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Paper Citation Record · LEDGER

Abelian and Dihedral equiangular tight frames of redundancy $2$

As of 13 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 0 inbound Pith citation observations for arXiv:2509.01753.

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

pith.paper-citation-record.v1
2509.01753 v2

Coverage vector

measured 44 of 44 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-05T12:25:49.211955Z

measured 44 of 44 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+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

44 of 44 outbound references displayed

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  • verified fuzzy26
  • unresolved16
  • parse uncertain0
  • malformed identifier1
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c50c5538-2fe6-426d-8dec-ce8095e94bea · outbound

This paper cites an unresolved cited work.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 1

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 74d06b42-5c8c-4490-8f54-b57822515384 · outbound

This paper cites an unresolved cited work.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 2

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source=pdf_text observed=2026-08-05T12:25:46.028352Z digest=sha256:ff5246ebe5ad55a869c20ffac57e4d1954bef5a2daafd335a625a2e216ddb1d8

Observation 9a406818-dced-4ffb-bb07-550e04b49981 · outbound

This paper cites 5, 113908.

Abelian and Dihedral equiangular tight frames of redundancy $2$ 5, 113908

Reference 3

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Observation f172cfab-0dda-4457-a7c0-be06df664423 · outbound

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Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 4

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Observation 7fd50d95-2284-4131-9bfc-b226e9b35349 · outbound

This paper cites an unresolved cited work.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 5

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Observation e681d673-5529-4b7c-b295-68312fe4d607 · outbound

This paper cites an unresolved cited work.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 6

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source=pdf_text observed=2026-08-05T12:25:46.478673Z digest=sha256:7ddc6eb77e0466d92e7466e718587cb35089d7734b2690e36dd8320747241324

Observation 6cacde0a-8b62-4e9c-978c-dbec011a9834 · outbound

This paper cites 8, 4410–4423.

Abelian and Dihedral equiangular tight frames of redundancy $2$ 8, 4410–4423

Reference 7

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source=pdf_text observed=2026-08-05T12:25:46.607149Z digest=sha256:6e581ef076c172ea3f7becb5dd85420b7f05319de8b855a97e8855a47c58adbb

Observation 28bc2bb9-5fb2-43ac-b601-187d3e9391be · outbound

This paper cites Davidson, C*-algebras by example , Fields Institute for Research in Mathematical Sciences Toronto: Fields Institute monographs, American Mathematical Society, 1996.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Davidson, C*-algebras by example , Fields Institute for Research in Mathematical Sciences Toronto: Fields Institute monographs, American Mathematical Society, 1996

Reference 8

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source=pdf_text observed=2026-08-05T12:25:46.713000Z digest=sha256:59ebc21f00cfa2ce1ccb7b72808d24340d068cbcb9b4c81a0a7711bff8287295

Observation 32e4e948-a530-43fe-9a34-1907006e09fd · outbound

This paper cites Stafford, On the automorphisms of Paley’s type ii Hadamard matrix , Discrete Mathematics 308 (2008), no.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Stafford, On the automorphisms of Paley’s type ii Hadamard matrix , Discrete Mathematics 308 (2008), no

Reference 9

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source=pdf_text observed=2026-08-05T12:25:46.841180Z digest=sha256:54165a5faf0ba7bb8bdabd90ae73e9e196f2504fa6663ff1967d5e3f0391c37e

Observation 2ae76678-1894-4581-9622-2504689567d4 · outbound

This paper cites an unresolved cited work.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 10

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source=pdf_text observed=2026-08-05T12:25:46.901424Z digest=sha256:cd6c47d202bf758955b033ac0c7fa3fc39427b750308d8282f893352c9f4082c

Observation ef57de6c-ff42-4651-8fb6-7814990a7b6d · outbound

This paper cites 11, 4245–4250.

Abelian and Dihedral equiangular tight frames of redundancy $2$ 11, 4245–4250

Reference 11

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source=pdf_text observed=2026-08-05T12:25:46.977953Z digest=sha256:a224bbd4bde07e086ac66d2de5a18610a20e14aeba9dd61fc9abddefabdd80fa

Observation 9ccde468-9274-46e7-808a-2068f6ece05d · outbound

This paper cites an unresolved cited work.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 12

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source=pdf_text observed=2026-08-05T12:25:47.030792Z digest=sha256:3fe642743b5496c739c1c0b91b2ca7e502e0a758853952eb60ce5da4f7ae2183

Observation 8ce53ba8-a2b2-4e92-935a-0b1129d1c4d7 · outbound

This paper cites On the optimal arrangement of $2d$ lines in $\mathbb{C}^d$.

Abelian and Dihedral equiangular tight frames of redundancy $2$ On the optimal arrangement of $2d$ lines in $\mathbb{C}^d$

Reference 13

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source=pdf_text observed=2026-08-05T12:25:47.125676Z digest=sha256:0754672fe24afcf68285539ab9fdfd3bd546339173e8ebb4a1e9982a20f976a6

Observation e0accb9c-39c4-4812-abe5-51e2ad506b16 · outbound

This paper cites Mixon, and Jesse D.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Mixon, and Jesse D

Reference 14

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source=pdf_text observed=2026-08-05T12:25:47.191135Z digest=sha256:0354ce5e3e911a7a7bc069c382ccd3ca09dfc81584b6c60970db767974a91d38

Observation ec2b5b06-30d3-4c12-aff8-a2d1dfb22138 · outbound

This paper cites Mixon, and John Jasper, Equiangular tight frames from hyperovals , IEEE Trans.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Mixon, and John Jasper, Equiangular tight frames from hyperovals , IEEE Trans

Reference 15

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source=pdf_text observed=2026-08-05T12:25:47.295409Z digest=sha256:4adaebdde4aaec91e617933cdd46456b8ed42da5f97569c75fcf6b3370795689

Observation ab0ab3b2-1aaa-4e5e-8e92-f92004239f46 · outbound

This paper cites Schmitt, Harmonic equiangular tight frames comprised of regular simplices, Linear Algebra Appl.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Schmitt, Harmonic equiangular tight frames comprised of regular simplices, Linear Algebra Appl

Reference 16

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source=pdf_text observed=2026-08-05T12:25:47.383607Z digest=sha256:81c80f19aa9eec4b608b7a4489ad0407259da876d70748114215c9cb7a1bf3f5

Observation 54e9c64e-3b16-41d8-93ef-f856cd985729 · outbound

This paper cites 1, 85–96.

Abelian and Dihedral equiangular tight frames of redundancy $2$ 1, 85–96

Reference 17

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source=pdf_text observed=2026-08-05T12:25:47.478362Z digest=sha256:0fba1187a84dc4367978161c4c3922aa75ea37afb77a8950abcab033e8eedc2b

Observation 3f2fe338-52ca-4a1a-9dfd-5071e1f3b627 · outbound

This paper cites 4, 685–695.

Abelian and Dihedral equiangular tight frames of redundancy $2$ 4, 685–695

Reference 18

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source=pdf_text observed=2026-08-05T12:25:47.536787Z digest=sha256:5f1ad9914b163f4b850fb1e13ad8ce53957585a74f762361518f29e4dd5ff6f4

Observation f01cb783-7421-48c7-b03f-e93bbc167281 · outbound

This paper cites 8, Cambridge University Press, 2020, p.

Abelian and Dihedral equiangular tight frames of redundancy $2$ 8, Cambridge University Press, 2020, p

Reference 19

Resolution
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source=pdf_text observed=2026-08-05T12:25:47.561783Z digest=sha256:1c84ef639310910285c8f7c61ed424a64bb586864bd47596e9408fbfad1caa8f

Observation b3352eab-ca2e-46ae-a6bc-c62341dda878 · outbound

This paper cites 3, 731–763.

Abelian and Dihedral equiangular tight frames of redundancy $2$ 3, 731–763

Reference 20

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source=pdf_text observed=2026-08-05T12:25:47.626908Z digest=sha256:1ef6f4a7e9caadf6da6f88623d95d6f7031f92e69730d3ac90d60f78c0cdf52e

Observation 02b81827-e0ff-40c0-bf0a-a43f53e8f4a0 · outbound

This paper cites More on the optimal arrangement of $2d$ lines in $\mathbb{C}^d$.

Abelian and Dihedral equiangular tight frames of redundancy $2$ More on the optimal arrangement of $2d$ lines in $\mathbb{C}^d$

Reference 21

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T12:25:47.777009Z digest=sha256:fe0b55a1aa5fb5520115de283d2ca679b9e7c8b09ac001056f2eafa3929bf388

Observation 857b3e53-db01-44f6-92b8-057cac49f717 · outbound

This paper cites Iverson, John Jasper, and Dustin G.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Iverson, John Jasper, and Dustin G

Reference 22

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source=pdf_text observed=2026-08-05T12:25:47.850557Z digest=sha256:7d6cb554db2eab5d974e6129dc7e2174d1ac287da8b4cdd12cc3868a6b2c7154

Observation 690bdc63-826f-4cb1-8090-7836fd54e6c6 · outbound

This paper cites Kantor, Automorphism groups of Hadamard matrices , Journal of Combinatorial Theory, Series A 6 (1969), 279–281.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Kantor, Automorphism groups of Hadamard matrices , Journal of Combinatorial Theory, Series A 6 (1969), 279–281

Reference 23

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source=pdf_text observed=2026-08-05T12:25:47.970004Z digest=sha256:f2e221274b0c8fede4e1898cf8ecc86eaef8cdf0226722f94be1acc5bebe3fba

Observation 15877308-83e7-4215-aff0-68d873c651d8 · outbound

This paper cites an unresolved cited work.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 24

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source=pdf_text observed=2026-08-05T12:25:48.038155Z digest=sha256:d51780bc5d4657d4e1b7bef18b699628d3cd32e58cf6523a27c0a71af1941aed

Observation b250ded5-0fd1-474d-9cec-256b098cf230 · outbound

This paper cites 2; new ser., 2, Clarendon Press ; Oxford University Press, Oxford [Oxfordshire], New York, 1987 (English).

Abelian and Dihedral equiangular tight frames of redundancy $2$ 2; new ser., 2, Clarendon Press ; Oxford University Press, Oxford [Oxfordshire], New York, 1987 (English)

Reference 25

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source=pdf_text observed=2026-08-05T12:25:48.167804Z digest=sha256:8f1fd00252d3181614a6a463709d63821a5dfb770867e1d193ea32e6d6f68d9f

Observation 4cc6a5c9-ce86-437d-aaaa-042fc38e3a99 · outbound

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Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 26

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source=pdf_text observed=2026-08-05T12:25:48.309326Z digest=sha256:c18696e41b7d4e0c6696b356b7c7e6184d39237db8c6c9930e7ebc52e13a0ebf

Observation a83ae314-a4be-4435-8475-bec120396cb5 · outbound

This paper cites 11138, SPIE, 2019, pp.

Abelian and Dihedral equiangular tight frames of redundancy $2$ 11138, SPIE, 2019, pp

Reference 27

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source=pdf_text observed=2026-08-05T12:25:48.427962Z digest=sha256:26f556cbdd776e41f7a0f87e3e752458fce5fed43ff5be1fb5509c102132c4e1

Observation 1e3281a7-38af-4bbf-8c2e-552bd18aa8ec · outbound

This paper cites an unresolved cited work.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 28

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source=pdf_text observed=2026-08-05T12:25:48.516530Z digest=sha256:722f26f72be5dae18411d4006a2d6b5b59b95e0e2b18ab337ff900318e713baf

Observation de578579-1c55-4b63-8aef-7a244a80623a · outbound

This paper cites Mixon, Hans Parshall, and Jianzong Pi, Neural collapse with unconstrained features , Sampl.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Mixon, Hans Parshall, and Jianzong Pi, Neural collapse with unconstrained features , Sampl

Reference 29

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source=pdf_text observed=2026-08-05T12:25:48.633270Z digest=sha256:2a4d4363bfc12ef31469054b40575a924cb904588c86eb2ad3efc2ee588b93cb

Observation b66a6e91-a5f8-4add-afc2-e815dfed9422 · outbound

This paper cites an unresolved cited work.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 30

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source=pdf_text observed=2026-08-05T12:25:48.787458Z digest=sha256:b64cb27be728cc26eb873f172e8d88967cb63e51244f8d3f2073f4aaa06158f1

Observation 4789c6c3-6ecb-4533-899a-b0c907caf907 · outbound

This paper cites an unresolved cited work.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 31

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source=pdf_text observed=2026-08-05T12:25:48.872639Z digest=sha256:2785718eba536b01399fafa741bfb70c7b30e6abb1989d6360ad24d511362506

Observation 740de6d8-b5b0-416d-8339-88756bcea7ca · outbound

This paper cites an unresolved cited work.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 32

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T12:25:48.969879Z digest=sha256:cbd256af9d1bf7ea5294eb15a4093c269fd586a883b65702eb23381f7c70e339

Observation 584776de-2bd9-4b43-8e17-6b45e0ed006e · outbound

This paper cites Rastegin, Uncertainty relations for quantum measurements from generalized equiangular tight frames, Ann.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Rastegin, Uncertainty relations for quantum measurements from generalized equiangular tight frames, Ann

Reference 33

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source=pdf_text observed=2026-08-05T12:25:49.066341Z digest=sha256:0158be19a1548149e5c7b3c414c69ac42e440e5bf354802d226432768f43f455

Observation 2ec72714-9157-45c6-975f-81cca1d65033 · outbound

This paper cites Renes, Robin Blume-Kohout, A.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Renes, Robin Blume-Kohout, A

Reference 34

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source=pdf_text observed=2026-08-05T12:25:49.162088Z digest=sha256:8bc14281b6e1a73bd0a6de8199c5c3ebad069aeac72d67c6df7237055447457d

Observation 324f64bb-5708-479a-8232-199aab997e16 · outbound

This paper cites an unresolved cited work.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 35

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T12:25:49.184788Z digest=sha256:946c9ea346befa6f21ebc3de371afa0c96a173ba0a3455f8eeb1429557ad6ffc

Observation 4caf4aa8-e0f1-4557-90d6-2b89316f7306 · outbound

This paper cites an unresolved cited work.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 36

Resolution
malformed identifier
raw_fallback, observed 2026-08-05T12:25:49.338292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T12:25:49.187826Z digest=sha256:f2b020c34f6757d8bf8b710ce2632d2ce6cf91d0c901d80df323c801a88fb2a9

Observation 6cc87237-2f48-4254-a7f1-9b35e12ae18d · outbound

This paper cites Heath, Jr., Grassmannian frames with applications to coding and communication, Appl.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Heath, Jr., Grassmannian frames with applications to coding and communication, Appl

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:25:49.329215Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T12:25:49.190732Z digest=sha256:8f7cc15cced6efc4080c73d291da6e932f3ea5fc5b4bd3817ad2e8668bef626b

Observation bce2ec26-e337-4825-9b93-1aa8cb3f017d · outbound

This paper cites 1, 83–112.

Abelian and Dihedral equiangular tight frames of redundancy $2$ 1, 83–112

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:25:49.320012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T12:25:49.193553Z digest=sha256:fc2081a341794b00ba3e519a9be3f41a2e8946f4e5f5148782a2f86d1f675c6d

Observation ff3b59c8-c435-4cfd-8c42-0d862710df5f · outbound

This paper cites 5, 1097–1120.

Abelian and Dihedral equiangular tight frames of redundancy $2$ 5, 1097–1120

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:25:49.311429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T12:25:49.196785Z digest=sha256:3fab4ecee255c306a5d40eae35297506d7c9db9faf929341bfea08dfa0157f9c

Observation fd480592-b52a-43bd-9b78-b080cf2c081c · outbound

This paper cites an unresolved cited work.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Unresolved cited work

Reference 40

Resolution
unresolved
raw_fallback, observed 2026-08-05T12:25:49.301830Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T12:25:49.200138Z digest=sha256:57bcd99a2ec0bd46eba1d8e17381a0bb4d5f9d0e16d6f7e2697681d356e1700a

Observation 1ac656c7-5ebd-4851-a8a0-1c24f0534eeb · outbound

This paper cites 2, 203–204.

Abelian and Dihedral equiangular tight frames of redundancy $2$ 2, 203–204

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:25:49.292073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T12:25:49.203060Z digest=sha256:60418fc812e78015e1bf6879d809aadcd3b65c0a2a12903d7a65a02981a31ae0

Observation 04f0a839-9168-43f4-bb11-3405453243e8 · outbound

This paper cites Weibel, An introduction to homological algebra , Cambridge University Press, April 1994.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Weibel, An introduction to homological algebra , Cambridge University Press, April 1994

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:25:49.283504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T12:25:49.206366Z digest=sha256:b53093c53853ae6df62021521a018392a5f50368fb8282aef519d6f891e06a3e

Observation 160ffce3-d173-4023-885a-d6bae3783ec5 · outbound

This paper cites Giannakis, Achieving the Welch bound with difference sets , IEEE Transactions on Information Theory 51 (2005), 1900–1907.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Giannakis, Achieving the Welch bound with difference sets , IEEE Transactions on Information Theory 51 (2005), 1900–1907

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:25:49.274841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T12:25:49.209185Z digest=sha256:0d2b014a5cd66e3612389c2d83caa1c528fc8d506b906c8bf8fb24c0f5d8fa44

Observation 679a8221-a5b2-412d-a3a5-a59ac4b8ef9a · outbound

This paper cites Zauner, Quantum designs—foundations of non-commutative theory of designs , Ph.D.

Abelian and Dihedral equiangular tight frames of redundancy $2$ Zauner, Quantum designs—foundations of non-commutative theory of designs , Ph.D

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T12:25:49.266239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T12:25:49.211955Z digest=sha256:c963b23d5a2a64ffbb698daf60d2c78c69226d09f11c5682acb9fc92fcbca40a

Pith citing papers

No inbound Pith citation observations are available.