Paper Citation Record · LEDGER

Thin homotopy and the signature of piecewise linear surfaces

As of 16 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 1 inbound Pith citation observation for arXiv:2506.16657.

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

pith.paper-citation-record.v1
2506.16657 v1

Coverage vector

measured 55 of 55 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:32:17.720912Z

measured 56 of 56 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-16T07:43:15.886960Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-16T07:47:33.174888Z

Reference resolution

55 of 55 outbound references displayed

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External citation measurements

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Outbound references

Observation a38a009f-6b51-4932-a5ea-b3ab181bbbf6 · outbound

This paper cites The A ∞ de Rham Theorem and Integration of Representations up to Homotopy.

Thin homotopy and the signature of piecewise linear surfaces The A ∞ de Rham Theorem and Integration of Representations up to Homotopy

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:32:18.380409Z

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Observation 257a460b-67d7-48b1-b561-3212b5f559f7 · outbound

This paper cites Higher Gauge Theory: 2-Connections on 2-Bundles.

Thin homotopy and the signature of piecewise linear surfaces Higher Gauge Theory: 2-Connections on 2-Bundles

Reference 2

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Thin homotopy and the signature of piecewise linear surfaces Unresolved cited work

Reference 3

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Thin homotopy and the signature of piecewise linear surfaces Unresolved cited work

Reference 4

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Observation f8bc84da-d5f0-4b11-8f54-5d5c86e20552 · outbound

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

Thin homotopy and the signature of piecewise linear surfaces The signature of a rough path: Uniqueness

Reference 5

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Thin homotopy and the signature of piecewise linear surfaces Unresolved cited work

Reference 6

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Thin homotopy and the signature of piecewise linear surfaces Unresolved cited work

Reference 7

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This paper cites Brown, P .J.

Thin homotopy and the signature of piecewise linear surfaces Brown, P .J

Reference 8

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This paper cites On the Second Relative Homotopy Group of an Adjunction Space: An Exposition of a Theorem of J.

Thin homotopy and the signature of piecewise linear surfaces On the Second Relative Homotopy Group of an Adjunction Space: An Exposition of a Theorem of J

Reference 9

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This paper cites Identities among relations.

Thin homotopy and the signature of piecewise linear surfaces Identities among relations

Reference 10

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Observation 6b2c4be2-16cf-4758-b85b-e57e196e38fe · outbound

This paper cites Caetano and R.

Thin homotopy and the signature of piecewise linear surfaces Caetano and R

Reference 11

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Reference 12

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Thin homotopy and the signature of piecewise linear surfaces Unresolved cited work

Reference 13

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This paper cites Jacobiennes généralisées, monodromie unipotente et intégrales itérées.

Thin homotopy and the signature of piecewise linear surfaces Jacobiennes généralisées, monodromie unipotente et intégrales itérées

Reference 14

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This paper cites Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents.

Thin homotopy and the signature of piecewise linear surfaces Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents

Reference 15

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Observation c8458e3b-1854-4ff4-9582-9294a0e69265 · outbound

This paper cites Iterated Integrals and Exponential Homomorphisms†.

Thin homotopy and the signature of piecewise linear surfaces Iterated Integrals and Exponential Homomorphisms†

Reference 16

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Observation c9902155-6483-4e4a-986a-3006e80ccf8b · outbound

This paper cites Integration of paths – a faithful representation of paths by noncommutative formal power series.

Thin homotopy and the signature of piecewise linear surfaces Integration of paths – a faithful representation of paths by noncommutative formal power series

Reference 17

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Observation bdf3cc05-08d4-4d8e-8513-9805a0b46215 · outbound

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

Thin homotopy and the signature of piecewise linear surfaces A multiplicative surface signature through its Magnus expansion

Reference 18

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

Thin homotopy and the signature of piecewise linear surfaces Characteristic functions of measures on geometric rough paths

Reference 19

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Observation 474f3040-bfc7-41b4-88ad-42b97a97a15a · outbound

This paper cites Signature Moments to Characterize Laws of Stochastic Processes.

Thin homotopy and the signature of piecewise linear surfaces Signature Moments to Characterize Laws of Stochastic Processes

Reference 20

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This paper cites Über Systeme von liearren partiellen Differentialgleichungen erster Ordnung.

Thin homotopy and the signature of piecewise linear surfaces Über Systeme von liearren partiellen Differentialgleichungen erster Ordnung

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:32:18.207577Z

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This paper cites Categorifying the Knizhnik–Zamolodchikov connection.

Thin homotopy and the signature of piecewise linear surfaces Categorifying the Knizhnik–Zamolodchikov connection

Reference 22

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Thin homotopy and the signature of piecewise linear surfaces Unresolved cited work

Reference 23

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Observation a3aae368-c7ef-47d8-a1df-14ca4ca69ac1 · outbound

This paper cites On the signature of an image.

Thin homotopy and the signature of piecewise linear surfaces On the signature of an image

Reference 24

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Observation 91e1dafb-3d30-4684-b830-8c7c092f6d81 · outbound

This paper cites Two-parameter sums signatures and corresponding quasisymmetric functions.

Thin homotopy and the signature of piecewise linear surfaces Two-parameter sums signatures and corresponding quasisymmetric functions

Reference 25

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Thin homotopy and the signature of piecewise linear surfaces Friz and Martin Hairer

Reference 26

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Thin homotopy and the signature of piecewise linear surfaces Friz and Nicolas B

Reference 27

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This paper cites Young Tableaux: With Applications to Representation Theory and Geometry.

Thin homotopy and the signature of piecewise linear surfaces Young Tableaux: With Applications to Representation Theory and Geometry

Reference 28

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This paper cites A topological approach to mapping space signatures.

Thin homotopy and the signature of piecewise linear surfaces A topological approach to mapping space signatures

Reference 29

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Thin homotopy and the signature of piecewise linear surfaces Unresolved cited work

Reference 30

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Thin homotopy and the signature of piecewise linear surfaces Iterated Integrals and Homotopy Periods

Reference 31

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This paper cites Uniqueness for the signature of a path of bounded variation and the reduced path group.

Thin homotopy and the signature of piecewise linear surfaces Uniqueness for the signature of a path of bounded variation and the reduced path group

Reference 32

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This paper cites Fundamentalgruppe und zweite Bettische Gruppe.

Thin homotopy and the signature of piecewise linear surfaces Fundamentalgruppe und zweite Bettische Gruppe

Reference 33

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This paper cites Membranes and higher groupoids.

Thin homotopy and the signature of piecewise linear surfaces Membranes and higher groupoids

Reference 34

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This paper cites Signatory: Differentiable computations of the signature and logsignature trans- forms, on both {CPU} and {GPU}.

Thin homotopy and the signature of piecewise linear surfaces Signatory: Differentiable computations of the signature and logsignature trans- forms, on both {CPU} and {GPU}

Reference 35

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Thin homotopy and the signature of piecewise linear surfaces Formal connections, higher holonomy functors and iterated integrals

Reference 36

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Thin homotopy and the signature of piecewise linear surfaces Diagram Complexes, Formality, and Configuration Space Integrals for Spaces of Braids

Reference 37

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Thin homotopy and the signature of piecewise linear surfaces The Surface Signature and Rough Surfaces

Reference 38

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Thin homotopy and the signature of piecewise linear surfaces Random Surfaces and Higher Algebra

Reference 39

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Thin homotopy and the signature of piecewise linear surfaces The Signature Kernel, May 2023

Reference 40

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Thin homotopy and the signature of piecewise linear surfaces Differential equations driven by rough signals

Reference 41

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Observation e6460b8a-4fb2-4d79-8139-494bf4d6396a · outbound

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Thin homotopy and the signature of piecewise linear surfaces Differential Equations Driven by Rough Paths

Reference 42

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Thin homotopy and the signature of piecewise linear surfaces On two-dimensional holonomy

Reference 43

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Observation 3dbe3d4d-82ee-47fb-861d-bbd9ca48ee11 · outbound

This paper cites Surface holonomy for non-abelian 2-bundles via double groupoids.

Thin homotopy and the signature of piecewise linear surfaces Surface holonomy for non-abelian 2-bundles via double groupoids

Reference 44

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This paper cites Signature methods in machine learning.

Thin homotopy and the signature of piecewise linear surfaces Signature methods in machine learning

Reference 45

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This paper cites Thin homotopy and the holonomy approach to gauge theories.

Thin homotopy and the signature of piecewise linear surfaces Thin homotopy and the holonomy approach to gauge theories

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:32:18.005415Z

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This paper cites Dimensions and characters of the derived series of the free Lie algebra.

Thin homotopy and the signature of piecewise linear surfaces Dimensions and characters of the derived series of the free Lie algebra

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:32:17.995442Z

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Observation 8121036a-5907-4541-b3b0-717b770d7e44 · outbound

This paper cites Lie Groups: An Introduction through Linear Groups.

Thin homotopy and the signature of piecewise linear surfaces Lie Groups: An Introduction through Linear Groups

Reference 48

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Observation c26e9fda-8e21-401e-a32f-15d9f3ffaf4f · outbound

This paper cites Towards an M5-Brane Model II: Metric String Structures.

Thin homotopy and the signature of piecewise linear surfaces Towards an M5-Brane Model II: Metric String Structures

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:32:17.973083Z

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This paper cites Smooth functors vs.

Thin homotopy and the signature of piecewise linear surfaces Smooth functors vs

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:32:17.961030Z

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Observation 89c9235d-8237-40c9-b68f-81b9728a6a03 · outbound

This paper cites Lie Algebras and Lie Groups: 1964 Lectures given at Harvard University.

Thin homotopy and the signature of piecewise linear surfaces Lie Algebras and Lie Groups: 1964 Lectures given at Harvard University

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:32:17.949936Z

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Observation bfa3d45d-de0b-4251-949d-16ccadd0f6af · outbound

This paper cites On the holonomic equivalence of two curves.

Thin homotopy and the signature of piecewise linear surfaces On the holonomic equivalence of two curves

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:32:17.939192Z

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Observation b8fbc8b0-e93b-406d-979f-d1b7fea9e65a · outbound

This paper cites Seq2Tens: An Efficient Representation of Sequences by Low-Rank Tensor Projections.

Thin homotopy and the signature of piecewise linear surfaces Seq2Tens: An Efficient Representation of Sequences by Low-Rank Tensor Projections

Reference 53

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Thin homotopy and the signature of piecewise linear surfaces On a non-Abelian Poincaré lemma

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:32:17.929087Z

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Observation 40eeca62-ed12-4acb-a6eb-cf565c4fa786 · outbound

This paper cites an unresolved cited work.

Thin homotopy and the signature of piecewise linear surfaces Unresolved cited work

Reference 55

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:32:17.918979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

Observation eab035e9-110a-4ba7-9aa9-4a60f14140e3 · inbound

Symmetries and Higher-Form Connections in Derived Differential Geometry cites this paper.

Symmetries and Higher-Form Connections in Derived Differential Geometry Thin homotopy and the signature of piecewise linear surfaces

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-05-16T07:47:33.176458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.