Paper Citation Record · LEDGER

Interacting Geodesics on Discrete Manifolds

As of 8 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2506.12054.

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

pith.paper-citation-record.v1
2506.12054 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:46:30.354755Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

31 of 31 outbound references displayed

verified exact1
verified fuzzy12
unresolved18
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7f4082c8-7c5e-4fd8-b13d-3bbffebbb233 · outbound

This paper cites Alexandroff.

Interacting Geodesics on Discrete Manifolds Alexandroff

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:46:36.968992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6ef10791-a64c-4af6-ba0e-f557a4de1c8d · outbound

This paper cites Bachmann.

Interacting Geodesics on Discrete Manifolds Bachmann

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:46:36.705415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6ca950f9-7a88-4058-a559-97123344157f · outbound

This paper cites Baker and S.

Interacting Geodesics on Discrete Manifolds Baker and S

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:46:36.467847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 28843a2a-0a98-45e0-8401-2ebd46aa5feb · outbound

This paper cites Brown and K.

Interacting Geodesics on Discrete Manifolds Brown and K

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:46:36.211290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4477f4ef-25b6-495b-aa4f-fbe9fd30620d · outbound

This paper cites Chopard and M.

Interacting Geodesics on Discrete Manifolds Chopard and M

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:46:35.939638Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 60ac4b37-e2ba-4f96-a3fb-045770fcbc87 · outbound

This paper cites an unresolved cited work.

Interacting Geodesics on Discrete Manifolds Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:46:35.712640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation bbb42c56-e8b0-4c6f-b4a6-259ae55675f2 · outbound

This paper cites Hardy, O.

Interacting Geodesics on Discrete Manifolds Hardy, O

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:46:35.497782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 20f621a6-3d3e-451c-983e-3e60080f5fe2 · outbound

This paper cites Hardy and Y.

Interacting Geodesics on Discrete Manifolds Hardy and Y

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:46:35.203012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e4b38dfe-a856-4655-9c1f-26f285b0ef20 · outbound

This paper cites Hasslacher.

Interacting Geodesics on Discrete Manifolds Hasslacher

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:46:35.000432Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d916ea5d-f81a-47d5-bff1-06f971d8e21f · outbound

This paper cites an unresolved cited work.

Interacting Geodesics on Discrete Manifolds Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:46:34.750437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 16416ee4-39d5-4017-98ad-7bf456f4b2a1 · outbound

This paper cites an unresolved cited work.

Interacting Geodesics on Discrete Manifolds Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:46:34.446291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 821bfaf2-3f2e-4052-a535-46160885c74d · outbound

This paper cites Hof and O.

Interacting Geodesics on Discrete Manifolds Hof and O

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:46:34.193875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 89a4ada4-a8ae-422d-b54a-77d85a126c95 · outbound

This paper cites Hofer and E.

Interacting Geodesics on Discrete Manifolds Hofer and E

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:46:33.854670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 64035478-16d3-48df-ba8a-40a72b3a0018 · outbound

This paper cites Ilachinski.

Interacting Geodesics on Discrete Manifolds Ilachinski

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:46:33.518072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6bb34f5a-ced0-49f8-8868-45fde98f26ab · outbound

This paper cites an unresolved cited work.

Interacting Geodesics on Discrete Manifolds Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:46:33.250172Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0f329a7a-1d3a-4e3c-8181-1fa63d2a09de · outbound

This paper cites an unresolved cited work.

Interacting Geodesics on Discrete Manifolds Unresolved cited work

Reference 16

Resolution: verified exact; raw_fallback, observed 2026-08-07T12:46:30.945425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c2800f85-105c-4fec-b5f7-c9ce90b10459 · outbound

This paper cites A graph theoretical Gauss-Bonnet-Chern Theorem.

Interacting Geodesics on Discrete Manifolds A graph theoretical Gauss-Bonnet-Chern Theorem

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T12:46:29.219847Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1ae409ee-7ecb-415f-a15c-e31251f9044c · outbound

This paper cites Dehn-Sommerville from Gauss-Bonnet.

Interacting Geodesics on Discrete Manifolds Dehn-Sommerville from Gauss-Bonnet

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T12:46:29.302974Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 94c8c2f0-2eb8-47d2-8950-75206b953fe5 · outbound

This paper cites More on Numbers and Graphs.

Interacting Geodesics on Discrete Manifolds More on Numbers and Graphs

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T12:46:29.394117Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b0ece8c-49ff-46e6-9238-d9b1f16be625 · outbound

This paper cites On Graphs, Groups and Geometry.

Interacting Geodesics on Discrete Manifolds On Graphs, Groups and Geometry

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T12:46:29.462023Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a3a78bca-a362-4ca2-b27e-088e99c8113f · outbound

This paper cites Finite topologies for finite geometries.

Interacting Geodesics on Discrete Manifolds Finite topologies for finite geometries

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T12:46:29.534833Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e3f5c7c-3650-4dc1-81eb-c72dbb169dbf · outbound

This paper cites an unresolved cited work.

Interacting Geodesics on Discrete Manifolds Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:46:32.999236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d737ae2e-9227-4f96-a36a-f091f3cf8626 · outbound

This paper cites an unresolved cited work.

Interacting Geodesics on Discrete Manifolds Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:46:32.788864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 319c300e-d163-40f1-92e4-3b5b7fc43b54 · outbound

This paper cites an unresolved cited work.

Interacting Geodesics on Discrete Manifolds Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:46:32.547697Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ca9e805b-5088-43cb-b4f7-dbff84c4f35a · outbound

This paper cites an unresolved cited work.

Interacting Geodesics on Discrete Manifolds Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:46:32.392632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 940e27ac-e3d3-4650-ba30-a229c0aea8bb · outbound

This paper cites an unresolved cited work.

Interacting Geodesics on Discrete Manifolds Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:46:32.251056Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5294c36e-65e0-4fe9-b3e8-6db69d6d007e · outbound

This paper cites ’t Hooft.

Interacting Geodesics on Discrete Manifolds ’t Hooft

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:46:32.091316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e040e293-41b2-4826-af89-82fdb13dfcaf · outbound

This paper cites an unresolved cited work.

Interacting Geodesics on Discrete Manifolds Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:46:31.884352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 80b29e56-21ea-44e6-88b1-49bc1f907dab · outbound

This paper cites an unresolved cited work.

Interacting Geodesics on Discrete Manifolds Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:46:31.645600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation cbcc9ca1-7398-4010-947b-d2f3864ec012 · outbound

This paper cites an unresolved cited work.

Interacting Geodesics on Discrete Manifolds Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:46:31.396907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 25c8bb83-7c6c-4aa5-ade2-bf0871a20c79 · outbound

This paper cites an unresolved cited work.

Interacting Geodesics on Discrete Manifolds Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:46:31.153376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

No inbound Pith citation observations are available.