Paper Citation Record · LEDGER

Generative model for optimal density estimation on unknown manifold

As of 19 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2506.19587.

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

pith.paper-citation-record.v1
2506.19587 v1

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:45:44.904969Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

20 of 20 outbound references displayed

verified exact1
verified fuzzy8
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4761b8c9-18e1-47c6-8fae-e91d08207e94 · outbound

This paper cites Decomposition through charts.

Generative model for optimal density estimation on unknown manifold Decomposition through charts

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:45.249972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 71eae614-7240-44f2-9a76-af6873f0f806 · outbound

This paper cites Let w ∈M∩ Bp(x, (4C3)−1ϵΓ), l∈{ 1,...,m} and v∈Bd(0,τ ) such thatw =Fg,φ◦g1 l (v).

Generative model for optimal density estimation on unknown manifold Let w ∈M∩ Bp(x, (4C3)−1ϵΓ), l∈{ 1,...,m} and v∈Bd(0,τ ) such thatw =Fg,φ◦g1 l (v)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:45.234008Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 543eb7bd-9e6c-4d82-a8d3-d1d82de254ae · outbound

This paper cites In the case whereΨ(u) /∈g2 j (Bd(0, log(n)1/2 + 1)), we haveζg j (u) = 0 so let us focus on the case whereΨ(u) belongs tog2 j (Bd(0, log(n)1/2 + 1)).

Generative model for optimal density estimation on unknown manifold In the case whereΨ(u) /∈g2 j (Bd(0, log(n)1/2 + 1)), we haveζg j (u) = 0 so let us focus on the case whereΨ(u) belongs tog2 j (Bd(0, log(n)1/2 + 1))

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:45.286068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f20c3ffd-fb19-46ea-8c41-5eafbe8a5a45 · outbound

This paper cites Score-Based Generative Modeling through Stochastic Differential Equations.

Generative model for optimal density estimation on unknown manifold Score-Based Generative Modeling through Stochastic Differential Equations

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T18:45:44.828355Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1eaf0a6-e717-4338-8037-0368c8eb8b55 · outbound

This paper cites Integral Probability Metrics on submanifolds: interpolation inequalities and optimal inference.

Generative model for optimal density estimation on unknown manifold Integral Probability Metrics on submanifolds: interpolation inequalities and optimal inference

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-15T18:45:44.839519Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 18accbe7-a017-4d13-b488-75e21d4ce77c · outbound

This paper cites an unresolved cited work.

Generative model for optimal density estimation on unknown manifold Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:45:45.268433Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d3b51748-b037-4cde-bdc2-3e8257da3751 · outbound

This paper cites sample of lawµ.

Generative model for optimal density estimation on unknown manifold sample of lawµ

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:45.217287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a6995d7a-3673-4de0-83aa-e7f207d9700a · outbound

This paper cites an unresolved cited work.

Generative model for optimal density estimation on unknown manifold Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:45:45.197356Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e678866d-67a8-47ee-8e73-8f641cf1f138 · outbound

This paper cites an unresolved cited work.

Generative model for optimal density estimation on unknown manifold Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:45:45.180408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b0c5772b-1736-4ba1-92a0-ba0be6b28418 · outbound

This paper cites Let πi be the projection on the tangent space ofM⋆ at the point g1 i (0) and Φ :πi◦g1 i (Bd(0, 2τ))→Bd(0, 2τ) defined by Φ(u) = (πi◦g1 i )−1(u).

Generative model for optimal density estimation on unknown manifold Let πi be the projection on the tangent space ofM⋆ at the point g1 i (0) and Φ :πi◦g1 i (Bd(0, 2τ))→Bd(0, 2τ) defined by Φ(u) = (πi◦g1 i )−1(u)

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:45.163279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f7473982-8e5e-4875-946a-704a8ac253e4 · outbound

This paper cites Let πi be the projection on the tangent space ofM⋆ at the point g1 i (0) and Φi :πi◦g1 i (Bd(0, 2τ))→Bd(0, 2τ) defined by Φi(x) = (πi◦g1 i )−1(x).

Generative model for optimal density estimation on unknown manifold Let πi be the projection on the tangent space ofM⋆ at the point g1 i (0) and Φi :πi◦g1 i (Bd(0, 2τ))→Bd(0, 2τ) defined by Φi(x) = (πi◦g1 i )−1(x)

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:45.146591Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4ab693d6-aa0f-430b-b3ec-86e6e3e180e1 · outbound

This paper cites Supposing thatµ⋆ satisfies Assumptions 1, in the caseN <A, we have dHd/2 1 (ˆµ,µ⋆)≤ 2≤ 2AN−1, (59) so we have the result.

Generative model for optimal density estimation on unknown manifold Supposing thatµ⋆ satisfies Assumptions 1, in the caseN <A, we have dHd/2 1 (ˆµ,µ⋆)≤ 2≤ 2AN−1, (59) so we have the result

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:45.130605Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 86735b0d-5396-434b-b44a-a4389f56b67d · outbound

This paper cites Smooth transport map via diffusion process.

Generative model for optimal density estimation on unknown manifold Smooth transport map via diffusion process

Reference 1970

Resolution: unresolved; no resolver link, observed 2026-08-15T18:45:44.834106Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bdf8a172-c386-4bd3-be14-accce283f4f8 · outbound

This paper cites On the Statistical Properties of Generative Adversarial Models for Low Intrinsic Data Dimension.

Generative model for optimal density estimation on unknown manifold On the Statistical Properties of Generative Adversarial Models for Low Intrinsic Data Dimension

Reference 1997

Resolution: unresolved; no resolver link, observed 2026-08-15T18:45:44.803376Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9edcefd7-65a2-4ba5-a504-5036cfdfdc06 · outbound

This paper cites A Good Score Does not Lead to A Good Generative Model.

Generative model for optimal density estimation on unknown manifold A Good Score Does not Lead to A Good Generative Model

Reference 2001

Resolution: unresolved; no resolver link, observed 2026-08-15T18:45:44.821247Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 903f3d76-de99-4500-ae73-4ee26175362c · outbound

This paper cites Jean-Daniel Boissonnat, Ramsay Dyer, and Arijit Ghosh.

Generative model for optimal density estimation on unknown manifold Jean-Daniel Boissonnat, Ramsay Dyer, and Arijit Ghosh

Reference 2003

Resolution: verified exact; doi, observed 2026-08-15T18:45:44.952931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4585ce03-e886-41e7-9e1f-90dac9d0e40a · outbound

This paper cites Alias-Free Generative Adversarial Networks.

Generative model for optimal density estimation on unknown manifold Alias-Free Generative Adversarial Networks

Reference 2006

Resolution: unresolved; no resolver link, observed 2026-08-15T18:45:44.815824Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c6bc2b1-087f-4336-94e4-b81a00454792 · outbound

This paper cites Application of conditional ddpm on the mnist dataset.

Generative model for optimal density estimation on unknown manifold Application of conditional ddpm on the mnist dataset

Reference 2016

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:45.301745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c38d1631-e576-43eb-9573-30acae01a2f5 · outbound

This paper cites Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions.

Generative model for optimal density estimation on unknown manifold Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-15T18:45:44.789705Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ba6e3bb-44ee-43d3-8f8c-92f378e781fe · outbound

This paper cites Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data.

Generative model for optimal density estimation on unknown manifold Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-15T18:45:44.808961Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

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