402198Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.760520Z digest=sha256:3d7b6ec846039d256654ba83f141c71f0fec796378cb2d1a3179f123801fd6ab

Observation 5b30c182-23a0-4fea-b4ac-469e7ca3c543 · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-09T20:12:02.393933Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.787687Z digest=sha256:0acfaa2ccda0df1d289aa0a84fe0b3557939b5a03f9ae6fbfceafffc5cf56ad9

Observation fcfc94f5-5142-4b0d-9e20-90bfdcb8dc81 · outbound

This paper cites Ball and J.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Ball and J

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T20:12:02.384224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.812486Z digest=sha256:cb87a1b9a2a5fe5b17205609d503c83ace4c05a5305ed74fe8c2bbaaa9b5ccbf

Observation ab70d17c-c5ca-4b40-bc44-684b8d44e85e · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-09T20:12:02.374938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.816230Z digest=sha256:dbf15174efd7f50fda9c4b4a7d3eb95ff1341b70feff8b49055c4f6dd3843182

Observation f212afe0-a8a7-43b5-a5a8-e1a4a5547c89 · outbound

This paper cites Brass, W.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Brass, W

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T20:12:02.365367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.820481Z digest=sha256:e6802421395502d292bff7701cab8669c47cd273245a0abd63eb6d61cd5ba9f4

Observation 4d74dc42-bbd6-45c0-9fb7-1ea6c419a1bf · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-09T20:12:02.357498Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.824837Z digest=sha256:d0fe17cf745f05a2a7c63b8f2f6d52d31dcd97ef882d0fc77f462ac169f7864e

Observation 54eec69b-a8f0-4f54-a687-f5511288e2c6 · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-09T20:12:02.348787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.828661Z digest=sha256:20e93a009a775677f3d0515610af1350c12adbd5fe7aeac445be13de4b6e70a1

Observation 350d96e4-84d2-4e8d-876d-cd65d9d639eb · outbound

This paper cites Eppstein.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Eppstein

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T20:12:02.340734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.832593Z digest=sha256:2cf52a63415b25d862ed9319a65bb38cec8b0c753186627a6fdd74d443074b41

Observation 634b2858-a1ad-473f-aa44-186ac4bbdd85 · outbound

This paper cites Flammenkamp.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Flammenkamp

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T20:12:02.332639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.836845Z digest=sha256:8460c64367cdf766f43fefe62fa82db612c52fbb65e81f538404ce0083ab46d0

Observation 010d764a-dfbe-46c0-b318-36178f1b6ed2 · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-09T20:12:02.323409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.840703Z digest=sha256:66c112778dc33c82582b17754d7895e73b97e1b16e727a90560e5fe774458345

Observation b423efdf-9414-4a8b-9ed5-8ed9253c10cf · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-09T20:12:02.314208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.843945Z digest=sha256:76a12caf83b35552775d22c9e90a4e2477870d36636f576efe0b6ef3ef5807b6

Observation 872e43bc-17be-4a13-994f-874047e78b9a · outbound

This paper cites Greenhill and B.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Greenhill and B

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T20:12:02.304736Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.939944Z digest=sha256:64af0223e246d3e05c5f57b88e21c5ea843df799ac5661fc8d51837af5e21401

Observation cd45dc64-ddeb-43db-81a6-2e1e489ed44a · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-09T20:12:02.294828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.943907Z digest=sha256:883d3a38113353da3949fa2762af37f1e5a607e5683e13e390499820a9173058

Observation 323c48cd-7487-493d-8767-8a212aca77f6 · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-09T20:12:02.284867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.947516Z digest=sha256:1b32c799df4077b5e6940a51148f77721d5d30dbaa3066799eb20925fbc3b5c5

Observation ef5d6ade-c602-4250-b74c-16ede345e9db · outbound

This paper cites Isaev and B.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Isaev and B

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T20:12:02.275876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.950788Z digest=sha256:d6d10d0392f4f71c87f71bb02099b8ef508c91afd87398ff06ff767a7ffc7d75

Observation 219e4506-d9ac-405d-ba62-70998ce2daee · outbound

This paper cites Klimoˇ sov´ a, C.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Klimoˇ sov´ a, C

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T20:12:02.267502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.953708Z digest=sha256:5b6625a4f036ba046b797620a3b85e85ab6fa1b6deb16e7f20f6407722737b14

Observation 0a9ac89b-5a92-4a1c-b1ce-9147bf6d5e7e · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-09T20:12:02.257209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.956828Z digest=sha256:a78b2154e767bb6fabbcf18c4ea0ab03e0010ad2fbb8c6c3dec10de8f03b666d

Observation b1cfc41a-7b7d-4695-8e00-71869a46023a · outbound

This paper cites Liebenau and N.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Liebenau and N

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T20:12:02.246063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.959816Z digest=sha256:6cce4110d69716fd827cbc1c47e19d63a1f3b2d64308c91db2dc8ff318c4b4f8

Observation 0ce919fc-a9c8-4418-8834-08a3a2fe90d7 · outbound

This paper cites Chernoff's Inequality - A very elementary proof.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Chernoff's Inequality - A very elementary proof

Reference 20

Resolution
unresolved
no resolver link, observed 2026-08-09T20:12:01.962787Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T20:12:01.962787Z digest=sha256:cd318a7a733dac49a45b62b296f4c2a9d15254511fa9e7eb0c07511efe764b6a

Observation 3804b70d-49c7-4f82-a45f-6e3fe2a6b1f7 · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-09T20:12:02.235363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.966357Z digest=sha256:51a06f76ff9e82e6d03e9dda7abf4d03b0ba69e9cc33200f9ba8a201df4201f3

Observation cf58b6d7-cd18-445a-814b-3b4e8184b5fd · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-09T20:12:02.225931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.969227Z digest=sha256:0bfd2e92fc8d2de7206661755219ec82371f442ed3dab0b12fdc986697d07593

Observation f0e7ae6c-ab52-4e77-b908-c6f2c00feb03 · outbound

This paper cites Pach and G.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Pach and G

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T20:12:02.196249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.972524Z digest=sha256:0928cccea32e4838ca64343aff1e6c64f9842e97d00361af2169e9474dc29547

Observation 98080192-6954-4833-899e-16d66e5271bf · outbound

This paper cites P´ or and D.

Settling the no-$(k+1)$-in-line problem when $k$ is not small P´ or and D

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T20:12:02.185213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:01.984337Z digest=sha256:97c6d2bd50383e88cd994a622857ae0f8d08e1fd2184e2a2c5ded285cea15459

Observation 5c67f6fb-c0db-4867-8e62-d8b3f2ace37a · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-09T20:12:02.173615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:02.002890Z digest=sha256:11bb733255d7b09cb364ae08b2277778e3c6baa258a09ecc75f226d590765d3b

Observation 6c1874ec-ee98-49c7-ab56-b43c19b94b4d · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-09T20:12:02.163146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:02.023604Z digest=sha256:52181247a2e946a54af3b35ba6248486a3eb2d54e7dbdb1a8af02b2db255fe9a

Observation 1369affe-3956-45b7-a2cc-dfefb505b1de · outbound

This paper cites an unresolved cited work.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Unresolved cited work

Reference 27

Resolution
unresolved
no resolver link, observed 2026-08-09T20:12:02.044767Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T20:12:02.044767Z digest=sha256:57a56fdc89e8a14da816c578d8f72414f71ed28bd5dc7de12a72f4a7c2eef8dd

Observation eb5f2920-1ffa-4674-9a58-f9f04e733df5 · outbound

This paper cites Szemer´ edi and W.

Settling the no-$(k+1)$-in-line problem when $k$ is not small Szemer´ edi and W

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T20:12:02.146202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-09T20:12:02.064076Z digest=sha256:157b08fb89e3f4f1d28d5aebf64923357ff2d4e4ea276c8a11ffd66e185b1b45

Pith citing papers

Observation 5178682d-ca67-4514-ad60-7e56a2593df3 · inbound

Large grid subsets without many cospherical points cites this paper.

Large grid subsets without many cospherical points Settling the no-$(k+1)$-in-line problem when $k$ is not small

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-15T19:16:40.130553Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:16:40.130553Z digest=sha256:16844e293d1f3d78ed89579cb43f11a3d5ceedf8ee572e5bd9ea382c8c2ff8cd

Observation afdb14d3-1115-4399-8b01-fdd2e12fbf49 · inbound

The extensible no-$(k(n)+1)$-in-line problem cites this paper.

The extensible no-$(k(n)+1)$-in-line problem Settling the no-$(k+1)$-in-line problem when $k$ is not small

Reference 8

Resolution
metadata mismatch
arxiv_id, observed 2026-07-02T00:16:23.857012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-06-28T13:33:32.727981Z digest=sha256:df832c845562e1e981e1cb319140863a264b929425b9854bbf394c2f58849783

Observation 38353f86-fec8-42c0-bb69-4baf2eda52d6 · inbound

No-$(k+1)$-in-line problem for $k \geqslant 3$ cites this paper.

No-$(k+1)$-in-line problem for $k \geqslant 3$ Settling the no-$(k+1)$-in-line problem when $k$ is not small

Reference 27

Resolution
verified exact
local_arxiv, observed 2026-07-07T21:34:09.299195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-07-07T21:25:11.018193Z digest=sha256:fd98463f01e82f0a4a8f4bbf723fd8c786bc48b100f5eeb679bd7d29928b5eaf