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Paper Citation Record · LEDGER

Abelian and Dihedral equiangular tight frames of redundancy $2$

As of 18 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

Typed states for the displayed outbound observations.

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

measured 44 of 44 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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:a46d6a9ccb5c946293f12cd252f5aaca6efd73fdc816a7fbae2617b6bb9c68d0

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

This paper cites an unresolved cited work.

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

Reference 4

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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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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source=pdf_text observed=2026-08-05T12:25:46.333955Z digest=sha256:a6f51c6fdcbc0a609f1c2a6d57051bbb8cee2aac9dd0600cea46c79750797265

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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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:46.478673Z digest=sha256:b2f7b54d50cb03beb1f57e43f9d157d912bbdc6f40eab0e6cb2093d0dd0bee44

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=sha256:97d812e262943fea5d2942a5e1773b27f69023162d940e37e5968c233b294c18

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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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:46.713000Z digest=sha256:915404056a38d805d55c7b67530d2c63a9a79b3e658b4225ec21422cafd61696

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=sha256:59d191b6a141b1d8ac7acc6102c687794e07073094c7859d5dfd2248855ce42b

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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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:46.901424Z digest=sha256:450e34e4793719d7334059a54ce54553c6227d3a0c1512fcb39a0e45e5e6313e

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=sha256:00a59578c6f3cdc3e20c9557d5a6239caf8f167c7a33af03afa8d0779c158aa2

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

Resolution
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:47.030792Z digest=sha256:aef3af15342ca31a632834052d1afcb83907ca37d939878110d1df0302cfa649

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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local_arxiv, observed 2026-08-05T12:25:49.256236Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:47.125676Z digest=sha256:1e0cbc48adf9a0f0c5a2761ddcf358a96a999b16b734b1939741a4e031b73023

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=sha256:64a20e082d045ef823cc8d3ef95f167295a76a6596328da98235a70f86653ce1

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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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:47.295409Z digest=sha256:a4c18f430b328a21d12411bf4e55b61da552b8f68ac043e26ecbbf2876834521

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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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:47.383607Z digest=sha256:7d7b013f6cda8a8f1de151d5e269ae255f77e9d2ec73d43ddbc14c2d701d876a

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:b6789d318939df9dc0d31f3cc593f29ee551b75824b735c7139cda924b936b67

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=sha256:48b99caeff263ca4b20567210cd0d53c6d707e736c64bf27781fa04f7c0d76b5

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:ff161c8d3cb75b4fcad3891698fe865172489624a520457d8c181eb6b1f337fd

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

Resolution
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:47.626908Z digest=sha256:92f92b32f58571d0411be72bf4694103ba154f7c03d7ac3521ad50d97b181b6f

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=sha256:2e680442c1f1a6295cf67fca252c9ed9646ce09364d72221e09e216d16b06461

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:bcf027cd3be9663520311123a584a3b00df1cec742fc164fd90072163f72e017

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=sha256:97a6fadcad4fe9fbffea2a1a6a48dee9e6c2235eea05e52f8432f92932620925

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=sha256:2a9043f6a793552d6ac68858b5941086edeb1b613143e3bf0829bc4f35f5c5db

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=sha256:586b8e02f677001c1850d534f25578bc722b98642a36f86bd7493f8197e0eb8d

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

This paper cites an unresolved cited work.

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=sha256:9f99fd60f2b8671f3828df267539157fccbb0a70a0abd7b2c2cdbac82c4934fb

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=sha256:159a95d069b4105c3acc5563182a62187a7f1e3ff8307ad01dbbec374b1ad14e

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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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:48.516530Z digest=sha256:10e814932a482887a4d823a977d1f2596f2d31a8f6d5d427b8f220b59879515a

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=sha256:7b53c2f2f233a2b290e1d26ca5f17573d414fcdd2989413e0df5e4eb6172110d

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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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:48.787458Z digest=sha256:3e5c5ea0733bbd7ad27e2af3cc08562e52ea493a710fede40725157694073291

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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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:48.872639Z digest=sha256:aa05d9d16a8b3f3ee35ea6f9a6e226eec5a1c1a5ce5a7ec15af0695aeda1a21f

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

Resolution
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:48.969879Z digest=sha256:c2776d3e0524f7ab9ec1e77d52157b9bf498c1a9815de92221240b6906b54565

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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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:49.066341Z digest=sha256:647e947508fd30c55ebbf42ed2420d3f71d5dead7aa963c5910e85fa105101cf

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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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:49.162088Z digest=sha256:60e0acc58d86811b405003c8b8e58b3caa2f58c4be81fd00a7cba4556473b195

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

Resolution
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raw_fallback, observed 2026-08-05T12:25:49.347893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:49.184788Z digest=sha256:156441966232b5d32736b67a4fd0d1781bbda412030d28ccd44434777393fb7e

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:49.187826Z digest=sha256:3e76e6070e663b97d7dd62a9f66a62d520b0c0908f75b56641c91bff3cba5684

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:49.190732Z digest=sha256:bae715e5cc163565d6fe05a3507fd515c726d61d2d2f14f2795b5901d32810ef

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:49.193553Z digest=sha256:45b0d773b5fb28a5b117cc8f77292c8fd0d72defc08d4c3c4fac552bf9d67b54

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:49.196785Z digest=sha256:ef264b5c05084d3f982eeb737dd434418f3058005c416abe8770f47623df19b9

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:49.200138Z digest=sha256:4c2380de61f031e5b6a465a72392bbedc7b68e7bf4bfc2f53582396d91bb949f

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:49.203060Z digest=sha256:3f2da8ec326e0086e493791815ce7e65aae138a8c59acf192b1c73f0f54b715f

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:49.206366Z digest=sha256:e687afe8896fae32642417643e91eac8d04a732a1d0623722d8e37ea3a7fa450

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:49.209185Z digest=sha256:4015e2539cd00664df7c6c1949506784371a18cab37578256b4c9e5283bcc2f0

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-05T12:25:49.211955Z digest=sha256:4dacf0dfc3df1c11f6b6b9cbf8eb19b407ebc24636d3f1051453152d8e07db67

Pith citing papers

No inbound Pith citation observations are available.