Paper Citation Record · LEDGER

Discretization and Statistical Consistency of Functional Flow Matching

As of 9 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2608.04531.

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

pith.paper-citation-record.v1
2608.04531 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:52:09.737286Z

measured 33 of 33 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

33 of 33 outbound references displayed

verified exact3
verified fuzzy20
unresolved9
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b0b17924-67f7-46d8-82b7-1d4d6a04bf78 · outbound

This paper cites Adams and John J.

Discretization and Statistical Consistency of Functional Flow Matching Adams and John J

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.993715Z

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 f8c58e1e-eaff-49f0-8a46-a4611028cb14 · outbound

This paper cites Albergo, Nicholas M.

Discretization and Statistical Consistency of Functional Flow Matching Albergo, Nicholas M

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.985506Z

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 e0eebb0d-b648-44fd-84fc-aaab074efd9b · outbound

This paper cites Birkh¨ auser, Basel, second edition, 2008.

Discretization and Statistical Consistency of Functional Flow Matching Birkh¨ auser, Basel, second edition, 2008

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.978610Z

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 9aa1561a-c6ea-426b-895d-c26d8e9e13a8 · outbound

This paper cites Error bounds for flow match- ing methods.Transactions on Machine Learning Research, 2024.

Discretization and Statistical Consistency of Functional Flow Matching Error bounds for flow match- ing methods.Transactions on Machine Learning Research, 2024

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.971002Z

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 d0aa4556-7033-466e-a22f-9f76777b465a · outbound

This paper cites Bogachev.Gaussian Measures.

Discretization and Statistical Consistency of Functional Flow Matching Bogachev.Gaussian Measures

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.963121Z

Source-reported events for the cited work

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Observation bf4c2089-3c3b-43f7-b570-c449b41a3bcc · outbound

This paper cites Oxford University Press, Oxford, 2013.

Discretization and Statistical Consistency of Functional Flow Matching Oxford University Press, Oxford, 2013

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.956148Z

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 ce871fb8-7156-4b8e-94c2-5af0374c1887 · outbound

This paper cites Scale-Adaptive Generative Flows for Multiscale Scientific Data.

Discretization and Statistical Consistency of Functional Flow Matching Scale-Adaptive Generative Flows for Multiscale Scientific Data

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T22:52:09.660529Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 64fc79c2-c82f-45f2-a6bf-c2b62da5f29c · outbound

This paper cites Cambridge University Press, Cambridge, second edition, 2014.

Discretization and Statistical Consistency of Functional Flow Matching Cambridge University Press, Cambridge, second edition, 2014

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.949168Z

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 590e69a9-7420-45f8-9e13-2867ba8e70ac · outbound

This paper cites Flow matching achieves almost minimax optimal convergence.

Discretization and Statistical Consistency of Functional Flow Matching Flow matching achieves almost minimax optimal convergence

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-06T22:52:09.666760Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f7ce5869-abd6-453e-8f25-86951d9cb461 · outbound

This paper cites Multilevel diffusion: Infinite dimensional score-based diffusion models for image generation.SIAM Journal on Mathematics of Data Science, 7(3):1337–1366,.

Discretization and Statistical Consistency of Functional Flow Matching Multilevel diffusion: Infinite dimensional score-based diffusion models for image generation.SIAM Journal on Mathematics of Data Science, 7(3):1337–1366,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.941751Z

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 8a21aad5-42bc-4564-85e1-17929c81c01c · outbound

This paper cites Springer, Cham, third edition,.

Discretization and Statistical Consistency of Functional Flow Matching Springer, Cham, third edition,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.934522Z

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 5d8fa450-0a9f-4b58-98a2-46f8fbb08f32 · outbound

This paper cites Functional flow matching.

Discretization and Statistical Consistency of Functional Flow Matching Functional flow matching

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.927311Z

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 b77e920f-0e54-4b59-82b4-1a15dcc5ceb2 · outbound

This paper cites On universal approximation and error bounds for Fourier neural operators.Journal of Machine Learning Research, 22(290):1–76, 2021.

Discretization and Statistical Consistency of Functional Flow Matching On universal approximation and error bounds for Fourier neural operators.Journal of Machine Learning Research, 22(290):1–76, 2021

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.920197Z

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 b626aa2d-36d6-442e-851f-aa103e04dca2 · outbound

This paper cites Neural operator: Learning maps between function spaces with applications to PDEs.Journal of Machine Learning Re- search, 24(89):1–97, 2023.

Discretization and Statistical Consistency of Functional Flow Matching Neural operator: Learning maps between function spaces with applications to PDEs.Journal of Machine Learning Re- search, 24(89):1–97, 2023

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.913191Z

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 9aab9eff-180b-42ed-8ec9-251fa086d932 · outbound

This paper cites Error estimates for DeepONets: A deep learning framework in infinite dimensions.Transactions of Mathematics and Its Applications, 6(1):tnac001, 2022.

Discretization and Statistical Consistency of Functional Flow Matching Error estimates for DeepONets: A deep learning framework in infinite dimensions.Transactions of Mathematics and Its Applications, 6(1):tnac001, 2022

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T22:52:09.688481Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8f8b55b2-53af-4e28-b739-232f60b29105 · outbound

This paper cites Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space.

Discretization and Statistical Consistency of Functional Flow Matching Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:52:09.775424Z

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 7ecd6f63-d80f-4bb8-b4c9-8a7d6c34a4ff · outbound

This paper cites Functional mean flow in hilbert space.

Discretization and Statistical Consistency of Functional Flow Matching Functional mean flow in hilbert space

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.905659Z

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 038c1c8c-0bd5-4b67-991d-58a865ed4f7d · outbound

This paper cites an unresolved cited work.

Discretization and Statistical Consistency of Functional Flow Matching Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:52:09.897965Z

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 47b3f788-ff4b-4438-aad5-60913eab1d69 · outbound

This paper cites Flow straight and fast: Learning to generate and transfer data with rectified flow.

Discretization and Statistical Consistency of Functional Flow Matching Flow straight and fast: Learning to generate and transfer data with rectified flow

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.890644Z

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 1ccd9015-7cb8-47d8-8268-4e05121fbd95 · outbound

This paper cites Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.Nature Machine Intelligence, 3:218–229, 2021.

Discretization and Statistical Consistency of Functional Flow Matching Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.Nature Machine Intelligence, 3:218–229, 2021

Reference 20

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T22:52:09.882471Z

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 0a80ad9c-093a-4f89-8f35-b4e498268ce3 · outbound

This paper cites Probability-Flow ODE in Infinite-Dimensional Function Spaces.

Discretization and Statistical Consistency of Functional Flow Matching Probability-Flow ODE in Infinite-Dimensional Function Spaces

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-06T22:52:09.705707Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 43d4e755-b3fc-4a5a-89aa-eb62ffd3cb4b · outbound

This paper cites Narcowich, Joseph D.

Discretization and Statistical Consistency of Functional Flow Matching Narcowich, Joseph D

Reference 22

Resolution: verified exact; doi, observed 2026-08-06T22:52:09.763270Z

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 74c68d8a-d68b-4825-b389-9c86fea4cdde · outbound

This paper cites Infinite- dimensional diffusion models.Journal of Machine Learning Research, 25(414):1–52,.

Discretization and Statistical Consistency of Functional Flow Matching Infinite- dimensional diffusion models.Journal of Machine Learning Research, 25(414):1–52,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.874118Z

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 9f59eb06-1288-40af-b360-291f9d4b0941 · outbound

This paper cites Statistical learning theory for neural operators.Journal of Machine Learning Research, 27(102):1–82, 2026.

Discretization and Statistical Consistency of Functional Flow Matching Statistical learning theory for neural operators.Journal of Machine Learning Research, 27(102):1–82, 2026

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.857655Z

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 a3f9c20e-e441-40ba-ae06-f1944837e4c2 · outbound

This paper cites Ross, Domniki Asimaki, and Kamyar Aziz- zadenesheli.

Discretization and Statistical Consistency of Functional Flow Matching Ross, Domniki Asimaki, and Kamyar Aziz- zadenesheli

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.849120Z

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 193864f6-cdda-4c59-bbd0-97b70769043e · outbound

This paper cites Three superposition principles: Currents, continu- ity equations and curves of measures.Journal of Functional Analysis, 272(3):1044–1103,.

Discretization and Statistical Consistency of Functional Flow Matching Three superposition principles: Currents, continu- ity equations and curves of measures.Journal of Functional Analysis, 272(3):1044–1103,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.840778Z

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 f9592fc0-a537-4044-a680-9a9f6040a9a1 · outbound

This paper cites Cambridge University Press, Cam- bridge, 2005.

Discretization and Statistical Consistency of Functional Flow Matching Cambridge University Press, Cam- bridge, 2005

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.832503Z

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 9d5185c5-8069-4835-b11f-7f23bac4ef84 · outbound

This paper cites Flow straight and fast in hilbert space: Functional rectified flow.

Discretization and Statistical Consistency of Functional Flow Matching Flow straight and fast in hilbert space: Functional rectified flow

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:52:09.824528Z

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 9ce70409-8fb0-49a6-acf6-9fa4466bd7cb · outbound

This paper cites an unresolved cited work.

Discretization and Statistical Consistency of Functional Flow Matching Unresolved cited work

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-06T22:52:09.726448Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3de7bedc-a86c-43d1-b640-be5c4464fc15 · outbound

This paper cites an unresolved cited work.

Discretization and Statistical Consistency of Functional Flow Matching Unresolved cited work

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-06T22:52:09.677980Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4c7a093a-8a5a-4210-b293-4187a28a3663 · outbound

This paper cites an unresolved cited work.

Discretization and Statistical Consistency of Functional Flow Matching Unresolved cited work

Reference 2024

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:52:09.866735Z

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 fddff482-0ee0-4804-a26a-12a58243e838 · outbound

This paper cites an unresolved cited work.

Discretization and Statistical Consistency of Functional Flow Matching Unresolved cited work

Reference 2025

Resolution: verified exact; doi, observed 2026-08-06T22:52:09.791752Z

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 d719b282-ab74-40e0-9fb8-8a997537b0a1 · outbound

This paper cites an unresolved cited work.

Discretization and Statistical Consistency of Functional Flow Matching Unresolved cited work

Reference 2026

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:52:09.816871Z

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.

Pith citing papers

No inbound Pith citation observations are available.