Paper Citation Record · LEDGER

The Maximum Likelihood Degree of Toric Models is Monotonic

As of 9 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2507.02719.

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

pith.paper-citation-record.v1
2507.02719 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:40:02.225836Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

28 of 28 outbound references displayed

verified exact3
verified fuzzy20
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c11df36a-ae01-4402-b9de-7ca72cc12866 · outbound

This paper cites The maximum likelihood degree of toric varieties.

The Maximum Likelihood Degree of Toric Models is Monotonic The maximum likelihood degree of toric varieties

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:07.438188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fecae017-fbfa-4125-a870-feb0ba75c540 · outbound

This paper cites Likelihood degenerations.

The Maximum Likelihood Degree of Toric Models is Monotonic Likelihood degenerations

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:07.243504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 14207936-cd0f-4656-912a-979eb056f44b · outbound

This paper cites On the maximum likelihood degree for Gaussian graphical models.

The Maximum Likelihood Degree of Toric Models is Monotonic On the maximum likelihood degree for Gaussian graphical models

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:40:03.224229Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ed669379-44ce-4e5f-85f4-250f50ce092c · outbound

This paper cites Likelihood geometry of reflexive polytopes.

The Maximum Likelihood Degree of Toric Models is Monotonic Likelihood geometry of reflexive polytopes

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:07.109202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8e7bce19-44d6-43a5-a639-dbc9ff80d723 · outbound

This paper cites Numerical Nonlinear Algebra.

The Maximum Likelihood Degree of Toric Models is Monotonic Numerical Nonlinear Algebra

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:00.660309Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab9215eb-bbe8-4e9c-94f2-6d66abc9ca6c · outbound

This paper cites Tropical toric maximum likelihood estimation.

The Maximum Likelihood Degree of Toric Models is Monotonic Tropical toric maximum likelihood estimation

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:40:02.950785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 548e2cc0-d882-477c-89ec-917f6b3daa60 · outbound

This paper cites Matroid stratification of ML degrees of independence models.

The Maximum Likelihood Degree of Toric Models is Monotonic Matroid stratification of ML degrees of independence models

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:06.959065Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c5876140-20a8-424c-bf9f-1eef10ed76e2 · outbound

This paper cites The maximum likelihood degree.

The Maximum Likelihood Degree of Toric Models is Monotonic The maximum likelihood degree

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:06.758429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation aad76e3d-c227-4a9b-b3d0-9e1ffde924f5 · outbound

This paper cites Quasi-independence models with rational maximum likelihood estimator.

The Maximum Likelihood Degree of Toric Models is Monotonic Quasi-independence models with rational maximum likelihood estimator

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:06.610012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 36ba36d0-31a1-4829-b1c0-bd38c752fcdb · outbound

This paper cites Lectures on Algebraic Statistics , volume 39 of Oberwolfach Seminars.

The Maximum Likelihood Degree of Toric Models is Monotonic Lectures on Algebraic Statistics , volume 39 of Oberwolfach Seminars

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:06.481661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 326b2c85-7a68-4228-aac9-d63adf32bd71 · outbound

This paper cites Engineered complete intersections: slightly degenerate Bernstein--Kouchnirenko--Khovanskii.

The Maximum Likelihood Degree of Toric Models is Monotonic Engineered complete intersections: slightly degenerate Bernstein--Kouchnirenko--Khovanskii

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:01.214162Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 940861bd-b484-4a2f-b7ea-9461f00b5df1 · outbound

This paper cites Zelevinsky.

The Maximum Likelihood Degree of Toric Models is Monotonic Zelevinsky

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:06.346884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8cb62542-d428-404c-9be0-d655726e0977 · outbound

This paper cites On the toric algebra of graphical models.

The Maximum Likelihood Degree of Toric Models is Monotonic On the toric algebra of graphical models

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:06.196503Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bc7baf56-e79d-4472-a73c-7a8d8f9a661c · outbound

This paper cites Maximum likelihood geometry in the presence of data zeros.

The Maximum Likelihood Degree of Toric Models is Monotonic Maximum likelihood geometry in the presence of data zeros

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:06.058320Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1f0e8f03-663d-44da-a94e-a2f20235c196 · outbound

This paper cites Performing the exact test of H ardy-- W einberg proportion for multiple alleles.

The Maximum Likelihood Degree of Toric Models is Monotonic Performing the exact test of H ardy-- W einberg proportion for multiple alleles

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:05.892574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 44a60223-ac09-4628-988c-bce914329559 · outbound

This paper cites The maximum likelihood data singular locus.

The Maximum Likelihood Degree of Toric Models is Monotonic The maximum likelihood data singular locus

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:05.716333Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3f3d0b8f-ba46-47b9-a801-5af2e281f7b1 · outbound

This paper cites Likelihood Geometry , pages 63--117.

The Maximum Likelihood Degree of Toric Models is Monotonic Likelihood Geometry , pages 63--117

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:05.570247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 16947876-e6b5-4ec5-b406-5d7d274c2dfd · outbound

This paper cites Logarithmic discriminants of hyperplane arrangements.

The Maximum Likelihood Degree of Toric Models is Monotonic Logarithmic discriminants of hyperplane arrangements

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:05.390989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 47c4f486-0808-4193-b4f8-3da4b4122fc8 · outbound

This paper cites Morgan and Andrew J.

The Maximum Likelihood Degree of Toric Models is Monotonic Morgan and Andrew J

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:05.215869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation cbc5f30e-09d8-4f58-be24-a175516303f0 · outbound

This paper cites Introduction to Tropical Geometry , volume 161.

The Maximum Likelihood Degree of Toric Models is Monotonic Introduction to Tropical Geometry , volume 161

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:05.015091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 17d61e4a-8d9b-4677-b3ef-c64b97c4732e · outbound

This paper cites an unresolved cited work.

The Maximum Likelihood Degree of Toric Models is Monotonic Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:40:04.699815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4d541362-0fec-42b8-b60c-db3a39aa53be · outbound

This paper cites Likelihood equations and scattering amplitudes.

The Maximum Likelihood Degree of Toric Models is Monotonic Likelihood equations and scattering amplitudes

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:04.441424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0d1b5bf8-4a11-491b-8a7c-4efca735df7f · outbound

This paper cites A monotonicity property of h -vectors and h^* -vectors.

The Maximum Likelihood Degree of Toric Models is Monotonic A monotonicity property of h -vectors and h^* -vectors

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:04.152239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 44fc0836-fcf1-449c-acd1-3130a1fdace9 · outbound

This paper cites Algebraic Statistics.

The Maximum Likelihood Degree of Toric Models is Monotonic Algebraic Statistics

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:03.899538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 145584e7-666d-42cf-89ad-eb3cc64e5c30 · outbound

This paper cites Maximum likelihood estimation from a tropical and a bernstein--sato perspective.

The Maximum Likelihood Degree of Toric Models is Monotonic Maximum likelihood estimation from a tropical and a bernstein--sato perspective

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:03.620029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 53f95b2e-35a4-4b48-9f2b-848dd86c0d91 · outbound

This paper cites an unresolved cited work.

The Maximum Likelihood Degree of Toric Models is Monotonic Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:40:03.427963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c63911fc-33ab-4924-80e6-cae2ea4cf68a · outbound

This paper cites Toric amplitudes and universal adjoints.

The Maximum Likelihood Degree of Toric Models is Monotonic Toric amplitudes and universal adjoints

Reference 27

Resolution: verified exact; raw_fallback, observed 2026-08-06T20:40:02.578980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bbe08c32-035a-4e3c-a0a5-53e7ec40f4cb · outbound

This paper cites Euler Stratifications of Hypersurface Families.

The Maximum Likelihood Degree of Toric Models is Monotonic Euler Stratifications of Hypersurface Families

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:02.225836Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.