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Paper Citation Record · LEDGER

The fractional Helly number for separable convexity spaces

As of 13 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 1 inbound Pith citation observation for arXiv:2412.01445.

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

pith.paper-citation-record.v1
2412.01445 v4

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T04:33:07.316799Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T22:09:37.472201Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-10T22:09:37.583510Z

Reference resolution

21 of 21 outbound references displayed

  • verified exact0
  • verified fuzzy9
  • unresolved12
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c630d765-8068-45bf-b1ff-e50391cc47aa · outbound

This paper cites an unresolved cited work.

The fractional Helly number for separable convexity spaces Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:33:07.647655Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.228526Z digest=sha256:3f136c20829810e21c09c705bd340de4400b6b15a44264836c4c776d996e583f

Observation 7d81e0a9-2df7-4b31-889e-44fefba11f92 · outbound

This paper cites Alon and D.

The fractional Helly number for separable convexity spaces Alon and D

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:33:07.634301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.234732Z digest=sha256:a47577aea24915f56baaf5c58421c074c90d84ccd99912d9cb73a738422d5c36

Observation e1fc9691-e63b-4fdd-b32b-7ef14b7eb909 · outbound

This paper cites an unresolved cited work.

The fractional Helly number for separable convexity spaces Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:33:07.621562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.239120Z digest=sha256:f7c299f74d36df2e41053bbcd2fa661cdac2e247e05a5856f43c084d02a22954

Observation 0ea0f19f-e135-485b-98b3-e5d5846fe79c · outbound

This paper cites an unresolved cited work.

The fractional Helly number for separable convexity spaces Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:33:07.607993Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.244218Z digest=sha256:ae4ce4a2f0cffe608795ad16392586f54105e894db857023edbd36b66bc22722

Observation ecb8605f-bc7b-44bc-afdc-41b660958c4c · outbound

This paper cites Bárány and G.

The fractional Helly number for separable convexity spaces Bárány and G

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:33:07.595982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.248180Z digest=sha256:5a177cb3a80e62b16b8d86e412ad6c12545ed0b6209f4d5d3ccce3cc741d3a2f

Observation 7eac5fa7-f7a5-41d6-9a65-a23acc6e4f88 · outbound

This paper cites Bárány and J.

The fractional Helly number for separable convexity spaces Bárány and J

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:33:07.583139Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.252451Z digest=sha256:aa358ffcc31653c30892b01d1108a7aa8d403a858e821883f69f0e59b17c801d

Observation 4f9832e4-1218-4f5a-9f60-fa183f8277f1 · outbound

This paper cites an unresolved cited work.

The fractional Helly number for separable convexity spaces Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:33:07.567912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.257115Z digest=sha256:652346088f919c39fd7fa912eefdd5038421cd2c61cc4e5065052aaf9d3fcbc1

Observation bb64aa7c-6cd5-4dbf-9d9d-a11557c6a78f · outbound

This paper cites an unresolved cited work.

The fractional Helly number for separable convexity spaces Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:33:07.553285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.261541Z digest=sha256:99be58de4f6525cfa5c990a552bfae97221eee2e374d13c53b1c71a6f31cdd45

Observation 60337c97-d13d-4470-aa6b-7f7152a90358 · outbound

This paper cites an unresolved cited work.

The fractional Helly number for separable convexity spaces Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:33:07.537163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.265595Z digest=sha256:6e3e8d9ef04c2270075cf8bcbe865ec00f042a2069f266830e8fbbe352f94ad3

Observation b1dc30c3-9b55-4f47-b45f-c097dfe1d364 · outbound

This paper cites Erd˝os and M.

The fractional Helly number for separable convexity spaces Erd˝os and M

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:33:07.522994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.270301Z digest=sha256:e81cf2aed6c38483441edfa702c3c71eed6fffcf610cc8b6737f7631d2b6fb0b

Observation 93d822b2-47d8-46e4-927c-c68dd18e7f18 · outbound

This paper cites an unresolved cited work.

The fractional Helly number for separable convexity spaces Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:33:07.506164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.275062Z digest=sha256:31f8ab5ce1924697e4f43913d486697cde67cfb8e2be6a27c18623d26dfb6d5a

Observation 20bdeb4c-a642-4b5b-8b6d-d8c9d0184929 · outbound

This paper cites an unresolved cited work.

The fractional Helly number for separable convexity spaces Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:33:07.489587Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.279363Z digest=sha256:d4876e17ec60ccaabddb445f11131d080f52fce150ea9348f7c7d784a1fcf667

Observation 0754a002-8241-49ef-be09-b0d48e5d6b07 · outbound

This paper cites an unresolved cited work.

The fractional Helly number for separable convexity spaces Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:33:07.475169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.283785Z digest=sha256:dbdad607fe5834146b3ab72fa4c4bb9680b7dc42413d000295856d587aba9f6a

Observation 1856532d-e736-4733-b612-cc71dfdb0443 · outbound

This paper cites Katchalski and A.

The fractional Helly number for separable convexity spaces Katchalski and A

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:33:07.460402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.288184Z digest=sha256:69347cf40b6133984b32b471a549731cbc9564bd4841212ccc38582ec7d76bb8

Observation 2b55c958-db23-4849-b9a8-ac44e5d58d42 · outbound

This paper cites an unresolved cited work.

The fractional Helly number for separable convexity spaces Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:33:07.445403Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.292286Z digest=sha256:c23f3a1b989a9b5d89102d2fc0132bdda7f2df9622af89b052c1d2e75b85b4a9

Observation 60cd9702-b410-4ba0-bdd6-847ea9c91f05 · outbound

This paper cites Martinez-Legaz and I.

The fractional Helly number for separable convexity spaces Martinez-Legaz and I

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:33:07.432040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.296316Z digest=sha256:3dae81cc6618b1ef67933d14b2da939e8cab31574cbd547c50b6dafff1753355

Observation 38775694-4c13-4e4d-897e-0e9178b1b692 · outbound

This paper cites Matoušek.

The fractional Helly number for separable convexity spaces Matoušek

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:33:07.416081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.300168Z digest=sha256:5c7dfa36ffed23ca563c1dbdc5b164ba07d609ed0df7c7880b242404ea3c775e

Observation 95c4f4da-aefc-4f7a-8f02-5d589c216aa9 · outbound

This paper cites Matoušek.

The fractional Helly number for separable convexity spaces Matoušek

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:33:07.398034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.304068Z digest=sha256:c5eb1653c93eda39513d91faf0b70eb0f518e7f6a66996a436e32c75145fdc21

Observation 8007b4ae-0ee4-4c03-bc09-cf5374d43870 · outbound

This paper cites Moran and A.

The fractional Helly number for separable convexity spaces Moran and A

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T04:33:07.382927Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.308200Z digest=sha256:58c04d4ee16296974e1d5d8334ea5921cfb4201ef2fe76db1ac0c729939f0d6a

Observation f1056d88-2855-4891-9c44-77e34102cbcd · outbound

This paper cites an unresolved cited work.

The fractional Helly number for separable convexity spaces Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:33:07.368569Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.312866Z digest=sha256:82f0606a8a73a3c5dc5de65cf3f4a9f214bed989dc0507fe598944ad7fec3df5

Observation 7f1b74c6-fa3a-4314-80e8-f8bbba0b25f6 · outbound

This paper cites an unresolved cited work.

The fractional Helly number for separable convexity spaces Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-12T04:33:07.354501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T04:33:07.316799Z digest=sha256:3e1ca57972bf718b588cc6cbcbdd9c4e110ff6061a9f2e1622a4e89a1699c8ac

Pith citing papers

Observation 8d09f7d4-a7ac-4714-88d1-eb7d7de075af · inbound

Helly-type theorems for separated $d$-intervals cites this paper.

Helly-type theorems for separated $d$-intervals The fractional Helly number for separable convexity spaces

Reference 20

Resolution
verified exact
local_arxiv, observed 2026-08-10T22:09:37.590631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-10T22:09:37.472201Z digest=sha256:f60c60b3e10ebe3da8a5240cebd8e9c0b66ecaa902a1b363fbcedd5d939417cc