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Paper Citation Record · LEDGER

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory

As of 8 August 2026, this Paper Citation Record lists 78 of 78 outbound references and 0 inbound Pith citation observations for arXiv:2607.08788.

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

pith.paper-citation-record.v1
2607.08788 v1

Coverage vector

measured 78 of 78 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-13T07:17:37.978825Z

measured 78 of 78 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

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measured 0 of 1 external citation measurements

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Reference resolution

78 of 78 outbound references displayed

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Outbound references

Observation 07473623-f301-48f5-8678-1986f1748695 · outbound

This paper cites Natarajan, and K.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Natarajan, and K

Reference 1

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Observation f8e7ed95-aa4d-4e16-947f-6c8d7ec87596 · outbound

This paper cites Graph isomorphism in quasipolynomial time.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Graph isomorphism in quasipolynomial time

Reference 2

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:b6d27c82b2fd3ed213e94d3ec051e438d23ba009cd9411f1ab02bbf2cca87483

Observation 3c5a5cb1-8d2f-4f86-9e9d-d92261de1071 · outbound

This paper cites Cambridge University Press, 2nd edition, 1993.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Cambridge University Press, 2nd edition, 1993

Reference 3

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:ebfbdd3ee3b59573259235a78c5661685baac36d3b2097beb2a736769846d801

Observation 88c99feb-fd29-4074-a571-4506514ac835 · outbound

This paper cites Brockett.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Brockett

Reference 4

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:2396feeb81ffba1f5e70f6c1ce69af05d548197edcf8e5fc0c7891b27d6be71e

Observation 4a210ef4-823a-4e94-a80a-6abba6186631 · outbound

This paper cites Jacobi angles for simultaneous diagonalization.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Jacobi angles for simultaneous diagonalization

Reference 5

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:404973698277a2c43606ef06d424849fc3cc68b39717b9c10cb854e28db1e008

Observation 7cca100f-4a2f-471d-b292-3f050bc9dafb · outbound

This paper cites Riley Casper, F.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Riley Casper, F

Reference 6

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:1a7ab76deffd119115a5a01684d016d97ca495a65b1a1804659c358963e40d07

Observation 29d1d83d-ccc3-4651-aba7-d7edafe2333e · outbound

This paper cites Riley Casper and Milen Yakimov.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Riley Casper and Milen Yakimov

Reference 7

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:b41b9cc4602d3c5500fb972631c88bf8b643405ff36f38e0c9fb5f19ee8d0d2a

Observation da74a1d6-56e0-4d2c-92ce-cfec890314ad · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 8

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:9af3b73156ac0c05496eb4564087f7bfa8b815433caf9f80a5ddc6789831fb60

Observation 3de091a0-b2b9-404d-8a12-c2b678be7686 · outbound

This paper cites Chu and Kenneth R.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Chu and Kenneth R

Reference 9

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:95a822a038113a7647ffba1c4010cc894af214a20b405be30ddf8ec0e695ab3e

Observation 72e9978e-50c7-4af5-ba1b-ef85df598243 · outbound

This paper cites Interscience, 1953.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Interscience, 1953

Reference 10

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:348de713b8926d67b6afa83bfd397c6f33a0aac598569ddd479c8ab885edca20

Observation fc0eb227-99ec-47de-abad-c692bacfd6b9 · outbound

This paper cites Cover and Joy A.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Cover and Joy A

Reference 11

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:b943e129fa4b2ed1d29cc8a895f199c6d52fe473fdaf8003281661519656ff8b

Observation b6e61be6-7133-4b5c-93a1-bb326ac33f21 · outbound

This paper cites Society for Industrial and Applied Mathematics, Philadelphia, 1992.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Society for Industrial and Applied Mathematics, Philadelphia, 1992

Reference 12

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:33146de0a1ec66e1b55c5bf7a8f5481f803cc7e9ee8de3c390f6d551ffe3b30b

Observation 8f7a2df3-3290-401e-ac66-f3d06ca06a33 · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 13

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:08b9ca628d302857fabf80a54882b12e376e890eebbdc87a0e9fbcd55110a7e6

Observation 7ebf452d-92b6-4f7c-8b9b-71159f5ff0cc · outbound

This paper cites Institute of Mathematical Statistics, Hayward, CA, 1988.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Institute of Mathematical Statistics, Hayward, CA, 1988

Reference 14

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:e8bb4cedade0919f4b1a728e5b5a011a7fb7d74eeff790d5d69c2ce8280136ea

Observation c9d8f0a3-4206-4d2a-b959-81597c9004d1 · outbound

This paper cites What can we do in a symmetry-constrained perspective? the importance of the total charge’s status in quantum reference frame frameworks.Quantum, 10:2126, 2026.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory What can we do in a symmetry-constrained perspective? the importance of the total charge’s status in quantum reference frame frameworks.Quantum, 10:2126, 2026

Reference 15

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:e237f4b8acee9b69fff16167f70f9f251ab24303593b2e43feebe6b99b02ce7c

Observation 28f3044c-69a8-4b9e-8296-3cf776e96c2c · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 16

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:d6ba973a13064fb13e921ab6f145f6694547785deba1b3e72c1f2c4a97ac6b67

Observation 4bf9da3a-00cf-41df-ab90-e1db794e951d · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 17

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:e435b43f9af34d4720dfd8ad1b357306b70e7606b478287300b09bb47b42cf90

Observation 5a45741d-a502-48f9-97ea-281a76ef5446 · outbound

This paper cites Dur ´an and F.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Dur ´an and F

Reference 18

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:6b7b6ea0a896668c0c9ac7c124713f801f6efbd32a06ee97685c772b31ddac88

Observation f091c1a4-4b0f-440c-b05d-b52d782d1238 · outbound

This paper cites Suboptimality of the Karhunen–Lo `eve transform for transform coding.IEEE Transactions on Information Theory, 50(8):1605–1619, 2004.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Suboptimality of the Karhunen–Lo `eve transform for transform coding.IEEE Transactions on Information Theory, 50(8):1605–1619, 2004

Reference 19

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:ec7800d06d6d0c7926ddadb6db5fee0077ac4b335c862f686a7fa2a0067f82c4

Observation 20f6840a-c8f7-49e9-a08c-f7457ee11814 · outbound

This paper cites On a theorem of Weyl concerning eigenvalues of linear transformations.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory On a theorem of Weyl concerning eigenvalues of linear transformations

Reference 20

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:ebe1040b35661c744e73ca204d36c17e9a9480f6aeb712454434154694771c50

Observation fde706d5-3a91-4bb2-a834-0ded6cb761c6 · outbound

This paper cites Resection of high frequency oscillations predicts seizure outcome in the individual patient.Scientific Reports, 7(1):13836, 2017.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Resection of high frequency oscillations predicts seizure outcome in the individual patient.Scientific Reports, 7(1):13836, 2017

Reference 21

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:cab65b17480924894fef35c977c08ff4bfa2a97b37aa2d5e3760827fbfcd97e4

Observation b5ff764f-3065-4506-b822-a72b1ab57515 · outbound

This paper cites Interictal iEEG during slow-wave sleep with HFO markings.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Interictal iEEG during slow-wave sleep with HFO markings

Reference 22

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Observation 1dae45a2-8491-4548-8b1e-605998b9713d · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 23

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:551e58950811741cc3abc1824cc9a354a504e8c37036bd364879c3882d8dd778

Observation 3f628f05-e334-419c-bd40-541cd3e5d9f3 · outbound

This paper cites Folland.A Course in Abstract Harmonic Analysis.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Folland.A Course in Abstract Harmonic Analysis

Reference 24

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Observation 9d46c596-cb0f-41e2-8ee2-f6a0428cbfd6 · outbound

This paper cites Springer, 2001.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Springer, 2001

Reference 25

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:2551c3a7423886edcd00fb503c687e82609b652e81dc16725fccf49878b47977

Observation 2ac1701c-fd0b-4117-a640-782cbc035b8e · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 26

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:25786634506e3d635088f156f6abc48775966b4af7cf4e132556c7e4f5413c30

Observation 79d62700-ac09-4124-8b93-68e49c347b32 · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 27

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:2db6d0e70f45edc228eeefbbad6a38980f9d344f292e6ac16b9c9ad305acff73

Observation 4af6be1b-9861-4a31-87b0-1824a63234fa · outbound

This paper cites Alberto Gr ¨unbaum and Luc Haine.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Alberto Gr ¨unbaum and Luc Haine

Reference 28

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:4ab81fb243691b13e7af7dcb4fd53bc11b58c18855f20a98c69c379c3d10342d

Observation 7e0f28e9-8da9-4776-bd71-99936a6c5f62 · outbound

This paper cites Alberto Gr ¨unbaum, Luigi Longhi, and Marvin Perlstadt.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Alberto Gr ¨unbaum, Luigi Longhi, and Marvin Perlstadt

Reference 29

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:ab8a4cfd666e0c440344c8a43ca8989bf5608227c6bc270bd0953d53296d4060

Observation 825a3c67-5a48-460c-a6ad-9bf087bc3d37 · outbound

This paper cites Alberto Gr ¨unbaum, In ´es Pacharoni, and Ignacio Zurri ´an.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Alberto Gr ¨unbaum, In ´es Pacharoni, and Ignacio Zurri ´an

Reference 30

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:f0527c46c33089b09448b63d912e86a3e3f61ba55dbc7f1956e302b4bd0859c0

Observation 73d4e3e4-81b2-4fae-9cb4-96b554b9f6ba · outbound

This paper cites Alberto Gr ¨unbaum, Luc Vinet, and Alexei Zhedanov.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Alberto Gr ¨unbaum, Luc Vinet, and Alexei Zhedanov

Reference 31

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:8a64a37fb9db1adf959ac4eeb0ed08cfc5e29e85d39fa0af4dee1b416437d2d8

Observation 66a228c8-8943-42f7-ba8f-cf10f714bc99 · outbound

This paper cites Alberto Gr ¨unbaum and Milen Yakimov.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Alberto Gr ¨unbaum and Milen Yakimov

Reference 32

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:c08ccab29b81c8630a3ef6872ca595fb5695c23acb66c88c2836173165c9e0a7

Observation 42323e24-75b4-4a80-9446-dc9a59fd487e · outbound

This paper cites Alberto Gr ¨unbaum and Milen Yakimov.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Alberto Gr ¨unbaum and Milen Yakimov

Reference 33

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:1447bb12c13c0f816f95cd7aac5f548d646bce6c2a7650bdbf5f7ba17e62a0f2

Observation d8c60f6b-ed00-4d51-bdf3-cc98e63a31c5 · outbound

This paper cites Zur theorie der orthogonalen funktionensysteme.Mathematische Annalen, 69(3):331– 371, 1910.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Zur theorie der orthogonalen funktionensysteme.Mathematische Annalen, 69(3):331– 371, 1910

Reference 34

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:f1ea9b13fd32b37609d3b5844c72930eeafed486d9d203716490bfd199f927d0

Observation c76ff1c8-b4fb-4cc4-b97a-da291210bb52 · outbound

This paper cites Commutative rings of difference operators and an adelic flag manifold.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Commutative rings of difference operators and an adelic flag manifold

Reference 35

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:2a4dbb8642a92411cfd5d89541e4306823338acf024383166841bfea400e642c

Observation acd455df-22ab-4e6c-ab3a-1e79c7eccf65 · outbound

This paper cites Moore.Optimization and Dynamical Systems.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Moore.Optimization and Dynamical Systems

Reference 36

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:f604704f29185843a1361fad9769f3e619e6883062b946395486bc6d1bbefed9

Observation 9c58cb8b-ef52-4b4f-924d-229da45dbff3 · outbound

This paper cites Analysis of a complex of statistical variables into principal components.Journal of Educational Psychology, 24:417–441, 498–520, 1933.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Analysis of a complex of statistical variables into principal components.Journal of Educational Psychology, 24:417–441, 498–520, 1933

Reference 37

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:ca979fbc4a9b312f9db34fb2b78671023e8079ce4ecddccbc8ad698da5bf5250

Observation 324dc4fe-b1c8-40a7-81bf-599afc9fe623 · outbound

This paper cites Exact Symmetry as Algebra: A Machine-Verified Tensor Calculus that Enforces Physical Selection Rules.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Exact Symmetry as Algebra: A Machine-Verified Tensor Calculus that Enforces Physical Selection Rules

Reference 38

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:931022564d24eada38650d58b946c07a528d6e3c4dddd44c821dbe61cedb4608

Observation 57829dc5-7b89-4402-9780-b6f3ae39fb39 · outbound

This paper cites Huang and P.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Huang and P

Reference 39

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:1913cd35b439521153ffbddec504bf856c0687afca69fbd8b6f4cb6cfdd2737d

Observation fcab7dfb-4371-49c5-a4f2-5f9a1d77ac0d · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 40

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:b5a023b352e3622d4852164e393dd25ccd87e66acbfa17544c7af86f10cb6f18

Observation 55ec2a5f-f71c-49d8-ad44-eb54c0b68936 · outbound

This paper cites ¨Uber lineare methoden in der wahrscheinlichkeitsrechnung.Annales Academiae Scientiarum Fennicae, Ser.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory ¨Uber lineare methoden in der wahrscheinlichkeitsrechnung.Annales Academiae Scientiarum Fennicae, Ser

Reference 41

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:6f9e94b2e1f5948efb982660fc406c9b48dd7940cac3f311e7bd31155ee10491

Observation e33b4421-d431-4e0a-9803-34fb37eca2bd · outbound

This paper cites Lesky, and Ren ´e F.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Lesky, and Ren ´e F

Reference 42

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:7c104b26fd6ce62b39a7df31b61325a358e880ed17c5aef03e0c127f19c74660

Observation b949e167-a382-40ba-b890-d9e7441dcf9c · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 43

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:ae7beb703f750e912e1445885ea581139e0975223b5674c29c1d2429220c1bb9

Observation 48ef271b-b982-4945-b21b-826de56798d9 · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 44

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:94f1d63c061a081c7de757f6e64f9afd336e3d1e21c5f81951dd38c0f1e4c5f0

Observation 4ebe9989-a0b3-446a-8da4-c23c23111e38 · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 45

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:a2455261726cbd4827149ea5056e2a15982719c41cc59a7ee0bb7c221c342f57

Observation ff724e55-82f7-432e-8400-26549916a5a5 · outbound

This paper cites Landau and Henry O.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Landau and Henry O

Reference 46

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:f83fa3faa256f6cfce47fb41280c3aefb954690c29de6effd330177db978327c

Observation a9fea912-2475-49a2-b1cc-0308536a9db5 · outbound

This paper cites Springer, 4th edition, 1978.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Springer, 4th edition, 1978

Reference 47

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:f2f6e4920e2af47a08cedcd26e663b9f69c364d31143dcd33e386891067f06db

Observation 03fd5956-44ba-42b5-8941-9e95565397ab · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 48

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:47fa6841df4a864932ea8dbe29d424ca8a3f0dde6276a9cae9be6104562f9571

Observation a677271c-3a15-4c87-8b7c-8326dd0626e8 · outbound

This paper cites Functions of positive and negative type, and their connection with the theory of integral equations.Philosophical Transactions of the Royal Society of London A, 209:415–446, 1909.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Functions of positive and negative type, and their connection with the theory of integral equations.Philosophical Transactions of the Royal Society of London A, 209:415–446, 1909

Reference 49

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:d23bbed8dcb6f384fbd830fa12eb8e4fb31bde150f25eb5054ffec41c0901e25

Observation 25c0835a-7ef7-4429-b8a7-33f7ea263413 · outbound

This paper cites Moody and Roger G.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Moody and Roger G

Reference 50

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:2bc3f97d60d5f99c5dcece8eeac59cb1855c2ec2671dc54e47d9c5d5da1c7f6c

Observation a56cf0fe-22e5-4e04-acaa-a0e103242fc7 · outbound

This paper cites The fractional order fourier transform and its application to quantum mechanics.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory The fractional order fourier transform and its application to quantum mechanics

Reference 51

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:02caaec634fb5344d0be6cf06e5c3f27e0b8e86959b7a6638b4f970a59f7a87e

Observation b21fd085-ef5d-4d67-8e94-abadfa03584b · outbound

This paper cites On lines and planes of closest fit to systems of points in space.Philosophical Magazine, Series 6, 2(11):559–572, 1901.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory On lines and planes of closest fit to systems of points in space.Philosophical Magazine, Series 6, 2(11):559–572, 1901

Reference 52

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:7c851470dc3403755a02a3d83b589b2ddc83f580f42d47c200d640f15325601d

Observation 86c1643c-c47b-4dec-bef5-8e10802afbb7 · outbound

This paper cites Percival and Andrew T.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Percival and Andrew T

Reference 53

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:20ec4f5e6ac78458e012b02cd5ee3ffbc30d32d7f5aff83f767c5e58f2d08f4c

Observation 990208ef-94fe-499b-a693-00f4fc40ac8f · outbound

This paper cites Joint approximate diagonalization of positive definite Hermitian matrices.SIAM Journal on Matrix Analysis and Applications, 22(4):1136–1152, 2001.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Joint approximate diagonalization of positive definite Hermitian matrices.SIAM Journal on Matrix Analysis and Applications, 22(4):1136–1152, 2001

Reference 54

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:145393e228d007967e651c12a4c37eb225ae9a6d0046d9e31dd4091f04ba37ed

Observation 6136e430-e832-4b40-a0e8-d730ea528d69 · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 55

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:3058f8568f5a0b634505e1f68cc719ce78510f3889bf315644c3b7d1c95604c3

Observation 0be385ad-33af-4791-aec9-5fe7f4fb1ad0 · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 56

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:ab45c99f982676a93d7139f0b30e99da62f9381df8597d632d2c4263e5c3f68e

Observation f54293b8-d219-4566-9596-6c1d2bb9ea80 · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 57

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:67abc84e59cdf97d47e08af4f3f46426c62db0912315edfcfd49547d5da25855

Observation 6547d939-629b-4992-9512-25ec5e617448 · outbound

This paper cites Representation Theory for Geometric Quantum Machine Learning.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Representation Theory for Geometric Quantum Machine Learning

Reference 58

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:145dbaf56664978b99b7c1574607b4a716415a7066709b215e43abf898360d01

Observation bcd4ff74-c82e-4d46-9e41-c82a7a832c26 · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 59

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:e8f39ea15e4a29ddf643f5444c1651bea34b663772dc1b78730c192bef9f2b6f

Observation 5212a97c-da16-4163-8e31-7679838701f8 · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 60

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:8a5a7a3019c18107a8caec12525e7ff65becf06e8c5462c1164faefbeab3334f

Observation 864d6e07-c38e-4881-ab47-32ae726c9b36 · outbound

This paper cites Springer, New York, 1977.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Springer, New York, 1977

Reference 61

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:7037e1cf87d56fa0c50a42020b633e549ea861bdd34f660a2162472a02747fce

Observation 5653d9ea-2b5c-4483-bf9c-34a4c2033acc · outbound

This paper cites Shuman, Sunil K.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Shuman, Sunil K

Reference 62

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:4ead6300bc584270c11583f6a82a167536a7f0515a5299e820553a749ba73bd0

Observation 12b4b853-5292-43bc-84e8-87ef8f2c4ea5 · outbound

This paper cites Prolate spheroidal wave functions, Fourier analysis and uncertainty—V: The discrete case.Bell System Technical Journal, 57(5):1371–1430, 1978.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Prolate spheroidal wave functions, Fourier analysis and uncertainty—V: The discrete case.Bell System Technical Journal, 57(5):1371–1430, 1978

Reference 63

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:2eb4c8a76a22169e0f4e6592da1c2df0f955f2f3d2ab2465b9ff50e840f04d8c

Observation 277fa492-5a52-4395-b4ef-0eb755bf2fcc · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 64

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no resolver link, observed 2026-07-13T07:17:37.978825Z

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:43b29a306414b5b98114e9c0e79c8c403175b4616aa889af5eafc79bbc8db963

Observation 881f955d-5e82-4d21-b8aa-337cf79a1a40 · outbound

This paper cites Smith and Robert B.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Smith and Robert B

Reference 65

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:c2f00f0799f88aa92c70560cc604ab0d67642bae1b2547cfc50ad2128e263db3

Observation 148f2b55-f1ae-4779-b484-d5d36b2d16ef · outbound

This paper cites Cambridge University Press, Cambridge, 1999.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Cambridge University Press, Cambridge, 1999

Reference 66

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:1364904a54ab72e9d2d225c7249089ff18ab1529c52cf725f2f764ae132485b7

Observation 565fc109-9cca-4bd0-bd87-9cc06e42a012 · outbound

This paper cites Algebraic Diversity: Group-Theoretic Spectral Estimation from Single Observations.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Algebraic Diversity: Group-Theoretic Spectral Estimation from Single Observations

Reference 67

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:fd44512ca1a4cb23ebe181f5ec096d5d9b1fade61c9bb9592c240d2ee5a36be5

Observation 042fd19b-5660-4f39-a5ef-635e9d5b1554 · outbound

This paper cites Algebraic Diversity: Principles of a Group-Theoretic Approach to Signal Processing.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Algebraic Diversity: Principles of a Group-Theoretic Approach to Signal Processing

Reference 68

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:3d1596fca801b20f1841f9979edcde313c63834737f92ace0abd9837b6637044

Observation a28c98eb-2550-4b6e-876a-2145a24aa66c · outbound

This paper cites Continuous Algebraic Diversity: Unifying Spectral, Wavelet, and Time-Frequency Analysis via Lie Group Actions.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Continuous Algebraic Diversity: Unifying Spectral, Wavelet, and Time-Frequency Analysis via Lie Group Actions

Reference 69

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:691d5281e111594668a2962d7bad3a56e1d5aa4f11a71249291a9c9d27bbe3f4

Observation 88a507cf-bf54-4c6b-9d0c-767973a4d491 · outbound

This paper cites Polynomial-Time Optimal Group Selection via the Double-Commutator Eigenvalue Problem.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Polynomial-Time Optimal Group Selection via the Double-Commutator Eigenvalue Problem

Reference 70

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:585a3c7715f3053f535f7aa1f7a990695f725e475018af1ffa3961ceb1d988f8

Observation 4fd6aa6b-88c3-42ab-a8a7-571c99fa6ca1 · outbound

This paper cites Unification of Signal Transform Theory.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unification of Signal Transform Theory

Reference 71

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:bfee0a54e78e71fbabd03f7ef0471f267b280b967266a5f90931f4f5eabf9f23

Observation 258c22c4-9016-41ec-9eb3-1d2f60229556 · outbound

This paper cites Tracy and Harold Widom.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Tracy and Harold Widom

Reference 72

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:73326d454e026834d514f287a0ab26708b0bf99ce6cbf8cf9bfb01703061a6d9

Observation 6bcf1042-40ad-4bac-aeca-121ecb2bbecd · outbound

This paper cites Tracy and Harold Widom.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Tracy and Harold Widom

Reference 73

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:a76bd8e425e90d6b50eb6c7279627973981e069b94637e1711b57070178a3dfe

Observation e1ca5fc0-df7e-41d2-a13f-03bdf78b49db · outbound

This paper cites Sch ¨onberger, Juan Nunez-Iglesias, Franc ¸ois Boulogne, Joshua D.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Sch ¨onberger, Juan Nunez-Iglesias, Franc ¸ois Boulogne, Joshua D

Reference 74

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Source-reported events for the cited work

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:ef21942adb9aa94e331071ef71fdedf2fc87fff86b63dd54f06fb0ca19a04deb

Observation 04ed0c66-1b3a-42ea-a939-3f74d01401c1 · outbound

This paper cites Cambridge University Press, 2018.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Cambridge University Press, 2018

Reference 75

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Observation 26c5cd3a-cf00-4df4-a7bd-0faa7c03ca20 · outbound

This paper cites A reduction of a graph to a canonical form and an algebra arising during this reduction.Nauchno-Technicheskaya Informatsia, Ser.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory A reduction of a graph to a canonical form and an algebra arising during this reduction.Nauchno-Technicheskaya Informatsia, Ser

Reference 76

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:cf0dfdfff3ad600214ec302cbeb4f97a67fcd5a852d309d3b9825539b7a33dc4

Observation 430260a5-c8fe-4924-a192-3339a1c7e62e · outbound

This paper cites Williams, Ioannis G.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Williams, Ioannis G

Reference 77

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:06606608c567238cb4d0fca2feeebeee9c1f6bdb91abad5a7f1978bfa80b3d69

Observation 5c78db78-17e4-4ee8-b38a-25f45bcab07a · outbound

This paper cites an unresolved cited work.

Matched Generators for the Karhunen--Lo\`eve Transform: A Double-Commutator Eigenvalue Theory Unresolved cited work

Reference 78

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source=pdf_text observed=2026-07-13T07:17:37.978825Z digest=sha256:61aff218202ff9fc18fd8ce7336e338bfa6244e31b1b41b81e491d6bbcdc1961

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