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Paper Citation Record · LEDGER

Entrywise application of non-linear functions on orthogonally invariant matrices

As of 21 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2412.06943.

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

pith.paper-citation-record.v1
2412.06943 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T19:26:31.995669Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+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

25 of 25 outbound references displayed

  • verified exact0
  • verified fuzzy13
  • unresolved12
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 79ad3acf-d6da-4389-9a4b-a664c4d5fa72 · outbound

This paper cites 118, Cambridge university press, 2010.

Entrywise application of non-linear functions on orthogonally invariant matrices 118, Cambridge university press, 2010

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:32.428015Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.924899Z digest=sha256:0d813d105f46e271452af7efd0fdd57489339b27c77068ae518e6466619c03f3

Observation c707a283-780f-4fc9-aa9c-f71c44e53c21 · outbound

This paper cites an unresolved cited work.

Entrywise application of non-linear functions on orthogonally invariant matrices Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:32.419599Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 6e7bf388-6109-4e2c-a149-2bc2afc6b7be · outbound

This paper cites an unresolved cited work.

Entrywise application of non-linear functions on orthogonally invariant matrices Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:32.409545Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.932129Z digest=sha256:3c0e2f35a16d0c084c8ebc43e81dde82600b2277e8e2cfca40b82fc337c6f3ee

Observation 14bfd5b4-e157-45eb-9add-2378ff99cb29 · outbound

This paper cites Capitaine and M.

Entrywise application of non-linear functions on orthogonally invariant matrices Capitaine and M

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:32.337055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.935127Z digest=sha256:687eb6808edca8749a9a3960975f09816526e1451ba830fe391f222b4762e150

Observation cfe2484c-f477-4c38-8ed4-7575c052692a · outbound

This paper cites an unresolved cited work.

Entrywise application of non-linear functions on orthogonally invariant matrices Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:32.220976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.938048Z digest=sha256:10e47f14e972a82317db0d43c63633cfc0280fad668112569afd32c5512cb8bf

Observation 76cf6b61-29d6-4ee0-962f-84c859904a11 · outbound

This paper cites III : Higher order freeness and free cumulants , Documenta Mathematica 12 (2007), 1--70.

Entrywise application of non-linear functions on orthogonally invariant matrices III : Higher order freeness and free cumulants , Documenta Mathematica 12 (2007), 1--70

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:32.180631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.940824Z digest=sha256:ae4364747456601cb327102a89bd6bd1911f26f40405296490f42644d8614bc1

Observation c66b4ba4-eb9a-4728-8b0a-5acc0327b73a · outbound

This paper cites 17, 953--982.

Entrywise application of non-linear functions on orthogonally invariant matrices 17, 953--982

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:32.172473Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.943696Z digest=sha256:4d0dd36bf5bbfb3a444006a2c166b12b5ae1d5fd739d06f3bcf02d83bc1d7715

Observation c6a097ca-484c-4741-9eaf-be9deb2579b2 · outbound

This paper cites 3, 773--795.

Entrywise application of non-linear functions on orthogonally invariant matrices 3, 773--795

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:32.164826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.946513Z digest=sha256:23be77bcce7a5689db915add3cdb3fe73bb51fc2c4370f642b8b9a62185dd4ae

Observation 954eb902-4a48-4785-b107-f19abde83525 · outbound

This paper cites 04, 1350010.

Entrywise application of non-linear functions on orthogonally invariant matrices 04, 1350010

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:32.157084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.949220Z digest=sha256:ba18f09d4ba12be03e8d3194955c456fd34336aeaa5ef4ec608c3d2fe19ad26f

Observation 9fbb48f0-fe4f-40db-aebb-4585959456c4 · outbound

This paper cites an unresolved cited work.

Entrywise application of non-linear functions on orthogonally invariant matrices Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:32.149326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.951478Z digest=sha256:3d656a0d9ea15eef51e8bcc58b84427a4e3615137546de4d2451eadbcfd6014b

Observation dbd626db-41ac-4e8f-82ca-08176cd8b9bf · outbound

This paper cites Designs via Free Probability.

Entrywise application of non-linear functions on orthogonally invariant matrices Designs via Free Probability

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-11T19:26:31.954391Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-11T19:26:31.954391Z digest=sha256:f112c61832d3c99565851971657775e278c0c94022ff38b5ff1a009cf96fc7d7

Observation c22ae42a-cf35-4de7-b513-e099cad25c47 · outbound

This paper cites an unresolved cited work.

Entrywise application of non-linear functions on orthogonally invariant matrices Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:32.141191Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.958239Z digest=sha256:cf0270ef1cb3d3397361b4c4d00efb84aa47e455eb1a5c3501f9f9a12f0a3ea3

Observation 8044279c-537d-420e-8d66-8ca110c76993 · outbound

This paper cites an unresolved cited work.

Entrywise application of non-linear functions on orthogonally invariant matrices Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:32.133809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.961404Z digest=sha256:aace1bbaf00eb3ad83eb4dcaef5b5a27f2fda1e8c16349ed0b8916d41475ed32

Observation ac81067c-2cbc-4e3f-ac6e-5292d1a30e01 · outbound

This paper cites 426--471.

Entrywise application of non-linear functions on orthogonally invariant matrices 426--471

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:32.125158Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.964622Z digest=sha256:ecbc0118ea37424fa89cc0c8e1553afd218e13d08f98b9c83fcafe770972ece7

Observation 78116908-0507-4280-8c84-09a8c0534ab7 · outbound

This paper cites an unresolved cited work.

Entrywise application of non-linear functions on orthogonally invariant matrices Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:32.115909Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.967456Z digest=sha256:558a692e276dc0ebac6a7eac267c4df6b1d5054d62ed74efdbf5c095a0579575

Observation 38cdb8b5-3c70-4dbe-9958-e677066c2762 · outbound

This paper cites 2, 1190--1248.

Entrywise application of non-linear functions on orthogonally invariant matrices 2, 1190--1248

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:32.106821Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.970202Z digest=sha256:4219d70728b386156d4873a35e386dc66bd4b89477e3854c211936d3d53e62a5

Observation fc6439f5-fd87-4681-b498-8abc3331dd78 · outbound

This paper cites 3, 319--329.

Entrywise application of non-linear functions on orthogonally invariant matrices 3, 319--329

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:32.098190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.973111Z digest=sha256:3b394695a90258a679c5b2d49b43363722ef316e5709624f54168de03675685c

Observation 772508fa-e317-4aac-9fa1-923ae883ef0e · outbound

This paper cites 11, 113301.

Entrywise application of non-linear functions on orthogonally invariant matrices 11, 113301

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:32.090530Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.975564Z digest=sha256:2ca8b83172610b2694cdc35e706d65c67e74ac4506e9bc633219b517df568916

Observation 7354add6-9b97-48df-9713-9248a00165c6 · outbound

This paper cites an unresolved cited work.

Entrywise application of non-linear functions on orthogonally invariant matrices Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:32.082840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.978091Z digest=sha256:c0cefbacd800a4fb36841358264241c479fb2828064ce0d0078002539fc3d1a3

Observation 99b6287c-3d0b-47ab-86b5-5aac7890f799 · outbound

This paper cites an unresolved cited work.

Entrywise application of non-linear functions on orthogonally invariant matrices Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:32.075124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 85f9326c-3bda-4215-9c89-0d0c4c01f81f · outbound

This paper cites 13, Cambridge University Press, 2006.

Entrywise application of non-linear functions on orthogonally invariant matrices 13, Cambridge University Press, 2006

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:32.066355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.984679Z digest=sha256:2f7035ec490609471c5ce48c04bfd395dd20ff33859027ae9c6a4bb7da291650

Observation 594bc698-85b6-4612-b328-f92269ed604f · outbound

This paper cites 17, 170603.

Entrywise application of non-linear functions on orthogonally invariant matrices 17, 170603

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:32.056661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.987458Z digest=sha256:2f37c467ac90e25db0e88b5faa5b523f283f36cf5a3d8468b5a8f128517241ca

Observation c7129fe8-245b-4e73-a3ac-33ce45368ce6 · outbound

This paper cites an unresolved cited work.

Entrywise application of non-linear functions on orthogonally invariant matrices Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:32.047415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.990424Z digest=sha256:14399d9cf50b1f53f5c87bc812a110cdcf0866cac90f8e59d010a41d9c59aa17

Observation 478de86d-0f3e-46a3-8bfa-a96ec6336a47 · outbound

This paper cites an unresolved cited work.

Entrywise application of non-linear functions on orthogonally invariant matrices Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-11T19:26:32.038778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-11T19:26:31.993114Z digest=sha256:455ee68fcfad28dddc4b8aaed4f16d0cd1b0dc6184b66240d2e67a78b1a3d262

Observation 6d765498-23ed-4e34-bd03-b5d2ff5a683a · outbound

This paper cites T heory of M \"o bius functions , Probability Theory and Related Fields 2 (1964), no.

Entrywise application of non-linear functions on orthogonally invariant matrices T heory of M \"o bius functions , Probability Theory and Related Fields 2 (1964), no

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T19:26:32.029339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Pith citing papers

No inbound Pith citation observations are available.