Paper Citation Record · LEDGER

Computing Path Signature Varieties in Macaulay2

As of 13 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 3 inbound Pith citation observations for arXiv:2506.01429.

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

pith.paper-citation-record.v1
2506.01429 v1

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:52:31.067760Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T21:53:53.991192Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-05T09:10:52.126750Z

Reference resolution

16 of 16 outbound references displayed

verified exact2
verified fuzzy13
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3c9feacf-3f8a-455b-963a-eed0bf27519b · outbound

This paper cites Varieties of Signature Tensors.

Computing Path Signature Varieties in Macaulay2 Varieties of Signature Tensors

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T11:52:31.002819Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 92a26822-720e-458f-97e6-a41e18bf9449 · outbound

This paper cites Decomposing tensor spaces via path signatures.

Computing Path Signature Varieties in Macaulay2 Decomposing tensor spaces via path signatures

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:52:31.297928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d97c6ae0-30ac-48ad-9b70-5db6519b2f0e · outbound

This paper cites Numerically solving polynomial systems with Bertini.

Computing Path Signature Varieties in Macaulay2 Numerically solving polynomial systems with Bertini

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:52:31.285630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 475f15d9-d56c-449e-a2ee-3d10c10ea0b9 · outbound

This paper cites Toric geometry of path signature varieties.

Computing Path Signature Varieties in Macaulay2 Toric geometry of path signature varieties

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:52:31.273969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation aec2d11e-bd82-46fe-b84b-969c693617de · outbound

This paper cites Signatures of paths transformed by polynomial maps.

Computing Path Signature Varieties in Macaulay2 Signatures of paths transformed by polynomial maps

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:52:31.261781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 42942783-cb7f-49b5-9f60-9451518e12a0 · outbound

This paper cites Friz and Nicolas B.

Computing Path Signature Varieties in Macaulay2 Friz and Nicolas B

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:52:31.248849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d36a8f83-70b2-4daf-80c5-2e12a801d6ae · outbound

This paper cites The rough V eronese variety.

Computing Path Signature Varieties in Macaulay2 The rough V eronese variety

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:52:31.236325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 6d1f40aa-d348-40a5-b1da-e5e6c0730070 · outbound

This paper cites Macaulay2, a software system for research in algebraic geometry, 2002.

Computing Path Signature Varieties in Macaulay2 Macaulay2, a software system for research in algebraic geometry, 2002

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:52:31.223256Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 604b1d03-d6b5-4be0-869e-c6f2671f224e · outbound

This paper cites Rank and symmetries of signature tensors.

Computing Path Signature Varieties in Macaulay2 Rank and symmetries of signature tensors

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-07T11:52:31.133100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 411e53c9-82c7-4af1-a21a-02ae71e2fa14 · outbound

This paper cites Rough paths, signatures and the modelling of functions on streams.

Computing Path Signature Varieties in Macaulay2 Rough paths, signatures and the modelling of functions on streams

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:52:31.210200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 3b8c6e9a-44ee-469d-9c70-aafd8c0bf661 · outbound

This paper cites Invitation to nonlinear algebra , volume 211.

Computing Path Signature Varieties in Macaulay2 Invitation to nonlinear algebra , volume 211

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:52:31.197292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0b06f585-4667-4eb6-9022-9b3c6d3d9d23 · outbound

This paper cites An algebraic geometry of paths via the iterated-integrals signature.

Computing Path Signature Varieties in Macaulay2 An algebraic geometry of paths via the iterated-integrals signature

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-07T11:52:31.114619Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0705a81e-268a-4939-bdca-39a894778f51 · outbound

This paper cites Learning paths from signature tensors.

Computing Path Signature Varieties in Macaulay2 Learning paths from signature tensors

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:52:31.184071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 92c8367c-135c-4a07-9fb0-6f001b823ecf · outbound

This paper cites Lie elements and an algebra associated with shuffles.

Computing Path Signature Varieties in Macaulay2 Lie elements and an algebra associated with shuffles

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:52:31.171185Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ae4b962b-53ae-4adb-aaf1-449194e41f2b · outbound

This paper cites Reutenauer.

Computing Path Signature Varieties in Macaulay2 Reutenauer

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:52:31.158228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 04476b74-d09a-4424-8e05-bf7de0c7113b · outbound

This paper cites Algebraic statistics , volume 194.

Computing Path Signature Varieties in Macaulay2 Algebraic statistics , volume 194

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:52:31.145666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

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

Learning Barycenters from Signature Matrices cites this paper.

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 2fd482ce-a347-4b63-aa3e-2890c05c150e · inbound

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

SignatureTensors.jl: A Package for Signature Tensors in Julia Computing Path Signature Varieties in Macaulay2

Reference 73

Resolution: verified exact; arxiv_id, observed 2026-05-27T15:06:21.380187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4670e0aa-efe1-4a09-881b-cf607b5931c2 · inbound

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

SignatureTensors.jl: A Package for Signature Tensors in Julia Computing Path Signature Varieties in Macaulay2

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-07-05T09:10:52.128514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.