Paper Citation Record · LEDGER

Learning Barycenters from Signature Matrices

As of 13 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 3 inbound Pith citation observations for arXiv:2509.07815.

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

pith.paper-citation-record.v1
2509.07815 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T21:53:59.507589Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T16:19:53.838129Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-05T09:10:52.133335Z

Reference resolution

27 of 27 outbound references displayed

verified exact0
verified fuzzy19
unresolved8
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 57308404-5d35-4b41-adb2-c7352cef0b6b · outbound

This paper cites Améndola, P.

Learning Barycenters from Signature Matrices Améndola, P

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:05.999808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7a72026e-c01c-496b-889f-2eee51dadded · outbound

This paper cites Améndola, F.

Learning Barycenters from Signature Matrices Améndola, F

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:05.697294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d980b441-0a6c-4d63-b8ec-701a3fe3f352 · outbound

This paper cites Computing Path Signature Varieties in Macaulay2.

Learning Barycenters from Signature Matrices Computing Path Signature Varieties in Macaulay2

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T21:53:53.991192Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4c8586ba-2224-4153-b675-7b6320e2ef58 · outbound

This paper cites Bayer, P.

Learning Barycenters from Signature Matrices Bayer, P

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:05.349125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6ca0c47d-554f-4938-9a9e-6d724cfae11d · outbound

This paper cites Bonnier and H.

Learning Barycenters from Signature Matrices Bonnier and H

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:05.076084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 619189cb-d4e3-4b22-a75b-bcb8553a9793 · outbound

This paper cites Buser and H.

Learning Barycenters from Signature Matrices Buser and H

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:04.767251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 10753a4b-aad9-42fb-b5ed-1c6a3a9258c9 · outbound

This paper cites Chevyrev and A.

Learning Barycenters from Signature Matrices Chevyrev and A

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T21:53:54.801558Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b6eb6e7-9218-4a7c-98a4-eb7f60c5c336 · outbound

This paper cites Clausel, J.

Learning Barycenters from Signature Matrices Clausel, J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:04.509010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 225ec0a6-231d-4712-b999-e75458bcbf6b · outbound

This paper cites Cuchiero, G.

Learning Barycenters from Signature Matrices Cuchiero, G

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:04.139721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation fb9b6a2d-add9-4b32-9625-cc135195a308 · outbound

This paper cites Decker, C.

Learning Barycenters from Signature Matrices Decker, C

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:03.799128Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 14e6f6db-a257-40ae-ba21-d340b6ccdb57 · outbound

This paper cites Diehl and R.

Learning Barycenters from Signature Matrices Diehl and R

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:03.451351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4b339bdf-74cc-4cd3-84a2-b09224d2b165 · outbound

This paper cites an unresolved cited work.

Learning Barycenters from Signature Matrices Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-04T21:54:03.204135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 615d3a0a-0bac-471b-adcb-56a7c23b20bd · outbound

This paper cites an unresolved cited work.

Learning Barycenters from Signature Matrices Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-04T21:54:02.957012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 791b0e6f-64ef-4704-9ce1-70e190970849 · outbound

This paper cites an unresolved cited work.

Learning Barycenters from Signature Matrices Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-04T21:54:02.782828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0f597da2-990d-43e2-bd88-7c236a344311 · outbound

This paper cites an unresolved cited work.

Learning Barycenters from Signature Matrices Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-04T21:54:02.630375Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7ddcf8b3-5b17-4077-829b-d36759c9cdd3 · outbound

This paper cites Kidger and T.

Learning Barycenters from Signature Matrices Kidger and T

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:02.527691Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6a5f3ca9-a78a-4452-b91e-f3ca64832a33 · outbound

This paper cites Koecher and A.

Learning Barycenters from Signature Matrices Koecher and A

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:02.180749Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d7d83a69-6571-42af-be26-d2a47b92ff7a · outbound

This paper cites Laaksonen , Guide to competitive programming , Springer, 2020.

Learning Barycenters from Signature Matrices Laaksonen , Guide to competitive programming , Springer, 2020

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:01.893831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 36aeaa46-4013-4267-a21d-e026d324c257 · outbound

This paper cites Moakher , Means and averaging in the group of rotations , SIAM journal on matrix analysis and applications, 24 (2002), pp.

Learning Barycenters from Signature Matrices Moakher , Means and averaging in the group of rotations , SIAM journal on matrix analysis and applications, 24 (2002), pp

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:01.673656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2fe9df67-98cf-47fe-8154-a0a37eb21b56 · outbound

This paper cites Ni , The expected signature of a stochastic process , PhD thesis, Oxford University, UK, 2012.

Learning Barycenters from Signature Matrices Ni , The expected signature of a stochastic process , PhD thesis, Oxford University, UK, 2012

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:01.476340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c29788c0-b3ec-4e47-8348-6c92b185452a · outbound

This paper cites https://www.oscar-system.org.

Learning Barycenters from Signature Matrices https://www.oscar-system.org

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:01.212306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a538d38e-2c73-4aad-81f0-ae963a1c2a16 · outbound

This paper cites Pennec and M.

Learning Barycenters from Signature Matrices Pennec and M

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:01.063952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 364eb053-06f2-49ca-9e67-db318b7d5f6c · outbound

This paper cites an unresolved cited work.

Learning Barycenters from Signature Matrices Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-04T21:54:00.820944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 102d2337-989e-450f-b887-af0da6f6c21a · outbound

This paper cites Pfeffer, A.

Learning Barycenters from Signature Matrices Pfeffer, A

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:00.643453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 10a88077-d760-4215-8dbc-127b8f5a7b00 · outbound

This paper cites an unresolved cited work.

Learning Barycenters from Signature Matrices Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-04T21:54:00.404860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8778c7aa-a495-4775-b141-4efd2ffc07e8 · outbound

This paper cites Reutenauer , Free Lie algebras , Oxford University press, 1993.

Learning Barycenters from Signature Matrices Reutenauer , Free Lie algebras , Oxford University press, 1993

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:54:00.165994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b873dd92-27bc-42dd-9828-1489ed34e02b · outbound

This paper cites Salvi, T.

Learning Barycenters from Signature Matrices Salvi, T

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:53:59.734334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

Observation d518f2de-4760-45d7-bdfe-af2d7bba4b0d · inbound

An Efficient Algorithm for Path Recovery from Signature Tensors cites this paper.

An Efficient Algorithm for Path Recovery from Signature Tensors Learning Barycenters from Signature Matrices

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-03T16:19:53.838129Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b1dc5bd-c19c-4705-bde7-e621bc7fb349 · inbound

SignatureTensors.jl: A Package for Signature Tensors in Julia cites this paper.

SignatureTensors.jl: A Package for Signature Tensors in Julia Learning Barycenters from Signature Matrices

Reference 72

Resolution: verified exact; arxiv_id, observed 2026-05-11T13:31:03.558788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4194ef02-0ed7-4d54-94ad-e3c1aa9aa0f2 · inbound

SignatureTensors.jl: A Package for Signature Tensors in Julia cites this paper.

SignatureTensors.jl: A Package for Signature Tensors in Julia Learning Barycenters from Signature Matrices

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-07-05T09:10:52.135310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.