Paper Citation Record · LEDGER

Conjugation, loop and closure invariants of the iterated-integrals signature

As of 11 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 1 inbound Pith citation observation for arXiv:2412.19670.

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

pith.paper-citation-record.v1
2412.19670 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T00:11:41.010736Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T15:15:49.502761Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-11T15:15:49.655273Z

Reference resolution

26 of 26 outbound references displayed

verified exact1
verified fuzzy18
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8e62abf6-a018-4b8a-8373-2e253544f094 · outbound

This paper cites The infinite brownian loop on a symmetric space.

Conjugation, loop and closure invariants of the iterated-integrals signature The infinite brownian loop on a symmetric space

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.827548Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation bd155570-494e-411c-bc9e-b2e9341c1754 · outbound

This paper cites Varieties of Signature Tensors.

Conjugation, loop and closure invariants of the iterated-integrals signature Varieties of Signature Tensors

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.801840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 0cfc92b7-2300-45ae-bd18-5dbed040651d · outbound

This paper cites Cyclic quasi-symmetric functions.

Conjugation, loop and closure invariants of the iterated-integrals signature Cyclic quasi-symmetric functions

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.760115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6e34a95b-a6f0-4717-95d1-e60e00a67229 · outbound

This paper cites Convex hulls of curves: Volumes and signatures.

Conjugation, loop and closure invariants of the iterated-integrals signature Convex hulls of curves: Volumes and signatures

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.732630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3b1c8119-0b95-405c-9fee-f5b121199e9f · outbound

This paper cites The signature of a rough path: uniqueness.

Conjugation, loop and closure invariants of the iterated-integrals signature The signature of a rough path: uniqueness

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T00:11:40.790938Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2bca945-5374-419e-a786-5a0cd838a53f · outbound

This paper cites an unresolved cited work.

Conjugation, loop and closure invariants of the iterated-integrals signature Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-11T00:11:41.685690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation be617a32-69aa-47f4-867a-9b92b09bdc55 · outbound

This paper cites Invariants and coinvariants of the symmetric group in noncommuting variables.

Conjugation, loop and closure invariants of the iterated-integrals signature Invariants and coinvariants of the symmetric group in noncommuting variables

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.663573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c76aa049-7f8d-4ebe-9256-57ff6812ee4b · outbound

This paper cites On the sn-module structure of the noncommutative harmonics.

Conjugation, loop and closure invariants of the iterated-integrals signature On the sn-module structure of the noncommutative harmonics

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.624923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 7a1ecc00-6ef8-424b-a350-d2d56588a7a1 · outbound

This paper cites A multiplicative surface signature through its Magnus expansion.

Conjugation, loop and closure invariants of the iterated-integrals signature A multiplicative surface signature through its Magnus expansion

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T00:11:40.831746Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2fbc247-3250-4b09-ba64-ea3d47861ae9 · outbound

This paper cites Integration of paths---a faithful representation of paths by non-commutative formal power series.

Conjugation, loop and closure invariants of the iterated-integrals signature Integration of paths---a faithful representation of paths by non-commutative formal power series

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.598916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f0145eec-158c-40c3-8ee6-58f27fb2b28d · outbound

This paper cites A primer on the signature method in machine learning.

Conjugation, loop and closure invariants of the iterated-integrals signature A primer on the signature method in machine learning

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T00:11:40.850646Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dca4f31c-ab8c-472a-863a-3679a4edc7b1 · outbound

This paper cites Characteristic functions of measures on geometric rough paths.

Conjugation, loop and closure invariants of the iterated-integrals signature Characteristic functions of measures on geometric rough paths

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.569051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e4c61099-6001-447b-be44-723c6cae77af · outbound

This paper cites Time-warping invariants of multidimensional time series.

Conjugation, loop and closure invariants of the iterated-integrals signature Time-warping invariants of multidimensional time series

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.542434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d0e0c92f-44fc-4f17-91ef-4504e3fc30ff · outbound

This paper cites Signature invariants characterize orbits of paths under compact matrix group action.

Conjugation, loop and closure invariants of the iterated-integrals signature Signature invariants characterize orbits of paths under compact matrix group action

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.515678Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 225c63f3-acd8-46cd-b2e4-4fe4f5111189 · outbound

This paper cites Areas of areas generate the shuffle algebra, 2021.

Conjugation, loop and closure invariants of the iterated-integrals signature Areas of areas generate the shuffle algebra, 2021

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.479746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 954beab9-1eff-4b44-bc63-e3f77aeae7e6 · outbound

This paper cites The moving-frame method for the iterated-integrals signature: Orthogonal invariants.

Conjugation, loop and closure invariants of the iterated-integrals signature The moving-frame method for the iterated-integrals signature: Orthogonal invariants

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.457119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4c85e245-3ebb-4c9f-9f68-c14e0e5f4520 · outbound

This paper cites Invariants of multidimensional time series based on their iterated-integral signature.

Conjugation, loop and closure invariants of the iterated-integrals signature Invariants of multidimensional time series based on their iterated-integral signature

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.435556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation bce83732-04f7-400c-8fec-306f0a3651f8 · outbound

This paper cites Multidimensional stochastic processes as rough paths: theory and applications , volume 120.

Conjugation, loop and closure invariants of the iterated-integrals signature Multidimensional stochastic processes as rough paths: theory and applications , volume 120

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T00:11:40.924799Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1bb262cd-097c-4a59-a91f-80ea4156c7ff · outbound

This paper cites Algebraic Topology.

Conjugation, loop and closure invariants of the iterated-integrals signature Algebraic Topology

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T00:11:40.936016Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d04ccede-e570-4808-ae48-6adb492a1a6b · outbound

This paper cites Cyclic polytopes through the lens of iterated integrals.

Conjugation, loop and closure invariants of the iterated-integrals signature Cyclic polytopes through the lens of iterated integrals

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-11T00:11:41.120061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 343e5a2b-dc38-42d1-bd74-9fab9881a7b9 · outbound

This paper cites Physical activity recognition by smartphones, a survey.

Conjugation, loop and closure invariants of the iterated-integrals signature Physical activity recognition by smartphones, a survey

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.384163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e8c7d8f1-2c70-4855-9975-de975b6107c7 · outbound

This paper cites an unresolved cited work.

Conjugation, loop and closure invariants of the iterated-integrals signature Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-11T00:11:41.360793Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 13436571-65ba-44bb-b522-1890da3e880d · outbound

This paper cites The on-line encyclopedia of integer sequences, 2024.

Conjugation, loop and closure invariants of the iterated-integrals signature The on-line encyclopedia of integer sequences, 2024

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.339370Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 92d825a0-a508-4e4e-bd7d-2c883e976dd2 · outbound

This paper cites Free Lie Algebras.

Conjugation, loop and closure invariants of the iterated-integrals signature Free Lie Algebras

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.317507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 26685bb4-7226-4b97-bcd1-2c62fa85d4a5 · outbound

This paper cites Continuous Martingales and Brownian Motion.

Conjugation, loop and closure invariants of the iterated-integrals signature Continuous Martingales and Brownian Motion

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.295974Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 7d7e937c-a069-466d-9cd0-1e71fe7986e9 · outbound

This paper cites Poincar\' e 's proof of the so-called birkhoff-witt theorem, 1999.

Conjugation, loop and closure invariants of the iterated-integrals signature Poincar\' e 's proof of the so-called birkhoff-witt theorem, 1999

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:11:41.265577Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

Observation 934dd311-1a0b-47f8-bc24-44656665b126 · inbound

Cyclic polytopes through the lens of iterated integrals cites this paper.

Cyclic polytopes through the lens of iterated integrals Conjugation, loop and closure invariants of the iterated-integrals signature

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-11T15:15:49.672196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.