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Paper Citation Record · LEDGER

At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture

As of 22 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:2608.01776.

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

pith.paper-citation-record.v1
2608.01776 v1

Coverage vector

measured 10 of 10 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T21:16:51.380326Z

measured 10 of 10 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 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

10 of 10 outbound references displayed

  • verified exact3
  • verified fuzzy3
  • unresolved4
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e52cf805-22be-49dd-9e30-c72766f9c2df · outbound

This paper cites McLachlan and David Peel.Finite Mixture Models.

At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture McLachlan and David Peel.Finite Mixture Models

Reference 1

Resolution
unresolved
no resolver link, observed 2026-08-04T21:16:50.698113Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T21:16:50.698113Z digest=sha256:f94b2079f7f1fb80502a5febd67bb5796c24dec147f4a2f058badba6aa0525f5

Observation b8140be4-0121-45a6-9a36-ce424c789ba0 · outbound

This paper cites Carreira-Perpi˜ n´ an and Christopher K.

At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture Carreira-Perpi˜ n´ an and Christopher K

Reference 2

Resolution
verified exact
doi, observed 2026-08-04T21:16:51.435440Z

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.

source=pdf_text observed=2026-08-04T21:16:50.765740Z digest=sha256:15b3a6b85f85738058af63c4360e2747fa2a5d7a1d653b655260469b9edda545

Observation 9358ab6f-cb0f-4c8d-bc38-6bf5aa75c25e · outbound

This paper cites Carreira-Perpi˜ n´ an and Christopher K.

At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture Carreira-Perpi˜ n´ an and Christopher K

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:16:51.510870Z

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.

source=pdf_text observed=2026-08-04T21:16:50.822985Z digest=sha256:be9c351225599217d87431331245a339cef66fd2e5ccd94ce80a6c722ce93363

Observation 9ed69f4a-a150-4a31-880e-fdf6a5b7169d · outbound

This paper cites an unresolved cited work.

At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture Unresolved cited work

Reference 4

Resolution
unresolved
no resolver link, observed 2026-08-04T21:16:50.885166Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T21:16:50.885166Z digest=sha256:880cbc2ff714b0932c16ae648fd666127be2a1dd6ff745f4f1fe84c69a8d4ab0

Observation 041f843f-02f7-42ba-9334-cfa9fd716647 · outbound

This paper cites Singular learning theory: connecting algebraic geometry and model selection in statistics.

At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture Singular learning theory: connecting algebraic geometry and model selection in statistics

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:16:51.499290Z

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.

source=pdf_text observed=2026-08-04T21:16:50.959704Z digest=sha256:a24bcff2a3fb96b9f596c65289db24df3ddf7151ad58163e08b39c8f7359a6aa

Observation c816226f-a1d5-4885-adbb-1a25c3a9d1c2 · outbound

This paper cites Maximum number of modes of Gaussian mixtures.Information and Inference: A Journal of the IMA, 9(3):587–600,.

At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture Maximum number of modes of Gaussian mixtures.Information and Inference: A Journal of the IMA, 9(3):587–600,

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:16:51.488144Z

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.

source=pdf_text observed=2026-08-04T21:16:51.051089Z digest=sha256:1852eab31464748b56d63f914b35005a9c7ce2c2acae04c6a923d5fb5a8ae469

Observation fc61892f-cdf4-4b59-9bf9-78efec33475c · outbound

This paper cites Bounds on the Number of Modes of a Gaussian Mixture Density.

At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture Bounds on the Number of Modes of a Gaussian Mixture Density

Reference 7

Resolution
verified exact
local_arxiv, observed 2026-08-04T21:16:51.475435Z

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.

source=pdf_text observed=2026-08-04T21:16:51.209882Z digest=sha256:6a98f65965811001aa84b3a11284c1903cae045789f653034f937e5b983fc2ab

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

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

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.

source=pdf_text observed=2026-08-04T21:16:51.311691Z digest=sha256:4f2ac4d88791cccbdb4e4713ba7bd2ed20a8e0ac094a13e390dbfb91354371b6

Observation 6263aa2e-29d6-4451-8851-2a669f38e829 · outbound

This paper cites Cambridge University Press, 2004.

At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture Cambridge University Press, 2004

Reference 9

Resolution
unresolved
no resolver link, observed 2026-08-04T21:16:51.380326Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T21:16:51.380326Z digest=sha256:13a2f73bb989d7ff68226fc746e40eca785d5a3f443a4b35d5d868e5bc7e2b5a

Observation c3df453d-f9c4-46a7-a18f-d6df18cf7369 · outbound

This paper cites an unresolved cited work.

At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture Unresolved cited work

Reference 2020

Resolution
unresolved
no resolver link, observed 2026-08-04T21:16:51.142290Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T21:16:51.142290Z digest=sha256:a56475b3b22d388b263c2f864401c4f607158cfd918b0c206378d731170ed7db

Pith citing papers

No inbound Pith citation observations are available.