Paper Citation Record · LEDGER

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses

As of 8 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2506.03733.

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

pith.paper-citation-record.v1
2506.03733 v3

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:09:31.614331Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

23 of 23 outbound references displayed

verified exact1
verified fuzzy16
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4b80e5ad-28da-4724-810e-5f59701cd647 · outbound

This paper cites Azuma and M.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Azuma and M

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:36.174939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d029b0e8-b522-4c69-aa29-660ff9a13e19 · outbound

This paper cites an unresolved cited work.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:09:35.951098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7fd8cf4a-7118-400a-92b1-cb455f993288 · outbound

This paper cites Gurvits and H.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Gurvits and H

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:35.816613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 06186344-73b1-4f4e-a834-33a0f5a87639 · outbound

This paper cites Ha and S.-H.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Ha and S.-H

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:35.666902Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c50c9620-2fe2-43c5-a982-941e19382dea · outbound

This paper cites Global locations of Schmidt number witnesses.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Global locations of Schmidt number witnesses

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-07T11:09:31.783652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2fd1fb68-90fc-4e06-a8eb-cd41453885dd · outbound

This paper cites Jamio/suppress lkowski,Linear transformations which preserve trace and positive s emideﬁnite operators, Rep.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Jamio/suppress lkowski,Linear transformations which preserve trace and positive s emideﬁnite operators, Rep

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:35.501970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7095a758-e676-4ca4-b261-3e2f044ff256 · outbound

This paper cites Kye, Facial structures for positive linear maps between matrix a lgebras, Canad.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Kye, Facial structures for positive linear maps between matrix a lgebras, Canad

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:35.344010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b6c818a2-25c3-42ed-8955-ac3a6744dbe4 · outbound

This paper cites Kye, Boundaries of the cone of positive linear maps and subcones i n matrix algebras, J.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Kye, Boundaries of the cone of positive linear maps and subcones i n matrix algebras, J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:35.123138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0b5afcc5-08ad-4231-b34e-1276aebf294a · outbound

This paper cites Kye, On the convex set of all completely positive linear maps in ma trix algebras, Math.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Kye, On the convex set of all completely positive linear maps in ma trix algebras, Math

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:34.898369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dd675fd2-04fe-4a78-9fd0-285b35e2dba9 · outbound

This paper cites Kye, Facial structures for various notions of positivity and app lications to the theory of entanglement, Rev.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Kye, Facial structures for various notions of positivity and app lications to the theory of entanglement, Rev

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:34.718477Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4819e77d-1baa-4ed5-a462-d486eecf2138 · outbound

This paper cites Kye, Exposedness of elementary positive maps between matrix alg ebras, Linear Multilinear Alg.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Kye, Exposedness of elementary positive maps between matrix alg ebras, Linear Multilinear Alg

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:34.461278Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 29422378-ab09-440b-92c7-f989127f87c6 · outbound

This paper cites Positive Maps in Quantum Information Theory.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Positive Maps in Quantum Information Theory

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:34.240700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 820c79d9-519f-40dd-b4b3-dfe926d9e2ef · outbound

This paper cites Lewenstein, B.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Lewenstein, B

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:34.021790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e4dde224-e292-494d-81ef-f4872acf7301 · outbound

This paper cites Li and C.-F.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Li and C.-F

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:33.838575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4de8a82c-b8fd-4f18-b505-f61875daf429 · outbound

This paper cites Marciniak, Rank properties of exposed positive maps, Linear Multilinear Alg.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Marciniak, Rank properties of exposed positive maps, Linear Multilinear Alg

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:33.627227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f022d83a-381f-4775-8a2c-536b7f82ac6c · outbound

This paper cites an unresolved cited work.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:09:33.437679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 40bc0612-2d2a-47a8-869a-bb74b8886e3c · outbound

This paper cites Sanpera, D.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Sanpera, D

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:33.248046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4c5282c5-e857-42f0-9f0a-feb8e755a6fd · outbound

This paper cites Skowronek, E.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Skowronek, E

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:33.027818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e9424250-bed9-41ee-94f5-56ea56a1880c · outbound

This paper cites an unresolved cited work.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:09:32.807874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a0b52277-9b3b-4ab0-b9d9-d949bc85348e · outbound

This paper cites an unresolved cited work.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:09:32.587658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 94ed9585-1ec1-480d-9145-8da950a9e501 · outbound

This paper cites an unresolved cited work.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:09:32.341347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 415ffe5f-093a-432e-b078-0614e96ae79d · outbound

This paper cites an unresolved cited work.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:09:32.125861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5dc4c465-3560-4bab-993b-040b3d79e70a · outbound

This paper cites Yang, J.-L.

Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses Yang, J.-L

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:09:31.940985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.