Paper Citation Record · LEDGER

Tropical Ptolemy Transformations and Invariants of Braids

As of 8 August 2026, this Paper Citation Record lists 9 of 9 outbound references and 0 inbound Pith citation observations for arXiv:2506.12085.

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

pith.paper-citation-record.v1
2506.12085 v1

Coverage vector

measured 9 of 9 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:20:44.698199Z

measured 9 of 9 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

9 of 9 outbound references displayed

verified exact5
verified fuzzy1
unresolved1
parse uncertain0
malformed identifier2
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 30938681-ab49-4313-81e1-68bba6504d5b · outbound

This paper cites Manturov,Knot Theory, Chapman & Hall/CRC Press, Boca Raton, FL, 2004.

Tropical Ptolemy Transformations and Invariants of Braids Manturov,Knot Theory, Chapman & Hall/CRC Press, Boca Raton, FL, 2004

Reference 1

Resolution: verified exact; doi, observed 2026-08-07T05:20:44.777535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c5c3dfcd-36bf-4f61-af2e-b3ce94c6f961 · outbound

This paper cites Manturov, Denis A.

Tropical Ptolemy Transformations and Invariants of Braids Manturov, Denis A

Reference 2

Resolution: malformed identifier; doi_truncated, observed 2026-08-07T05:20:44.767498Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 14615f3d-80f7-4b0f-8449-56e81484063a · outbound

This paper cites Aurenhammer, R.

Tropical Ptolemy Transformations and Invariants of Braids Aurenhammer, R

Reference 3

Resolution: malformed identifier; doi_truncated, observed 2026-08-07T05:20:44.758130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b2b79a31-7b3b-458e-b92a-f00f24ea3f0d · outbound

This paper cites Manturov,Artin’s braids, braids for three space, and groupsΓ4 n and Gk n, Journal of Knot Theory and Its Ramifications, 28(3):1950063, 2019.

Tropical Ptolemy Transformations and Invariants of Braids Manturov,Artin’s braids, braids for three space, and groupsΓ4 n and Gk n, Journal of Knot Theory and Its Ramifications, 28(3):1950063, 2019

Reference 4

Resolution: verified exact; doi, observed 2026-08-07T05:20:44.748504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b382cb13-5bab-4903-9339-6ce3c653424c · outbound

This paper cites The groups $\Gamma_{n}^{4}$, braids, and $3$-manifolds.

Tropical Ptolemy Transformations and Invariants of Braids The groups $\Gamma_{n}^{4}$, braids, and $3$-manifolds

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T05:20:44.685305Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 05b2dcaa-bb3d-4758-a15b-d316079dbe68 · outbound

This paper cites Fedoseev, V.O.

Tropical Ptolemy Transformations and Invariants of Braids Fedoseev, V.O

Reference 6

Resolution: verified exact; doi, observed 2026-08-07T05:20:44.738386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ed538b9e-9732-4250-925f-3cfbb1ec19bb · outbound

This paper cites Rohozhkin, Pentagon equations, Delaunay triangulations and pure braid group invariant, Journal of Knot Theory and Its Ramifications, vol.

Tropical Ptolemy Transformations and Invariants of Braids Rohozhkin, Pentagon equations, Delaunay triangulations and pure braid group invariant, Journal of Knot Theory and Its Ramifications, vol

Reference 7

Resolution: verified exact; doi, observed 2026-08-07T05:20:44.727965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 82cde990-207b-4679-ac6b-29633f4de2be · outbound

This paper cites Felikson,Ptolemy Relation and Friends, arXiv.3202.06379, 2 April 2023.

Tropical Ptolemy Transformations and Invariants of Braids Felikson,Ptolemy Relation and Friends, arXiv.3202.06379, 2 April 2023

Reference 8

Resolution: verified exact; raw_fallback, observed 2026-08-07T05:20:44.888580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 764b773d-b003-4f89-b3a9-8aef4bf78b25 · outbound

This paper cites 161, American Mathematical Society, Providence, RI, 2015.

Tropical Ptolemy Transformations and Invariants of Braids 161, American Mathematical Society, Providence, RI, 2015

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:20:44.906574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.