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Paper Citation Record · LEDGER

On the structure of optimal free Dirichlet regions in mass transportation problems

As of 20 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2606.30826.

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

pith.paper-citation-record.v1
2606.30826 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-01T01:46:20.533807Z

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 exact5
  • verified fuzzy15
  • unresolved3
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 17d08012-9694-42b3-95ba-be2b1639ac16 · outbound

This paper cites Bertsekas and Steven E.

On the structure of optimal free Dirichlet regions in mass transportation problems Bertsekas and Steven E

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.414793Z

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.

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Observation c95e1789-9677-45f3-b80c-25c81ba7c48b · outbound

This paper cites 46 LUCAS D.

On the structure of optimal free Dirichlet regions in mass transportation problems 46 LUCAS D

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.435614Z

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.

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Observation 4aa25a58-533f-4456-ad63-9f2892f4bfe4 · outbound

This paper cites 4, 631-678.

On the structure of optimal free Dirichlet regions in mass transportation problems 4, 631-678

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.420667Z

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.

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Observation f04bcf11-6422-414f-bfd0-11e6c8cf3041 · outbound

This paper cites 4, 1107-1130.

On the structure of optimal free Dirichlet regions in mass transportation problems 4, 1107-1130

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.410585Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:a94ea9843770c922183c2fe9d453be14a35ac8d8c42d2b250ac5e65ff09475cb

Observation 2ac1f01f-0445-4040-bc1d-be8e401d9216 · outbound

This paper cites an unresolved cited work.

On the structure of optimal free Dirichlet regions in mass transportation problems Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-07-07T05:53:20.417653Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:3d321942ff4af510f440096f622bb15021e8715feb8f611f9b3ac50e81fe438d

Observation 5eafefac-20aa-498b-9d6d-d1a4a1c0bb30 · outbound

This paper cites 3, 2108-2140.

On the structure of optimal free Dirichlet regions in mass transportation problems 3, 2108-2140

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.425858Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:65aa5befb2604d922c62b369ab166f1bfe422d2e98eaeefbc8ded70576992d12

Observation 736d3db5-8f7e-42c1-9ccc-5c37dad07f15 · outbound

This paper cites 406, 502-516.

On the structure of optimal free Dirichlet regions in mass transportation problems 406, 502-516

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.412162Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:997dc1e254c4dcc318c618cd49831b3ab473d057298acbdd1efa4340b8159b57

Observation 83453c85-7395-46b3-80d1-0f23c066d62c · outbound

This paper cites an unresolved cited work.

On the structure of optimal free Dirichlet regions in mass transportation problems Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-07-07T05:53:20.433468Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:0c834a750d76f36da9f70ba47995fd7edd643cc09ce471448bd5d43fbb540ce5

Observation a53a637a-fa6d-4942-aa3a-ffe587156fa4 · outbound

This paper cites an unresolved cited work.

On the structure of optimal free Dirichlet regions in mass transportation problems Unresolved cited work

Reference 9

Resolution
verified exact
doi, observed 2026-07-01T06:05:29.479184Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:eff2511d645af2b5083dae50751513204adac4b1f51ecbb2bc72ed669faa746b

Observation 8363a669-89d0-4aa0-a5e0-679469945d08 · outbound

This paper cites Monge-Kantorovich Fitting With Sobolev Budgets.

On the structure of optimal free Dirichlet regions in mass transportation problems Monge-Kantorovich Fitting With Sobolev Budgets

Reference 10

Resolution
verified exact
arxiv_id, observed 2026-07-01T12:45:44.752647Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:d28ec77c2a4b299fe532e622996aaea1c861397fb5e4cf33d9d8e14dac9a4186

Observation cb338eac-eebe-4ea5-b3ad-61d59fee944f · outbound

This paper cites Kuratowski, Topology: Volume II, Volume 2, Elsevier, Oxford, England, UK, 2014.

On the structure of optimal free Dirichlet regions in mass transportation problems Kuratowski, Topology: Volume II, Volume 2, Elsevier, Oxford, England, UK, 2014

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.409325Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:d061bec6a4bcce407dde7a548545a218deb1e5b7ac0a9bf28d4df96f2218ba4a

Observation d55fe1df-8849-4e41-b956-2d3865d56afc · outbound

This paper cites Lemenant, About the Regularity of Average Distance Minimizers in R2, Journal of Convex Analysis 18 (2011), no.

On the structure of optimal free Dirichlet regions in mass transportation problems Lemenant, About the Regularity of Average Distance Minimizers in R2, Journal of Convex Analysis 18 (2011), no

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.428423Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:af09847dbf8f68a5a5bdcc7e1321f3014d1f5f0ed6ce437dd54439cf41019707

Observation e8779f83-2cb0-4e2a-b3a7-296a4684cf34 · outbound

This paper cites an unresolved cited work.

On the structure of optimal free Dirichlet regions in mass transportation problems Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-07-07T05:53:20.438047Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:3e543f8c689845b39eddfc34b990b3fc8b503621c7054beb310f3f1dae5edd5e

Observation c94e271b-8b4c-4144-b101-35b79fc9ca0e · outbound

This paper cites 2, 229-248.

On the structure of optimal free Dirichlet regions in mass transportation problems 2, 229-248

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.407150Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:bfdd7c3728c3b00c96bd899ed760317bc9a2c7ef7b6b43cdadfe26887f4c7acc

Observation 2c98a66c-8d39-4bd1-8a06-d31b4be65110 · outbound

This paper cites 1, 41-63.

On the structure of optimal free Dirichlet regions in mass transportation problems 1, 41-63

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.423266Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:d08c10eca88fca5729fa44b7ec34ec0f8f25403f12e1d58fef0c781db9555753

Observation a8525c46-3eff-43d3-94f1-a9e62aa1c39e · outbound

This paper cites an unresolved cited work.

On the structure of optimal free Dirichlet regions in mass transportation problems Unresolved cited work

Reference 16

Resolution
verified exact
arxiv_id, observed 2026-07-01T06:05:29.471846Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:594f9aee13b703addb2e33055503287fcebb3828c931ba245f42c3ae306b17e6

Observation 70449bfe-e5a9-40b9-9286-cdd044bf446b · outbound

This paper cites 8, 1-25, DOI 10.1051/cocv/2021002.

On the structure of optimal free Dirichlet regions in mass transportation problems 8, 1-25, DOI 10.1051/cocv/2021002

Reference 17

Resolution
verified exact
arxiv_id, observed 2026-07-01T06:05:29.475127Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:73588ec02ab69a1a97ecebdac6213ffdf983cca2f527cd5a37a7f36b19f637bc

Observation 6666c1fb-494a-4d1c-af29-045696fe53a2 · outbound

This paper cites an unresolved cited work.

On the structure of optimal free Dirichlet regions in mass transportation problems Unresolved cited work

Reference 18

Resolution
verified exact
doi, observed 2026-07-01T06:05:29.477139Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:a583fcb799fbd23fc1cf15a2f87cd61d2995e5746bcc6cc33f33b1267957cac1

Observation e7ead53c-a6a2-4ee9-abaa-59d0c26e4970 · outbound

This paper cites Structure of average distance minimizers in general dimensions.

On the structure of optimal free Dirichlet regions in mass transportation problems Structure of average distance minimizers in general dimensions

Reference 19

Resolution
metadata mismatch
arxiv_id, observed 2026-07-01T12:45:44.750082Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:34bf4a52df85e3fac7fd668f216611881ccd48ef4f5822008eb3717eb1580e27

Observation c65469cf-9b44-413b-864a-110289259078 · outbound

This paper cites Santambrogio and P.

On the structure of optimal free Dirichlet regions in mass transportation problems Santambrogio and P

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.390397Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:becd884260931ba2daf1059f8ec5f3759e7d43d96cd69bc34185525f70ab9da9

Observation 25d84a14-9e8c-4613-b46e-fce36bcfc3e8 · outbound

This paper cites 5, 3114 - 3131.

On the structure of optimal free Dirichlet regions in mass transportation problems 5, 3114 - 3131

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.400011Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:f7d6c71935d0910ec45fbffe68a61aa4a2300b9b7d5d538e2d152005d9f9e3c1

Observation 29454f22-7607-4d5a-8b0a-a7181ab4c77c · outbound

This paper cites 1, 169-184.

On the structure of optimal free Dirichlet regions in mass transportation problems 1, 169-184

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.431329Z

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.

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Observation b7734441-9c57-4e17-a1b0-aec49239f100 · outbound

This paper cites 3, 3290 - 3309.

On the structure of optimal free Dirichlet regions in mass transportation problems 3, 3290 - 3309

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.394760Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:fe8556fb1991e50ce343a0e8f096d6131bc5292d406ae9ba7c97d00cb41f09a6

Observation fa3ba285-b969-4873-bcf7-6dde9ad227e0 · outbound

This paper cites 4, 522-552.

On the structure of optimal free Dirichlet regions in mass transportation problems 4, 522-552

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T05:53:20.403606Z

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.

source=pdf_text observed=2026-07-01T01:46:20.533807Z digest=sha256:077fa49d534019c741b8197c2b000ec16ca8e97f8f899d61140828c9605bd44b

Pith citing papers

No inbound Pith citation observations are available.