Paper Citation Record · LEDGER

Density-Robust Spherical Coordinates from Persistent Cohomology

As of 20 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2607.24650.

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

pith.paper-citation-record.v1
2607.24650 v2

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-31T09:10:14.381815Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+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

24 of 24 outbound references displayed

verified exact8
verified fuzzy0
unresolved16
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malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d7862b56-75e8-4f83-877a-35bf7d422530 · outbound

This paper cites Corrections and Supplementaries to My Paper Concerning Krull-Remak- Schmidt’s Theorem.

Density-Robust Spherical Coordinates from Persistent Cohomology Corrections and Supplementaries to My Paper Concerning Krull-Remak- Schmidt’s Theorem

Reference 1

Resolution: verified exact; doi, observed 2026-07-31T09:10:59.794748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 194db5f0-47d8-4177-aa51-046179ed3456 · outbound

This paper cites Ripser: efficient computation of Vietoris–Rips persistence barcodes.

Density-Robust Spherical Coordinates from Persistent Cohomology Ripser: efficient computation of Vietoris–Rips persistence barcodes

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.099018Z

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Observation 1124a25d-a6e4-48a3-a606-206cfddcdbc5 · outbound

This paper cites A General Solution to Orthogonal Procrustes Problems.

Density-Robust Spherical Coordinates from Persistent Cohomology A General Solution to Orthogonal Procrustes Problems

Reference 3

Resolution: verified exact; doi, observed 2026-07-31T09:10:59.617640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation af573574-ba39-42c6-9222-011235260bde · outbound

This paper cites Subsampling, aligning, and averaging to find circular coordinates in recurrent time series.

Density-Robust Spherical Coordinates from Persistent Cohomology Subsampling, aligning, and averaging to find circular coordinates in recurrent time series

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.145303Z

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Observation 0d6409a0-424b-4470-b1eb-f398a5e25e60 · outbound

This paper cites Decomposition of Persistence Modules.

Density-Robust Spherical Coordinates from Persistent Cohomology Decomposition of Persistence Modules

Reference 5

Resolution: verified exact; doi, observed 2026-07-31T09:10:59.368195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c34b03dd-61a1-49ef-846d-2535039b7ea7 · outbound

This paper cites Topology and data.

Density-Robust Spherical Coordinates from Persistent Cohomology Topology and data

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.178211Z

Source-reported events for the cited work

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Observation 819988c7-63ec-4424-8ebd-18dbbe15f3a9 · outbound

This paper cites Decomposition of Pointwise Finite-Dimensional Persistence Mod- ules.

Density-Robust Spherical Coordinates from Persistent Cohomology Decomposition of Pointwise Finite-Dimensional Persistence Mod- ules

Reference 7

Resolution: verified exact; doi, observed 2026-07-31T09:10:59.212277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2180b01a-8e39-4ab0-bfaa-5d352ca97256 · outbound

This paper cites Persistent homology-a survey.

Density-Robust Spherical Coordinates from Persistent Cohomology Persistent homology-a survey

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.190912Z

Source-reported events for the cited work

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Observation 0d7d022c-6527-4f18-a7c1-25b6e9ff4adb · outbound

This paper cites Barcodes: The Persistent Topology of Data.

Density-Robust Spherical Coordinates from Persistent Cohomology Barcodes: The Persistent Topology of Data

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.214739Z

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Observation 993e0750-4d9f-4cae-9bec-4b85e055a3e2 · outbound

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Density-Robust Spherical Coordinates from Persistent Cohomology Unresolved cited work

Reference 10

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Observation 098d2675-7689-4da0-9830-1e1c9faed85d · outbound

This paper cites Cambridge, UK: Cambridge University Press, 2002 (cit.

Density-Robust Spherical Coordinates from Persistent Cohomology Cambridge, UK: Cambridge University Press, 2002 (cit

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.265091Z

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Observation a0a5925e-1cbb-4e75-89da-b76d85f746e3 · outbound

This paper cites Numba: A LL VM-based Python JIT Compiler.

Density-Robust Spherical Coordinates from Persistent Cohomology Numba: A LL VM-based Python JIT Compiler

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.293576Z

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Observation 3c6531d2-86bc-4278-901d-01c3ca1802d6 · outbound

This paper cites Visualizing Data Using t-SNE.

Density-Robust Spherical Coordinates from Persistent Cohomology Visualizing Data Using t-SNE

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.311470Z

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Observation cd62eafb-d1a3-4bbd-b4eb-b0f08f4c35c4 · outbound

This paper cites UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction.

Density-Robust Spherical Coordinates from Persistent Cohomology UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.314742Z

Source-reported events for the cited work

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Observation 0256282b-5a71-4ace-bfc8-d9b7c315e2d7 · outbound

This paper cites Geomstats: A Python Package for Riemannian Geometry in Machine Learning.

Density-Robust Spherical Coordinates from Persistent Cohomology Geomstats: A Python Package for Riemannian Geometry in Machine Learning

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.326469Z

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Observation 9f186903-10ba-4e7e-816d-3a7ad8a2efbf · outbound

This paper cites Circular Coordinates for Density-Robust Analysis.

Density-Robust Spherical Coordinates from Persistent Cohomology Circular Coordinates for Density-Robust Analysis

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.328951Z

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Observation 4afe00cf-bd2a-4203-ab0e-0ffb1f8bcfdf · outbound

This paper cites an unresolved cited work.

Density-Robust Spherical Coordinates from Persistent Cohomology Unresolved cited work

Reference 17

Resolution: verified exact; doi, observed 2026-07-31T09:10:58.977026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2038adc3-e6b8-4746-b054-596546f41341 · outbound

This paper cites Nonlinear Dimensionality Reduction by Locally Linear Embedding.

Density-Robust Spherical Coordinates from Persistent Cohomology Nonlinear Dimensionality Reduction by Locally Linear Embedding

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.335591Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 35ba9efc-8a48-407d-8436-dbefd7df5bcb · outbound

This paper cites Spherical coordinates from persistent coho- mology.

Density-Robust Spherical Coordinates from Persistent Cohomology Spherical coordinates from persistent coho- mology

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.354741Z

Source-reported events for the cited work

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Observation b8f80ea2-8155-4cfe-91ef-ae12f2795487 · outbound

This paper cites Dualities in Persistent (Co)Homology.

Density-Robust Spherical Coordinates from Persistent Cohomology Dualities in Persistent (Co)Homology

Reference 20

Resolution: verified exact; doi, observed 2026-07-31T09:10:58.758183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8e894068-efc2-46fb-98ea-a7f0f01b45e9 · outbound

This paper cites Persistent cohomology and circular coordinates.

Density-Robust Spherical Coordinates from Persistent Cohomology Persistent cohomology and circular coordinates

Reference 21

Resolution: verified exact; doi, observed 2026-07-31T09:10:58.582330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8f303ad9-8a93-4407-a7dc-d8e5710137f0 · outbound

This paper cites A Global Geometric Framework for Nonlinear Dimensionality Reduction.

Density-Robust Spherical Coordinates from Persistent Cohomology A Global Geometric Framework for Nonlinear Dimensionality Reduction

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.376527Z

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Observation e1d85b1a-8b12-4279-8e2b-a653cb9ca330 · outbound

This paper cites SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python.

Density-Robust Spherical Coordinates from Persistent Cohomology SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python

Reference 23

Resolution: verified exact; doi, observed 2026-07-31T09:10:58.413383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a6e1e764-bc7c-4dc0-9661-ea4d71da7b9d · outbound

This paper cites Computing persistent homology.

Density-Robust Spherical Coordinates from Persistent Cohomology Computing persistent homology

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-31T09:10:14.381815Z

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Pith citing papers

No inbound Pith citation observations are available.