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Paper Citation Record · LEDGER

On $k$-antichains in the unit $n$-cube

As of 16 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:1908.04727.

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

pith.paper-citation-record.v1
1908.04727 v1

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T13:48:18.906169Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

20 of 20 outbound references displayed

  • verified exact4
  • verified fuzzy15
  • unresolved1
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 53737088-9c86-4085-8c95-e0e2eeb7d000 · outbound

This paper cites Anderson, Combinatorics of finite sets.

On $k$-antichains in the unit $n$-cube Anderson, Combinatorics of finite sets

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.273251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.812692Z digest=sha256:92c1feb78a7eef5c93c774f57a72a7cca96ad0245ddf312942621d9101166594

Observation f202f4fc-daf0-44cb-842b-5919dcd02926 · outbound

This paper cites Blokhuis, A.E.

On $k$-antichains in the unit $n$-cube Blokhuis, A.E

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.258001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.818647Z digest=sha256:bedc8e820032981940ca31671f554530269a38f7b3958daa0c3e39674ae837b0

Observation 892023ff-5448-4e24-a435-c48a97b02c21 · outbound

This paper cites The de Bruijn-Erd\H{o}s theorem from a Hausdorff measure point of view.

On $k$-antichains in the unit $n$-cube The de Bruijn-Erd\H{o}s theorem from a Hausdorff measure point of view

Reference 3

Resolution
verified exact
local_arxiv, observed 2026-08-14T13:48:19.009682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.823887Z digest=sha256:ba5a63d4aab5ecbd374cc04659882089223733e0cc3137211a566fc1868aecf2

Observation 2f308475-c459-4202-befb-dc2b106a3a95 · outbound

This paper cites Engel, A continuous version of a Sperner-type theorem, Elektron.

On $k$-antichains in the unit $n$-cube Engel, A continuous version of a Sperner-type theorem, Elektron

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.241936Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.828898Z digest=sha256:b6c53fafbf44ba948f68bf3cc2eeeea307f3234dc3977778d8dcd6b8b2e5bca3

Observation 1243cbd2-f754-41ab-9591-a7c465f24306 · outbound

This paper cites Engel, Sperner Theory, Encyclopedia of Mathematics and its Applications, 65.

On $k$-antichains in the unit $n$-cube Engel, Sperner Theory, Encyclopedia of Mathematics and its Applications, 65

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.224787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.833738Z digest=sha256:c756fab02d71a83623c059535144c32c165af23b3330ab50e707111a5deadc05

Observation 6cffb473-375d-40a1-9b74-4501d6fc7cfa · outbound

This paper cites A fractal perspective on optimal antichains and intersecting subsets of the unit $n$-cube.

On $k$-antichains in the unit $n$-cube A fractal perspective on optimal antichains and intersecting subsets of the unit $n$-cube

Reference 6

Resolution
verified exact
local_arxiv, observed 2026-08-14T13:48:18.989775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.838735Z digest=sha256:b9e993e696b39e09a82dce141183508bdc2b1c7805bb17235e351521af45cc5d

Observation 7deaefd3-b23e-44f2-8628-c6f5461432bd · outbound

This paper cites Projection inequalities for antichains.

On $k$-antichains in the unit $n$-cube Projection inequalities for antichains

Reference 7

Resolution
verified exact
local_arxiv, observed 2026-08-14T13:48:18.969093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.843730Z digest=sha256:3361e0ce6f434cc12946b58ff7a40ff209c2cf42b5bad794ebd3bf57ce52b28b

Observation 20f880e8-3f91-4fc1-aef6-faa46ad11225 · outbound

This paper cites Erd˝ os, On a lemma of Littlewood and Offord, Bull.

On $k$-antichains in the unit $n$-cube Erd˝ os, On a lemma of Littlewood and Offord, Bull

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.206693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.848894Z digest=sha256:3c1b79673850012b9f94783675521742c50939c9684027eb0e8b53e002710673

Observation 5fc8e5e3-cc5a-4716-b66a-b94f92e233a4 · outbound

This paper cites Evans, R.F.

On $k$-antichains in the unit $n$-cube Evans, R.F

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.190644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.853814Z digest=sha256:ddaf36aa2db6928c77fd167fa41fb97f8d2fce94aaba07249b3b26afce38449a

Observation 697f13a8-4a5b-4340-ab87-8d682c3b1013 · outbound

This paper cites Foran, The Length of the Graph of a One to One Function f rom [0, 1] to [0, 1], Real Anal.

On $k$-antichains in the unit $n$-cube Foran, The Length of the Graph of a One to One Function f rom [0, 1] to [0, 1], Real Anal

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.170519Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.858259Z digest=sha256:b76f62d3ae35677e8b9120923ab03442d1b6e2292c8c90fb28e34114062e40f5

Observation a5b0e5d4-c54c-4515-9ea5-24067a23fc1a · outbound

This paper cites Frankl, R.M.

On $k$-antichains in the unit $n$-cube Frankl, R.M

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.154413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.862964Z digest=sha256:b787dc86467ab05e0925d5e786ff6278940abaa0154c53a6dddf4a3ffa8dec8b

Observation 3f70ace9-aba8-472f-8e7e-c6d97c1896e8 · outbound

This paper cites Katona, Continuous versions of some extremal hyp ergraph problems, Com- binatorics (Proc.

On $k$-antichains in the unit $n$-cube Katona, Continuous versions of some extremal hyp ergraph problems, Com- binatorics (Proc

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.138331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.867733Z digest=sha256:0d96b0120b447cf7321944dda867bb194082648b36f0d59aaf917f3ed3f4cb83

Observation 34697dba-3f6d-478e-859a-2181b8012159 · outbound

This paper cites Katona, Continuous versions of some extremal hyp ergraph problems II, Acta Math.

On $k$-antichains in the unit $n$-cube Katona, Continuous versions of some extremal hyp ergraph problems II, Acta Math

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.122367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.872794Z digest=sha256:5bbb9d9f81b4c1fff3fba96f1ebdd248dc30afc23aa0a3268ad6efa34f62edcf

Observation 21ce174f-5dba-49df-8579-180a191214aa · outbound

This paper cites Klain, G.C.

On $k$-antichains in the unit $n$-cube Klain, G.C

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.106421Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.877335Z digest=sha256:941a5f4bd730fd745941a0dfe7b0cb0e440a1fdf007754651fcf3f86f31506fa

Observation 0d36e501-f8a6-465a-ba77-39d62614e85f · outbound

This paper cites Katchalski, R.

On $k$-antichains in the unit $n$-cube Katchalski, R

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.090440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.882536Z digest=sha256:a2f22a027ace17843e7949a4fdaca2536c8ddd265ccab8e11e5c18a016e9ab5b

Observation 1165f2a0-450a-4240-a5d6-ab43fb4663db · outbound

This paper cites A continuous analogue of Erd\H{o}s' $k$-Sperner theorem.

On $k$-antichains in the unit $n$-cube A continuous analogue of Erd\H{o}s' $k$-Sperner theorem

Reference 16

Resolution
verified exact
local_arxiv, observed 2026-08-14T13:48:18.947861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.886666Z digest=sha256:03e870126af6cecb67c93ee7ccef0d47d3690affc6c8c35a7a728fb3ce7a7951

Observation 23a5d7f3-57d9-4178-801c-04676af94e7a · outbound

This paper cites an unresolved cited work.

On $k$-antichains in the unit $n$-cube Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:48:19.073557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.891856Z digest=sha256:8e34b87ebcf26043d27752a0de0779b7e8eeb2f4e9d468c8ba79a6e24758e382

Observation b3c98b65-ba30-4f04-ad70-94cd332f9319 · outbound

This paper cites Saks, Theory of the Integral , Dover Publications, 1964.

On $k$-antichains in the unit $n$-cube Saks, Theory of the Integral , Dover Publications, 1964

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.058040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.896777Z digest=sha256:3e809524c4f98cc9a718d347babf2d3e5db83466068702b81f567c7aa7ac3471

Observation e1d387bd-426b-44e0-848c-1028cf7442c9 · outbound

This paper cites Schneider, Convex bodies: the Brunn-Minkowski theory , Second expanded edition, Encyclopedia of Mathematics and its Applications, vol.

On $k$-antichains in the unit $n$-cube Schneider, Convex bodies: the Brunn-Minkowski theory , Second expanded edition, Encyclopedia of Mathematics and its Applications, vol

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.042812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.901577Z digest=sha256:dd0492f46432aaf2a4ff9b10a5dbe27aa436e73568b6b385c959b75bbfc07c4a

Observation 47ca6140-6d2c-4ed7-99e4-f10751712313 · outbound

This paper cites Sperner, Ein Satz ¨ uber Untermengen einer endlichen Menge, Math.

On $k$-antichains in the unit $n$-cube Sperner, Ein Satz ¨ uber Untermengen einer endlichen Menge, Math

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:48:19.026357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:48:18.906169Z digest=sha256:db97ba6e704155629ad823a796bf9d46fbad4e76ae9edb1db74b97e5c3e681a2

Pith citing papers

No inbound Pith citation observations are available.