Paper Citation Record · LEDGER

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited

As of 10 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 1 inbound Pith citation observation for arXiv:2506.01746.

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

pith.paper-citation-record.v1
2506.01746 v1

Coverage vector

measured 44 of 44 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:41:43.705113Z

measured 45 of 45 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-15T13:47:39.786286Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-15T13:50:02.410066Z

Reference resolution

44 of 44 outbound references displayed

verified exact0
verified fuzzy25
unresolved19
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d7948622-61aa-469a-8523-528ccc700494 · outbound

This paper cites make the job.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited make the job

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:45.299347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a31dc407-f27b-4c08-8902-05d04716b784 · outbound

This paper cites F (x) = x2, U = R, ϕF (ξ, x) = (ξ − x)2.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited F (x) = x2, U = R, ϕF (ξ, x) = (ξ − x)2

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:45.285816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 11f73266-4257-4324-9bb7-6d734917f7bb · outbound

This paper cites F (x) = xa, a >1, U = (0, +∞), and ϕF (ξ, x) = ξa + (a − 1)xa − a ξ xa−1.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited F (x) = xa, a >1, U = (0, +∞), and ϕF (ξ, x) = ξa + (a − 1)xa − a ξ xa−1

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:45.271481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3874fe52-71a3-438e-8439-ef2f36aa74f1 · outbound

This paper cites F (x) = − log(x), U = (0, +∞), and ϕF (ξ, x) = log x ξ + ξ x − 1.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited F (x) = − log(x), U = (0, +∞), and ϕF (ξ, x) = log x ξ + ξ x − 1

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:45.256374Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 00b7a92b-0cf3-4c93-ba7a-c3bb37267fe3 · outbound

This paper cites Kullback–Leibler divergence/similarity measure.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Kullback–Leibler divergence/similarity measure

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:45.242194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 72ed174b-9cad-4d49-b53d-7e4c4017d00d · outbound

This paper cites F (x) = x log x + (1 − x) log(1 − x), U = (0, 1), and ϕF (ξ, x) = ξ log ξ x + (1 − ξ) log 1 − ξ 1 − v.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited F (x) = x log x + (1 − x) log(1 − x), U = (0, 1), and ϕF (ξ, x) = ξ log ξ x + (1 − ξ) log 1 − ξ 1 − v

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:45.226901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3a60a9c3-e39f-4772-a0cf-a0e4a22cdb0e · outbound

This paper cites F (x) = Fa(x) = log(1 + eax)/a, a >0, U = R, and ϕF (ξ, x) = 1 a log 1 + eaξ 1 + eax ! − eax eax + 1(ξ − x).

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited F (x) = Fa(x) = log(1 + eax)/a, a >0, U = R, and ϕF (ξ, x) = 1 a log 1 + eaξ 1 + eax ! − eax eax + 1(ξ − x)

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:45.213170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6df5eabc-7e72-464a-911d-a4533e102a9e · outbound

This paper cites F (x) = Fa(x) = log(cosh(ax)) a , a >0, U = R.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited F (x) = Fa(x) = log(cosh(ax)) a , a >0, U = R

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:45.198906Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 62c84893-1a06-46f1-9e4d-6597e52696d6 · outbound

This paper cites Fρ(x) = eax, a ∈ R, U = R, ϕFρ(ξ, x) = ϕF1(a ξ, a x) where ϕF1(ξ, x) = eξ − ex − ev(ξ − x).

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Fρ(x) = eax, a ∈ R, U = R, ϕFρ(ξ, x) = ϕF1(a ξ, a x) where ϕF1(ξ, x) = eξ − ex − ev(ξ − x)

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:45.182795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 717f7856-be1a-4dde-8c81-d27e8945c1be · outbound

This paper cites F (x) = |x|2, x ∈ U = Rd.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited F (x) = |x|2, x ∈ U = Rd

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:44.321724Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0bf52866-59be-4fc7-b847-6700ee19acab · outbound

This paper cites F (x) = x∗Sx, x ∈ U = Rd, S ∈ S++(d, R) := S +(d, R) ∩ GL(d, R) (symmetric and positive definite), and ϕF (ξ, x) = (ξ − x)∗S(ξ − x) := |ξ − x|2 S.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited F (x) = x∗Sx, x ∈ U = Rd, S ∈ S++(d, R) := S +(d, R) ∩ GL(d, R) (symmetric and positive definite), and ϕF (ξ, x) = (ξ − x)∗S(ξ − x) := |ξ − x|2 S

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:44.307078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation dcd5f01b-811e-4e86-9fc6-be4060eba156 · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:44.290419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 296e234d-e100-4029-beb7-e9e526b1c789 · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:44.274741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 19b65240-24c8-4ff9-a505-21356fca5e06 · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:44.257373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c61f81c8-c9fb-417d-8ca5-9c72039c1f54 · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:44.238992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 81638b1f-3ce3-4003-9c59-5d3a0504fed1 · outbound

This paper cites ∂GF r,n ∂xi (x) # i=1,...,n = r 2 Diag∇2F (xi) i=1,...,n.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited ∂GF r,n ∂xi (x) # i=1,...,n = r 2 Diag∇2F (xi) i=1,...,n

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:44.220872Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1e098de8-db1b-4363-a477-f502fbe6400a · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:44.202498Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 565ab612-e4f6-4b24-b963-d014ae71c12f · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:44.186716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2631ab2e-b73a-4f48-9c04-2cb6e6fd79dd · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:44.167742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1fc9a908-632c-436f-a3d7-ed27ebb14ee9 · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:44.150491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 57ac40dd-b591-49f2-a99e-d9eb610e84ef · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:44.134441Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation afa0b5c7-771c-418b-b6ef-fe015c4411f9 · outbound

This paper cites Banerjee, S.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Banerjee, S

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:44.118033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 17b108ea-47fb-496b-bde3-9e7b90743632 · outbound

This paper cites Boutoille.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Boutoille

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:44.100765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 48a49124-ab88-43a7-90d0-77da660ce7c3 · outbound

This paper cites Bouton and G.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Bouton and G

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:44.083051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation aefb648b-92a2-4701-b5f2-63de555aa676 · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T11:41:43.593170Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 33eca8b8-105a-482d-a272-2a0bcf3fbf97 · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:44.054307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c4203fef-4cc9-4881-b5a9-673a27a5b3c1 · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:44.036052Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1d71af56-3c55-4004-9a05-2ce7422fb739 · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:44.018405Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6f31f2eb-5cf1-488d-b170-f9fd5f71d95d · outbound

This paper cites Gersho and R.M.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Gersho and R.M

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:44.002788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 50135b9d-7445-46bf-a170-dad2234d0487 · outbound

This paper cites Graf and H.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Graf and H

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:43.986016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ae199664-aba8-4161-9c93-8fab5749565a · outbound

This paper cites Has, A Fischer, and M.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Has, A Fischer, and M

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:43.970069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 64518d17-2ecf-4eae-8601-090b5e5e13e4 · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:43.953540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 8a78fd66-a21a-4723-b3da-3a659e7140a0 · outbound

This paper cites Jourdain and G.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Jourdain and G

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:43.936915Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4ea132fd-a99d-48a2-8ced-9b4e986c41c8 · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:43.919680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ab4d60eb-9310-438c-baac-e0429d73cc52 · outbound

This paper cites Lamberton and G.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Lamberton and G

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:43.903602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0026f1ed-512e-4c87-84e8-d5269e5c0362 · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:43.886095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f0231133-9926-487d-8ab2-3e7b3b169a6b · outbound

This paper cites Luschgy and G.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Luschgy and G

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:43.868518Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2abbcd65-ade0-4747-9b80-2870a0be5b34 · outbound

This paper cites MacQueen.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited MacQueen

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:43.850828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2810b1a5-f23d-4717-a48b-8fdadf86d6e7 · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:43.832716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 150edd28-af16-42c9-b791-0c2b34f625a1 · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:43.814455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 89e170fa-ea6c-402f-b8a1-115194ca2943 · outbound

This paper cites Pag` es and J.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Pag` es and J

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:43.798987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 19c3fca4-10b5-4918-89d5-522f2f39b47a · outbound

This paper cites Sabin and R.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Sabin and R

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:43.781833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5ab7c8a8-c38b-4e38-b3cb-5f03ced761fe · outbound

This paper cites an unresolved cited work.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Unresolved cited work

Reference 43

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:41:43.761724Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation de70494f-72a2-4f04-9f30-8a6d79caa29b · outbound

This paper cites Trushkin.

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited Trushkin

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:41:43.744817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

Observation 1add529c-d062-4532-97b4-47e62960610f · inbound

Zador Theorem for optimal quantization with respect to Bregman divergences cites this paper.

Zador Theorem for optimal quantization with respect to Bregman divergences Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-05-15T13:50:02.411960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.