Paper Citation Record · LEDGER

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups

As of 8 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2507.00250.

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

pith.paper-citation-record.v1
2507.00250 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:32:06.222758Z

measured 18 of 18 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

18 of 18 outbound references displayed

verified exact4
verified fuzzy12
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1c6ca7fc-0a5a-466e-92e3-27720fa8c227 · outbound

This paper cites The quasihyperbolic plane.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups The quasihyperbolic plane

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:32:06.504654Z

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 e49b7698-80b2-4aed-89a6-1a8a5410fe8d · outbound

This paper cites Explicit Formulae for Geodesics in Left–Invariant Sub–Finsler Problems on Heisenberg Groups via Convex Trigonometry.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Explicit Formulae for Geodesics in Left–Invariant Sub–Finsler Problems on Heisenberg Groups via Convex Trigonometry

Reference 2

Resolution: verified exact; doi, observed 2026-08-06T21:32:06.294641Z

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 44e164c2-b39a-4ce8-b037-3cb5aa5c41ce · outbound

This paper cites An Isoperimetric Problem on the Lobachevsky Plane with a Left- Invariant Finsler Structure.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups An Isoperimetric Problem on the Lobachevsky Plane with a Left- Invariant Finsler Structure

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:32:06.494036Z

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 89895883-dbd9-4882-8e27-f1f22fee1050 · outbound

This paper cites Lorentzian Geometry on the Lobachevsky Plane.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Lorentzian Geometry on the Lobachevsky Plane

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:32:06.482255Z

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 bc972688-1647-44f4-b5e4-165a368c0b01 · outbound

This paper cites Sub-Lorentzian Problem on the Heisenberg Group.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Sub-Lorentzian Problem on the Heisenberg Group

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:32:06.470410Z

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 0dae1e7e-a144-4f19-8145-308e7d3a04d5 · outbound

This paper cites Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-06T21:32:06.345020Z

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 4a9528ea-7549-4f10-8bb1-3e4bcde65420 · outbound

This paper cites an unresolved cited work.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:32:06.458158Z

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 7e8b26b3-79c3-4827-b411-4cee20a6afff · outbound

This paper cites Agrachev, D.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Agrachev, D

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:32:06.446742Z

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 9d475500-cf08-4351-a4e3-dab92b736d20 · outbound

This paper cites Chang, I.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Chang, I

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:32:06.436393Z

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 f740bf95-1002-4eb8-806f-96fc4890d18c · outbound

This paper cites Grochowski, «Geodesics in the sub-Lorentzian geometry», Bulletin of the Pol- ish Academy of Sciences.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Grochowski, «Geodesics in the sub-Lorentzian geometry», Bulletin of the Pol- ish Academy of Sciences

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:32:06.425864Z

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 ecc7bab1-6921-45e9-9a48-d2265fe09039 · outbound

This paper cites Grochowski, «Properties of reachable sets in the sub-Lorentzian geometry», Journal of Geometry and Physics, 2009, vol.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Grochowski, «Properties of reachable sets in the sub-Lorentzian geometry», Journal of Geometry and Physics, 2009, vol

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:32:06.414844Z

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 b323ab7d-b9d3-445d-9c52-549cb2a5f28d · outbound

This paper cites Grong, A.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Grong, A

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:32:06.403157Z

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 5f9b811e-1fa7-42ca-bbbc-790285966cc5 · outbound

This paper cites Korolko and I.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Korolko and I

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:32:06.391884Z

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 f7549502-893a-4993-9d9a-dea8c0882cd7 · outbound

This paper cites Explicit formulae for geodesics in left invariant sub-Finsler problems on Heisenberg groups via convex trigonometry.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Explicit formulae for geodesics in left invariant sub-Finsler problems on Heisenberg groups via convex trigonometry

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-06T21:32:06.328776Z

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 6f93893d-f60e-4577-a8e6-b2cc14411ed2 · outbound

This paper cites an unresolved cited work.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:32:06.381217Z

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 512d723f-0a7f-4d0f-8af7-d2a5ea52d5c9 · outbound

This paper cites Sub-Lorentzian extremals defined by an antinorm.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Sub-Lorentzian extremals defined by an antinorm

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-06T21:32:06.311345Z

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 151f4298-0d8b-4ca7-892c-c458b121b490 · outbound

This paper cites Metrized left-invariant orders on topological groups.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Metrized left-invariant orders on topological groups

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:32:06.369248Z

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 ab6b1034-5a88-4460-b5ce-511558de925d · outbound

This paper cites Differential equations with discontinuous right-hand side.

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Differential equations with discontinuous right-hand side

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:32:06.356942Z

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.