Paper Citation Record · LEDGER

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes

As of 22 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 1 inbound Pith citation observation for arXiv:2607.17506.

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

pith.paper-citation-record.v1
2607.17506 v1

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T17:57:29.845307Z

measured 48 of 48 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T21:16:51.311691Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-04T21:16:51.455004Z

Reference resolution

47 of 47 outbound references displayed

verified exact0
verified fuzzy0
unresolved45
parse uncertain2
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 15323f59-787f-4fa1-90a9-e72542baf27e · outbound

This paper cites 2013 , type =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes 2013 , type =

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:26.192050Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 036a68e4-0621-4386-b6ec-2bd40c1f7959 · outbound

This paper cites Algebraic Statistics of Gaussian Mixtures , school =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Algebraic Statistics of Gaussian Mixtures , school =

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:26.273012Z

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Observation 1cc6fe0c-0b91-4684-bda1-b809cb12bda3 · outbound

This paper cites Coppel , title =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Coppel , title =

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:26.379511Z

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Observation 6b7e0eee-a2d9-4c05-8279-341a085dbe10 · outbound

This paper cites Studden , title =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Studden , title =

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:26.437497Z

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Observation c3122ca1-dea7-43e9-96e4-02f024bb7be5 · outbound

This paper cites an unresolved cited work.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:26.492857Z

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Observation 14042ccc-3dde-48a9-9bb3-7075fcc3c318 · outbound

This paper cites Transactions of the American Mathematical Society , volume =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Transactions of the American Mathematical Society , volume =

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:26.547952Z

Source-reported events for the cited work

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Observation 67bfb894-f2fa-4168-9b32-b85e3c2fb303 · outbound

This paper cites an unresolved cited work.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:26.579252Z

Source-reported events for the cited work

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Observation 3fba2652-893a-4a62-8dc6-75619dc2259e · outbound

This paper cites 1998 , doi =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes 1998 , doi =

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:26.638801Z

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Observation 603b211d-0d5e-4733-837c-4db71d376b81 · outbound

This paper cites and Parks, Harold R.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes and Parks, Harold R

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:26.695127Z

Source-reported events for the cited work

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Observation 594316aa-6687-433b-aa65-775ac9370847 · outbound

This paper cites an unresolved cited work.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Unresolved cited work

Reference 10

Resolution: parse uncertain; no resolver link, observed 2026-08-01T17:57:26.776813Z

Source-reported events for the cited work

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Observation 486d2d6f-a441-48ec-96d7-c7226f590640 · outbound

This paper cites 2026 , eprint=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes 2026 , eprint=

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:26.852463Z

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Observation 53bf5d51-1889-4ac1-b1d9-f905d07eda61 · outbound

This paper cites Elementary.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Elementary

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:26.928746Z

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Observation 67381dc0-b34a-4348-8a38-da1724bfa77e · outbound

This paper cites Transactions of the American Mathematical Society , volume=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Transactions of the American Mathematical Society , volume=

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:26.987213Z

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Observation 94fbb28d-5405-4e55-b36a-9195123047e6 · outbound

This paper cites 2012 , author =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes 2012 , author =

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:27.060789Z

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Observation 6e78bce4-d208-4a4f-b60b-e4490f5c1250 · outbound

This paper cites Information Geometry , volume=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Information Geometry , volume=

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:27.144215Z

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Observation 00508d51-b7c3-4830-b7a1-13fce9301e58 · outbound

This paper cites 2000 , publisher=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes 2000 , publisher=

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:27.236347Z

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Observation 6b117eca-e58d-449e-bdc5-f3707f6efb63 · outbound

This paper cites Inference and applications to clustering , author=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Inference and applications to clustering , author=

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:27.312629Z

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Observation bdeb4901-73fd-4fcd-b4c3-00175124e3bf · outbound

This paper cites an unresolved cited work.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Unresolved cited work

Reference 18

Resolution: parse uncertain; no resolver link, observed 2026-08-01T17:57:27.388501Z

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Observation 47f6f2a5-b6d6-4e4c-af57-bc955d1475ac · outbound

This paper cites Vorobjov , year=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Vorobjov , year=

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:27.439255Z

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Observation 943192d6-d03c-4217-a809-3e760e8150cc · outbound

This paper cites 1991 , doi=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes 1991 , doi=

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:27.510189Z

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Observation 9a1f9f16-f661-4859-ae40-423a4a91e771 · outbound

This paper cites Soviet Mathematics Doklady , volume=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Soviet Mathematics Doklady , volume=

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:27.582529Z

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Observation 5aed3ef1-2e73-411d-ae7e-0a08cfe50990 · outbound

This paper cites Selecta Mathematica , series =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Selecta Mathematica , series =

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:27.639292Z

Source-reported events for the cited work

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Observation 7c66b5dc-7d37-4086-abf2-b1913afe9fb2 · outbound

This paper cites Rolin and P.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Rolin and P

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:27.645265Z

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Observation e1f7f649-3ee6-45ce-a6f1-0910d418e6bd · outbound

This paper cites 1963 , publisher=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes 1963 , publisher=

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:27.729589Z

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Observation 700f6433-93f7-4bd0-9c2b-4e5860b6fad2 · outbound

This paper cites 1965 , volume=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes 1965 , volume=

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:27.816530Z

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Observation e3a1aa38-3a4b-49b4-8af2-5a4c92e83673 · outbound

This paper cites Global Analysis of Expectation Maximization for Mixtures of Two Gaussians , volume =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Global Analysis of Expectation Maximization for Mixtures of Two Gaussians , volume =

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:27.913768Z

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Observation ca9d1c97-b949-459d-a726-d7d1818fd53a · outbound

This paper cites Are There Local Maxima in the Infinite-Sample Likelihood of Gaussian Mixture Estimation?.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Are There Local Maxima in the Infinite-Sample Likelihood of Gaussian Mixture Estimation?

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:28.002508Z

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Observation 331a3e40-cced-4907-adcb-e54d6509cd91 · outbound

This paper cites Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences , volume =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences , volume =

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:28.051659Z

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Observation e6fe4116-d319-4a70-a85a-15cf2eebd860 · outbound

This paper cites an unresolved cited work.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:28.140648Z

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Observation 2f09cf3c-ef50-4f76-a58b-0a0c0e74d2f1 · outbound

This paper cites 1995 , author =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes 1995 , author =

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:28.170186Z

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Observation bae8be68-5e1b-4be7-920c-b38f7065a7ae · outbound

This paper cites an unresolved cited work.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:28.197625Z

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Observation 73acc63b-1d41-4fc9-bbc0-cccda32f7160 · outbound

This paper cites and Williams, Christopher K.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes and Williams, Christopher K

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:28.347214Z

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Observation 77447409-382e-4164-926b-260aa8fd44b7 · outbound

This paper cites Technometrics , volume =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Technometrics , volume =

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:28.481616Z

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Observation 7ba666ad-ba47-4bb1-9826-6b2b5df71856 · outbound

This paper cites Clifford.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Clifford

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:28.585710Z

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Observation 562770af-8295-4f8a-9224-9025b4ff5ed1 · outbound

This paper cites 1995 , publisher=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes 1995 , publisher=

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:28.691005Z

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Observation 5c2cbeb2-f2dd-4567-852d-a1f96f929683 · outbound

This paper cites Technometrics , volume =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Technometrics , volume =

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:28.758077Z

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Observation e23f4783-b3e1-4aa2-91aa-62f689ae4af6 · outbound

This paper cites 2008 , publisher=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes 2008 , publisher=

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:28.864347Z

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Observation 428447da-2179-485d-9b8a-597009eb84fc · outbound

This paper cites 2024 , eprint=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes 2024 , eprint=

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:28.955940Z

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Observation 34ec119c-72bf-4657-9657-3d1baeedae3a · outbound

This paper cites A Wasserstein-Type Distance in the Space of Gaussian Mixture Models , journal =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes A Wasserstein-Type Distance in the Space of Gaussian Mixture Models , journal =

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:29.065393Z

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Observation a612dbd2-d5ad-4bc7-af04-f3bd4876a8b9 · outbound

This paper cites and Tannenbaum, Allen , journal=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes and Tannenbaum, Allen , journal=

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:29.160178Z

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Observation 3cf9e813-9897-411d-81fb-6dd4966a4b1d · outbound

This paper cites and Hostetler, L.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes and Hostetler, L

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:29.238017Z

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Observation a6ad5524-240a-45a9-9a9c-2ee9d1d8982e · outbound

This paper cites Gaussian Mixture Models.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Gaussian Mixture Models

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:29.360507Z

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Observation 4838096a-18ea-4774-97c6-ec03b32bd30b · outbound

This paper cites The R Journal , volume=.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes The R Journal , volume=

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:29.440517Z

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Observation b057e622-9c3b-489f-8846-ce47080c4ff4 · outbound

This paper cites and Williams, Christopher K.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes and Williams, Christopher K

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:29.518070Z

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Observation 863162af-336a-45fc-9994-c0b2e339d1c7 · outbound

This paper cites Lindsay , title =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Lindsay , title =

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:29.634522Z

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Observation bb537920-607b-48e4-9bd6-30df25de8a93 · outbound

This paper cites Maximum number of modes of Gaussian mixtures.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes Maximum number of modes of Gaussian mixtures

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:29.758397Z

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Observation a10c4e2e-8f8c-4c5d-b8eb-c00cce57e906 · outbound

This paper cites 2013 , title =.

On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes 2013 , title =

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-01T17:57:29.845307Z

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Pith citing papers

Observation 2df156b0-b513-4b3b-bb8c-2642341674da · inbound

At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture cites this paper.

At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:16:51.459847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.