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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:bcaf7c8553fb298ed6cbea834805c1e2874855a629a4245b8f9c1153d4051212

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=sha256:49b92c465be9e66536cf31548a18c36dfb223eafffec0624f19d1d6eeadd4907

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:d7f2f1420883799a0ceb063e8a29f28d4fc51aa456b5dcf418f7db596896e2f6

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:d11e533371e42189dc92a3a0da571536909534f202b033cc8499d7c7956fdd65

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=sha256:2c2b00f44fd386e47362ed88e13d4ca275292e34b817e81380376c22266225da

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=sha256:7bbe6b8f489a2945c2520bbed4411d3ff2323d9486faa09d0c18374c088e7bdb

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:a2246463535379c52965f71e879c66d8ecf384a8725842786c41fd77abbf264d

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=sha256:39749a5c65d26d43452fd131becded3a74a2fb40d7c8854c658a9f1177a07e57

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=sha256:9a6dac35547d5be22b6f5c0633cbfc4e208bb98b64390768270e26a5353222ef

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=sha256:6aab369394b77768182b62e05a33e958b04528658c3216be3520f10f30ed8d4c

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:f841d6ab07929801ce647a09f5964dc0149ad33e6509ffba9e0c83ea434e8241

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:be48f07c807a01da929e23e2dbca03f973cf9be337daaa9e158597bece0608ea

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=sha256:30cdc24b4b32cde74b3ab3c0692c79f239d3ad4a3009109ebfcaf1f393a8d2b6

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=sha256:24e77333f8bc59521372d632cfd6fb103127358ca9ffaebf6952edb6e8392cf4

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:e8b392657596e411642ba195fc0eba3eb5aa978bc947020f8cb0dff131f6de12

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:a889bbafbb91d7be8459626ef9862d6f8d79a5da6c6c5ca01d43becafef5049f

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=sha256:20ed767ba4337d8b6b474f380dbe61759f08726c6113f3f836f0ed1c6a706bc5

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:b8a568a9cda0f8b94221ef11a9401db7dd7695df197e0520221f7495e3320d8a

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=sha256:3af98f44f5dea69d96090a1cb278dc7116f03837b883d006720a7c13177e993a

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:d577ea50d82ea71b928f107d682aea59deb672a0cf91fe5e4bfff1f1aecffead

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:ba763cb741b68c8e7d9a6870d9bead516753f9979c9dedc5796fb9df91c1eb1c

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:a6907023aa20fa5b69689b23224033f0fdb68cdfdc7cf95920e00ecab50932e3