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Paper Citation Record · LEDGER

Sub-Randers metrics

As of 13 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 1 inbound Pith citation observation for arXiv:2606.21922.

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

pith.paper-citation-record.v1
2606.21922 v2

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-26T11:38:53.048456Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T19:57:57.163055Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

22 of 22 outbound references displayed

  • verified exact0
  • verified fuzzy0
  • unresolved22
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 59e53297-31ec-4315-942d-8f219c4016da · outbound

This paper cites Agrachev, D.

Sub-Randers metrics Agrachev, D

Reference 1

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:c07e6d3c233c88b00ebed5a1f03d5f19846fc819cf2d2c142f8141a8e93a2eb2

Observation f842299c-cb4d-4cec-ab00-af983ca97613 · outbound

This paper cites an unresolved cited work.

Sub-Randers metrics Unresolved cited work

Reference 2

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:91dfb2ea1fd0912c0ef604b28da928d0202ef24b719884cef38b5d48b9b57527

Observation d3a57820-be72-474d-aa5c-a8a79e5bce07 · outbound

This paper cites an unresolved cited work.

Sub-Randers metrics Unresolved cited work

Reference 3

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:3348f0f5e1d0e21738966a864bae9112e792b3332fe3438042dee7be369e29ba

Observation c45895ca-0925-444f-9638-6e147d624140 · outbound

This paper cites an unresolved cited work.

Sub-Randers metrics Unresolved cited work

Reference 4

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:6b033d660ecfc9acd5d7a079cf51c36ea8c4cc881d1baca0e4e929f5bd9c0e70

Observation b4a5c33c-0baa-40cd-b52f-ac4a8ff667e9 · outbound

This paper cites Bao, S.S.

Sub-Randers metrics Bao, S.S

Reference 5

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:f59a752280c012e74c2c8444d847cba92ab779aa40051e36bba740bd4c75046c

Observation 0e883001-e0b0-4810-9fa2-ab10882d7f06 · outbound

This paper cites Bao,Randers space forms, Periodica Mathematica Hungarica48(1-2)(2004), 3-15.

Sub-Randers metrics Bao,Randers space forms, Periodica Mathematica Hungarica48(1-2)(2004), 3-15

Reference 6

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:521c5de14f998f7dc6b74ef980d1e6afd5e7ac99db9f66545f122f9a1d26927c

Observation 70b0edad-88d6-452e-9d62-1379efe24c0e · outbound

This paper cites an unresolved cited work.

Sub-Randers metrics Unresolved cited work

Reference 7

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:39b0082609a561d44d23e4a0b521787878bed727fd2eedc1e03846b677f788a4

Observation 2c1a754a-0532-4e5a-818f-8b3c72482fd3 · outbound

This paper cites Carath ´eodory,Untersuchungen ¨uber die Grundlagen der Termodynamik, Math.

Sub-Randers metrics Carath ´eodory,Untersuchungen ¨uber die Grundlagen der Termodynamik, Math

Reference 8

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:c267a464519d713c39610bf4a004f81954363fd976a2ebf172a9d87a5eb22b51

Observation 42e504aa-6ec1-4304-adbc-6ac24fe30f67 · outbound

This paper cites Cheng , Z.

Sub-Randers metrics Cheng , Z

Reference 9

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:e31a5c8cfa962fd7ec03b260ab138964374c712d13574a81fa8379863598da11

Observation b7349eeb-6143-47e9-830f-91e54197f861 · outbound

This paper cites Chow, ¨Uber Systeme von linearen partiellen Differentialgleichungen erster Ordnung, Math.

Sub-Randers metrics Chow, ¨Uber Systeme von linearen partiellen Differentialgleichungen erster Ordnung, Math

Reference 10

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:c6fc1bd12912a415b1805c8042ce5fd0d3b2b2d41da059bcba60cb555a179e7e

Observation 7e8bd5bb-df46-4f1c-8307-b91f94b6fd7d · outbound

This paper cites do Carmo,Riemannian geometry.

Sub-Randers metrics do Carmo,Riemannian geometry

Reference 11

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:5d4088e6022d49653b772aac23954c6d6f8992354a473fdebb53ec6eabd78350

Observation e12bdb43-45e8-4139-8f9e-21489e0ed024 · outbound

This paper cites Gromov,Carnot-Carath ´eodory spaces seen from within, In: Bella¨ıche, A., Risler, JJ.

Sub-Randers metrics Gromov,Carnot-Carath ´eodory spaces seen from within, In: Bella¨ıche, A., Risler, JJ

Reference 12

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:0904c94eb9a2ad8608669f9528e17f1a1ace6a2eb8848506529dc42cf5335c01

Observation 3ac23123-802e-4091-bbd1-0df210117ef3 · outbound

This paper cites Randers,On an Asymmetrical Metric in the Four-Space of General Relativity, Phy.

Sub-Randers metrics Randers,On an Asymmetrical Metric in the Four-Space of General Relativity, Phy

Reference 13

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:0717899959374be0706b5818b33e4c7fb5d074831397410e8a5b56e11ff0dd86

Observation 69676a00-a031-4b0d-ae6d-d636a3d37404 · outbound

This paper cites Mestdag, V.

Sub-Randers metrics Mestdag, V

Reference 14

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:572b178bc61a5c87f679a60b8e3969bb3a22102ae9091ab7df4085a50440b50a

Observation 74914f15-9ee4-4954-9f64-22af30cb8fde · outbound

This paper cites Mitchell,On Carnot-Carath ´eodory metrics, J.

Sub-Randers metrics Mitchell,On Carnot-Carath ´eodory metrics, J

Reference 15

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:fd25797c3576f2a3cd15c3e00ce0de4970694dac8446bed583712e46fd9fdabc

Observation d5e82c3a-ed3f-49f1-85f8-5c28b427e30f · outbound

This paper cites Montgomery,Abnormal minimizers, SIAM J.

Sub-Randers metrics Montgomery,Abnormal minimizers, SIAM J

Reference 16

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:1c2c0a9330ff87873289201df967d8e93b2b9a5383e09df5732f8b707f0d996e

Observation 9909ee69-1b5a-40af-a728-a520b0359e0b · outbound

This paper cites Montgomery,A tour of subriemannian geometries, their geodesics and applications, AMS, 2002.

Sub-Randers metrics Montgomery,A tour of subriemannian geometries, their geodesics and applications, AMS, 2002

Reference 17

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:6f6023b0525e9cff40780dcf44582656b3af2c8298c97093e27caf40644a41fb

Observation cd0a45cd-76b3-46ac-955f-ef6afe17865c · outbound

This paper cites Strichartz,Sub-Riemannian geometry.J.

Sub-Randers metrics Strichartz,Sub-Riemannian geometry.J

Reference 18

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:d8a4898ef730d7f6cc9c8b73f58fe00038050688a66144f22360ae58155bb867

Observation 6f36a52e-4870-4834-bfc5-e6be98839ec2 · outbound

This paper cites an unresolved cited work.

Sub-Randers metrics Unresolved cited work

Reference 19

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:2c6836492f2d243a49d6c8cdc676428e9db51f36530b94da43cf1070a2acdeac

Observation 7f39a3c9-d703-4d27-9866-8725a0500c2e · outbound

This paper cites an unresolved cited work.

Sub-Randers metrics Unresolved cited work

Reference 20

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:6bbb011c043f86aa6a5d74ca346514fedab4f78b2f0d63c22058267fc801d91b

Observation db64e45d-d25c-4df7-92db-37ff274d4e80 · outbound

This paper cites Yasuda, H.

Sub-Randers metrics Yasuda, H

Reference 21

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:5d325c0d490ed299ff99b698fefa7a3aa927a13aae7285baac2732b72de6befe

Observation 8dc16fbc-8d5d-47ac-8ccf-f5e9013aef9f · outbound

This paper cites Zermelo, ¨Uber das Navigationsproblem bei ruhender oder ver ¨anderlicher Windverteilung,Z.

Sub-Randers metrics Zermelo, ¨Uber das Navigationsproblem bei ruhender oder ver ¨anderlicher Windverteilung,Z

Reference 22

Resolution
unresolved
no resolver link, observed 2026-06-26T11:38:53.048456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T11:38:53.048456Z digest=sha256:786f669b0867620fbe23a88371d65f6628e0e2b641fbb91dce1d5b26e550fec7

Pith citing papers

Observation 5fd2d0f9-eb1e-46b2-8283-37b53172acff · inbound

Sub-Finslerian Interpolation Inequalities cites this paper.

Sub-Finslerian Interpolation Inequalities Sub-Randers metrics

Reference 2

Resolution
unresolved
no resolver link, observed 2026-08-01T19:57:57.163055Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T19:57:57.163055Z digest=sha256:1ecc1c56f01914093cae585cf10d383a2740993ad9785199afc89f65d9e45840