Paper Citation Record · LEDGER

Data Generation without Function Estimation

As of 19 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:2507.08239.

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

pith.paper-citation-record.v1
2507.08239 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:34:37.297908Z

measured 14 of 14 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

14 of 14 outbound references displayed

verified exact2
verified fuzzy7
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fe0ab977-9927-4b1e-a8d6-e2cec5290a57 · outbound

This paper cites Recall the Fourier transform of the radial function∥x∥−s is C∥w∥−d+s) for 0 < s < dwhere C is a constant depending on d and s [Frank and Matzke, 2025].

Data Generation without Function Estimation Recall the Fourier transform of the radial function∥x∥−s is C∥w∥−d+s) for 0 < s < dwhere C is a constant depending on d and s [Frank and Matzke, 2025]

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:34:38.507002Z

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 40dd1b1e-bbfb-4299-b06f-025795f0272a · outbound

This paper cites More precisely, the theorem implies that for all µ, νsuch that F (µ) = F (ν) = 0, the following holds: 0 = ∥F (µ) − F (ν)∥2 L2 = MMD(µ, ν).

Data Generation without Function Estimation More precisely, the theorem implies that for all µ, νsuch that F (µ) = F (ν) = 0, the following holds: 0 = ∥F (µ) − F (ν)∥2 L2 = MMD(µ, ν)

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:34:39.183703Z

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 0b4c6024-72df-4c22-8c77-fbf7929d4838 · outbound

This paper cites The Sharp Erd\H{o}s-Tur\'an Inequality.

Data Generation without Function Estimation The Sharp Erd\H{o}s-Tur\'an Inequality

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:34:37.601233Z

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 c60c8006-a375-4656-bcb5-118ec6999ec3 · outbound

This paper cites Suppose Ft(y) is almost surely L-Lipschitz in y.

Data Generation without Function Estimation Suppose Ft(y) is almost surely L-Lipschitz in y

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:34:39.000113Z

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 e778bb30-0c13-428f-aed3-14a3a54f121b · outbound

This paper cites an unresolved cited work.

Data Generation without Function Estimation Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:39.285439Z

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 9a06e5a9-38ee-4191-babf-688d2ecdbeed · outbound

This paper cites T is not implementable as it requires µt, the solution of the continuity equation (8).

Data Generation without Function Estimation T is not implementable as it requires µt, the solution of the continuity equation (8)

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:34:38.847348Z

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 df521369-4111-4491-9e16-774d7c953965 · outbound

This paper cites (42) As proven in the next lemma, Ft(y) is Lipschitz.

Data Generation without Function Estimation (42) As proven in the next lemma, Ft(y) is Lipschitz

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:34:38.680101Z

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 8e0294a6-faf0-4e96-b016-ee05004a72fb · outbound

This paper cites Without this reduction, computing W (s), as required in EFS, becomes numerically infeasible.

Data Generation without Function Estimation Without this reduction, computing W (s), as required in EFS, becomes numerically infeasible

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:34:38.246315Z

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 aa659794-c58c-48e4-91f4-6d2fd97753d1 · outbound

This paper cites an unresolved cited work.

Data Generation without Function Estimation Unresolved cited work

Reference 2012

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:39.719842Z

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 4a4b8846-3475-43b5-bf22-896c1c17558a · outbound

This paper cites A family of explicit minimizers for interaction energies.

Data Generation without Function Estimation A family of explicit minimizers for interaction energies

Reference 2013

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:34:38.000584Z

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 92f2425f-eb23-4a82-a4af-e1a9bb8d5247 · outbound

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

Data Generation without Function Estimation Score-Based Generative Modeling through Stochastic Differential Equations

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:36.286564Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 29d87673-f31d-4c78-9a2c-ed903143cdd6 · outbound

This paper cites Stochastic Particle Gradient Descent for Infinite Ensembles.

Data Generation without Function Estimation Stochastic Particle Gradient Descent for Infinite Ensembles

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:36.385333Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 60ab3b0a-e529-409d-b0c7-c36f8115602d · outbound

This paper cites Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner.

Data Generation without Function Estimation Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner

Reference 2019

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:34:40.783267Z

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 2f9803fb-06bd-4c84-9feb-ae5adfa6eea0 · outbound

This paper cites Field Matching: an Electrostatic Paradigm to Generate and Transfer Data.

Data Generation without Function Estimation Field Matching: an Electrostatic Paradigm to Generate and Transfer Data

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:36.517374Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.