Paper Citation Record · LEDGER

Well-invertible column subsets of sparse matrices are rare

As of 16 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 1 inbound Pith citation observation for arXiv:2607.05384.

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

pith.paper-citation-record.v1
2607.05384 v2

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T07:08:16.892784Z

measured 30 of 30 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T04:00:42.073669Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

29 of 29 outbound references displayed

verified exact0
verified fuzzy0
unresolved29
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0885519a-184f-4ba2-b9c0-fdeb3cb28f48 · outbound

This paper cites Bourgain and L.

Well-invertible column subsets of sparse matrices are rare Bourgain and L

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 31f54dd0-36f5-447d-840c-d070105776e4 · outbound

This paper cites Bourgain and L.

Well-invertible column subsets of sparse matrices are rare Bourgain and L

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 987f5794-ef0f-445e-8e75-cc41d9268d39 · outbound

This paper cites Bourgain and L.

Well-invertible column subsets of sparse matrices are rare Bourgain and L

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a5c8176-5e7c-4124-b4df-a2ee51614143 · outbound

This paper cites an unresolved cited work.

Well-invertible column subsets of sparse matrices are rare Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 35239739-2269-42f6-86ec-dca3010e7da7 · outbound

This paper cites Faster Linear Algebra Algorithms with Structured Random Matrices.

Well-invertible column subsets of sparse matrices are rare Faster Linear Algebra Algorithms with Structured Random Matrices

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4781d3ce-3adf-40fc-9779-bd995bb359f2 · outbound

This paper cites an unresolved cited work.

Well-invertible column subsets of sparse matrices are rare Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5354a3a4-0218-48ed-8ca7-e10a655764f4 · outbound

This paper cites Optimal Oblivious Subspace Embeddings with Near-optimal Sparsity.

Well-invertible column subsets of sparse matrices are rare Optimal Oblivious Subspace Embeddings with Near-optimal Sparsity

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f091fc4-9036-4bd3-bf09-d36e287f259b · outbound

This paper cites 4501–4559.

Well-invertible column subsets of sparse matrices are rare 4501–4559

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d30e77e-55e2-4227-beb3-e26cd60c7b21 · outbound

This paper cites Clarkson and David P.

Well-invertible column subsets of sparse matrices are rare Clarkson and David P

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 85a58598-e175-4edb-b227-3d538a7ab048 · outbound

This paper cites Cohen,Nearly tight oblivious subspace embeddings by trace inequalities, inProceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms, 2016, pp.

Well-invertible column subsets of sparse matrices are rare Cohen,Nearly tight oblivious subspace embeddings by trace inequalities, inProceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms, 2016, pp

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6b6929d1-3b62-4b01-9688-e3fc8726e276 · outbound

This paper cites Halmos and Herbert E.

Well-invertible column subsets of sparse matrices are rare Halmos and Herbert E

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12d56e09-32d6-441a-ba56-153b3104f200 · outbound

This paper cites an unresolved cited work.

Well-invertible column subsets of sparse matrices are rare Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 34844727-ca12-49da-8a57-475518f84fb3 · outbound

This paper cites 301, 13–30.

Well-invertible column subsets of sparse matrices are rare 301, 13–30

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bd537744-60c3-4046-be3a-3aa92245e36e · outbound

This paper cites Kane and Jelani Nelson,Sparser Johnson–Lindenstrauss transforms, Journal of the ACM61(2014), no.

Well-invertible column subsets of sparse matrices are rare Kane and Jelani Nelson,Sparser Johnson–Lindenstrauss transforms, Journal of the ACM61(2014), no

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a60cde4-ffd5-4e11-a7d1-f78ea659740a · outbound

This paper cites Mahoney,Randomized algorithms for matrices and data, Foundations and Trends in Machine Learning3 (2011), no.

Well-invertible column subsets of sparse matrices are rare Mahoney,Randomized algorithms for matrices and data, Foundations and Trends in Machine Learning3 (2011), no

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 84b8e43d-8342-46b0-aefb-2202723e01d1 · outbound

This paper cites Marcus, Daniel A.

Well-invertible column subsets of sparse matrices are rare Marcus, Daniel A

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c64bb49-b440-4695-97b5-4db8583dfa84 · outbound

This paper cites Interlacing Families III: Sharper Restricted Invertibility Estimates.

Well-invertible column subsets of sparse matrices are rare Interlacing Families III: Sharper Restricted Invertibility Estimates

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d2f76469-4f62-416a-a63a-773ba9f649af · outbound

This paper cites Tropp,Randomized numerical linear algebra: Foundations and algorithms, Acta Numerica29(2020), 403–572.

Well-invertible column subsets of sparse matrices are rare Tropp,Randomized numerical linear algebra: Foundations and algorithms, Acta Numerica29(2020), 403–572

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 199bae30-2576-4a44-bbd6-cd5830f9d456 · outbound

This paper cites an unresolved cited work.

Well-invertible column subsets of sparse matrices are rare Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee23f625-2c96-406a-b5ca-d01358b271f2 · outbound

This paper cites an unresolved cited work.

Well-invertible column subsets of sparse matrices are rare Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2018a1f1-45a1-425a-a545-474291e27eed · outbound

This paper cites Lower bounds for oblivious subspace embeddings.

Well-invertible column subsets of sparse matrices are rare Lower bounds for oblivious subspace embeddings

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4c11ba22-7ec1-43ab-b40f-b454a5177048 · outbound

This paper cites OSNAP: Faster numerical linear algebra algorithms via sparser subspace embeddings.

Well-invertible column subsets of sparse matrices are rare OSNAP: Faster numerical linear algebra algorithms via sparser subspace embeddings

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fdf45fef-cee2-4637-8b7b-e5a0439fc867 · outbound

This paper cites 24, Springer-Verlag, Berlin, 2003.

Well-invertible column subsets of sparse matrices are rare 24, Springer-Verlag, Berlin, 2003

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ef544562-2b8c-4ccf-b870-40f494898357 · outbound

This paper cites Spielman and Nikhil Srivastava,An elementary proof of the restricted invertibility theorem, Israel J.

Well-invertible column subsets of sparse matrices are rare Spielman and Nikhil Srivastava,An elementary proof of the restricted invertibility theorem, Israel J

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b31ac04c-0ea1-44c4-97d0-3fc53796f4d8 · outbound

This paper cites Oblivious Subspace Injection Is Not Enough for Relative Error.

Well-invertible column subsets of sparse matrices are rare Oblivious Subspace Injection Is Not Enough for Relative Error

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5ad1fea3-48c5-4455-a3ef-4de82634913d · outbound

This paper cites Comparison theorems for the extreme eigenvalues of a random symmetric matrix.

Well-invertible column subsets of sparse matrices are rare Comparison theorems for the extreme eigenvalues of a random symmetric matrix

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 57c3063a-bdec-437b-90fe-13f6c2164faa · outbound

This paper cites Vershynin,John’s decompositions: selecting a large part, Israel J.

Well-invertible column subsets of sparse matrices are rare Vershynin,John’s decompositions: selecting a large part, Israel J

Reference 27

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 76458c4e-f30b-47cf-8235-3329bee26290 · outbound

This paper cites Woodruff,Sketching as a tool for numerical linear algebra, Foundations and Trends in Theoretical Computer Science10(2014), no.

Well-invertible column subsets of sparse matrices are rare Woodruff,Sketching as a tool for numerical linear algebra, Foundations and Trends in Theoretical Computer Science10(2014), no

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d8c45602-a571-469a-b872-693ec6834562 · outbound

This paper cites 1, 201–218.

Well-invertible column subsets of sparse matrices are rare 1, 201–218

Reference 29

Resolution: unresolved; no resolver link, observed 2026-07-11T07:08:16.892784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation d757f632-dc08-4d95-bbb4-89e1ae774fb4 · inbound

Level-set entropy and sparse randomized embeddings cites this paper.

Level-set entropy and sparse randomized embeddings Well-invertible column subsets of sparse matrices are rare

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T04:00:42.073669Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.