Paper Citation Record · LEDGER

A system of Schr\"odinger's problems and functional equations

As of 12 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2501.00719.

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

pith.paper-citation-record.v1
2501.00719 v2

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T22:57:50.018905Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+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

40 of 40 outbound references displayed

verified exact0
verified fuzzy28
unresolved12
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5fd98ffa-77a1-4df1-acc7-4aff78139c0f · outbound

This paper cites The Knothe-Rosenblatt distance and its induced topology.

A system of Schr\"odinger's problems and functional equations The Knothe-Rosenblatt distance and its induced topology

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-10T22:57:49.838223Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 455ce694-72e7-4673-aca0-09fa59c1fafc · outbound

This paper cites Bernstein, Sur les liaisons entre les grandeurs al´ etoires , Verh.

A system of Schr\"odinger's problems and functional equations Bernstein, Sur les liaisons entre les grandeurs al´ etoires , Verh

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.627137Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 57b36675-8f95-4abd-b930-69d1b3850d74 · outbound

This paper cites an unresolved cited work.

A system of Schr\"odinger's problems and functional equations Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:57:50.612873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 917b6f79-2f8a-43dd-bd60-04a5fd7a749a · outbound

This paper cites an unresolved cited work.

A system of Schr\"odinger's problems and functional equations Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:57:50.598694Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b7135dba-2884-4b15-93ad-edd3de573ce6 · outbound

This paper cites Carlier, F.

A system of Schr\"odinger's problems and functional equations Carlier, F

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.583882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b760a6ed-3435-4caf-9bb9-369755cbb2eb · outbound

This paper cites an unresolved cited work.

A system of Schr\"odinger's problems and functional equations Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:57:50.569416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3e83b3bf-2d3e-48d9-b339-5079833ecc7d · outbound

This paper cites an unresolved cited work.

A system of Schr\"odinger's problems and functional equations Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:57:50.554930Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b4fb0e64-6de2-4d77-adcf-020e4e5674c1 · outbound

This paper cites Csiszar, I-divergence geometry of probability distributions and mini- mization problems, Ann.

A system of Schr\"odinger's problems and functional equations Csiszar, I-divergence geometry of probability distributions and mini- mization problems, Ann

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.540753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4255fdb4-2d3e-4f9a-b78e-0df1b8766101 · outbound

This paper cites Dai Pra, A stochastic control approach to reciprocal diffusion pro- cesses, Appl.

A system of Schr\"odinger's problems and functional equations Dai Pra, A stochastic control approach to reciprocal diffusion pro- cesses, Appl

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.526590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 386a4ae4-e6cd-49ae-948e-2faa8842c1e6 · outbound

This paper cites Dall’Aglio, Sugli estremi dei momenti delle funzioni di ripartizione doppia, Ann.

A system of Schr\"odinger's problems and functional equations Dall’Aglio, Sugli estremi dei momenti delle funzioni di ripartizione doppia, Ann

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.512223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c1cf2128-60dd-4e0a-9bd5-7503a235b9f2 · outbound

This paper cites an unresolved cited work.

A system of Schr\"odinger's problems and functional equations Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:57:50.497611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 308b4463-1d02-45b4-8a43-079c12bb21ad · outbound

This paper cites an unresolved cited work.

A system of Schr\"odinger's problems and functional equations Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:57:50.483149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4c3504d7-41a4-47fd-94a8-904edd71edf7 · outbound

This paper cites F¨ ollmer,Random fields and diffusion processes , in ´Ecole d’ ´Et´ e de Probabilit´ es de Saint-Flour XV–XVII, 1985–87, Lecture Notes in Math.

A system of Schr\"odinger's problems and functional equations F¨ ollmer,Random fields and diffusion processes , in ´Ecole d’ ´Et´ e de Probabilit´ es de Saint-Flour XV–XVII, 1985–87, Lecture Notes in Math

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.468725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8b3eb052-78f6-4478-83a2-6eac23a1b717 · outbound

This paper cites Fortet, R´ esolution d’un Syst` eme d’´ equations de M.

A system of Schr\"odinger's problems and functional equations Fortet, R´ esolution d’un Syst` eme d’´ equations de M

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.454103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 9a1787a7-29a4-4526-bf75-9dfd19e61a57 · outbound

This paper cites Ikeda and S.

A system of Schr\"odinger's problems and functional equations Ikeda and S

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.439616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c216d47b-5c26-4678-b83c-628dcfe2fafb · outbound

This paper cites Jamison, Reciprocal processes , Z.

A system of Schr\"odinger's problems and functional equations Jamison, Reciprocal processes , Z

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.425013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 189baa61-fb34-403d-9724-77f0d80a0999 · outbound

This paper cites Jamison, The Markov process of Schr¨ odinger, Z.

A system of Schr\"odinger's problems and functional equations Jamison, The Markov process of Schr¨ odinger, Z

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.410772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 19348250-ba85-4dab-bfb8-46b081f40097 · outbound

This paper cites Kamijima, A.

A system of Schr\"odinger's problems and functional equations Kamijima, A

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.396388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 19133f4c-0ded-4ed6-8592-c1f38fc3756e · outbound

This paper cites Knothe, Contributions to the theory of convex bodies , Michigan Mathematical J., 4 (1957), pp.

A system of Schr\"odinger's problems and functional equations Knothe, Contributions to the theory of convex bodies , Michigan Mathematical J., 4 (1957), pp

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.380591Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 39b87a75-91b7-49da-97db-73f221dcccb2 · outbound

This paper cites L´ eonard,From the Schr¨ odinger problem to the Monge–Kantorovich problem, J.

A system of Schr\"odinger's problems and functional equations L´ eonard,From the Schr¨ odinger problem to the Monge–Kantorovich problem, J

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.366075Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f085229d-184f-47e4-bd83-7a168fbbef09 · outbound

This paper cites L´ eonard,A survey of the Schr¨ odinger problem and some of its con- nections with optimal transport , Special Issue on Optimal Transport and Applications.

A system of Schr\"odinger's problems and functional equations L´ eonard,A survey of the Schr¨ odinger problem and some of its con- nections with optimal transport , Special Issue on Optimal Transport and Applications

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.351855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 706715db-7054-42e5-97fe-a6b3d212a1ec · outbound

This paper cites L´ evy, Th´ eorie de l’Addition des Variables Al´ eatoires, Gauthier- Villars, Paris, 1937.

A system of Schr\"odinger's problems and functional equations L´ evy, Th´ eorie de l’Addition des Variables Al´ eatoires, Gauthier- Villars, Paris, 1937

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.338291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 151ed5c6-6b55-49d8-9c65-ca31ae95b2b9 · outbound

This paper cites Mikami, Monge’s problem with a quadratic cost by the zero-noise limit of h-path processes , Probab.

A system of Schr\"odinger's problems and functional equations Mikami, Monge’s problem with a quadratic cost by the zero-noise limit of h-path processes , Probab

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.324121Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 9525de2a-4f03-451b-8573-f00eaa400588 · outbound

This paper cites an unresolved cited work.

A system of Schr\"odinger's problems and functional equations Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:57:50.309867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f9c214df-1494-4866-a8e1-112975a49d95 · outbound

This paper cites Mikami, A characterization of the Knothe–Rosenblatt processes by a convergence result , SIAM J.

A system of Schr\"odinger's problems and functional equations Mikami, A characterization of the Knothe–Rosenblatt processes by a convergence result , SIAM J

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.295837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation de0f9b85-8da8-4c94-8353-b82d5beeb6e8 · outbound

This paper cites Mikami, Regularity of Schr¨ odinger’s functional equation in the weak topology and moment measures , J.

A system of Schr\"odinger's problems and functional equations Mikami, Regularity of Schr¨ odinger’s functional equation in the weak topology and moment measures , J

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.281977Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 925ce4cf-8781-408d-bb06-21563af71849 · outbound

This paper cites Mikami, Stochastic Optimal Transportation: Stochastic Control with Fixed Marginals, SpringerBriefs in Mathematics, Springer , Sin- gapore, 2021.

A system of Schr\"odinger's problems and functional equations Mikami, Stochastic Optimal Transportation: Stochastic Control with Fixed Marginals, SpringerBriefs in Mathematics, Springer , Sin- gapore, 2021

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.267878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 545e734e-1d9a-4906-bc19-74269739c234 · outbound

This paper cites Mikami and M.

A system of Schr\"odinger's problems and functional equations Mikami and M

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.253900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6755b329-a0e7-4d18-9091-a4a68fa505a9 · outbound

This paper cites an unresolved cited work.

A system of Schr\"odinger's problems and functional equations Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:57:50.240271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a4a64a9c-c076-4472-95d2-7da1dba83a04 · outbound

This paper cites Peyr´ e and M.

A system of Schr\"odinger's problems and functional equations Peyr´ e and M

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.226299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 16c84824-af58-44b8-9837-6a3befb8253a · outbound

This paper cites Rachev and L.

A system of Schr\"odinger's problems and functional equations Rachev and L

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.211488Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4bf7cce4-c7ef-4ce8-9c49-d31b2945e845 · outbound

This paper cites Rosenblatt, Remarks on a multivariate transformation , Annals of Mathematical Statistics, 23 (1952), pp.

A system of Schr\"odinger's problems and functional equations Rosenblatt, Remarks on a multivariate transformation , Annals of Mathematical Statistics, 23 (1952), pp

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.197252Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 49d23469-4d09-47b7-98c4-68f33d807799 · outbound

This paper cites R¨ uschendorf and W.

A system of Schr\"odinger's problems and functional equations R¨ uschendorf and W

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.183512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a8693772-5ee0-461c-91f6-bf5c6ed9f4fb · outbound

This paper cites On the Reversal of the Laws of Nature.

A system of Schr\"odinger's problems and functional equations On the Reversal of the Laws of Nature

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.168510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 29e7892e-eb22-46d9-8076-fb92a9c424df · outbound

This paper cites Schr¨ odinger,Th´ eorie relativiste de l’electron et l’interpr´ etation de la m´ ecanique quantique, Ann.

A system of Schr\"odinger's problems and functional equations Schr¨ odinger,Th´ eorie relativiste de l’electron et l’interpr´ etation de la m´ ecanique quantique, Ann

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.152945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6dfd3db3-6962-4b80-9c0a-0cf2ea91038b · outbound

This paper cites an unresolved cited work.

A system of Schr\"odinger's problems and functional equations Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:57:50.134700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b40a3748-268a-4c43-8dcf-3030513c5876 · outbound

This paper cites Talagrand, Transportation cost for Gaussian and other product mea- sures, Geom.

A system of Schr\"odinger's problems and functional equations Talagrand, Transportation cost for Gaussian and other product mea- sures, Geom

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.117946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation af9397e3-e07c-4534-899e-f6e5ae56adc2 · outbound

This paper cites Villani, Topics in optimal transportation, Providence, Amer.

A system of Schr\"odinger's problems and functional equations Villani, Topics in optimal transportation, Providence, Amer

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:57:50.102293Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 9026ae79-220c-4dcd-be0f-c2b8adca2e56 · outbound

This paper cites an unresolved cited work.

A system of Schr\"odinger's problems and functional equations Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:57:50.086200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b49e5a17-c0c5-4000-9287-4eab4f42eb13 · outbound

This paper cites an unresolved cited work.

A system of Schr\"odinger's problems and functional equations Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:57:50.070835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

No inbound Pith citation observations are available.