Paper Citation Record · LEDGER

Exact closed-form recurrence probabilities for biased random walks at any step number

As of 22 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 1 inbound Pith citation observation for arXiv:2412.17994.

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

pith.paper-citation-record.v1
2412.17994 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T05:17:35.452530Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T05:17:35.401693Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-11T05:17:35.471788Z

Reference resolution

18 of 18 outbound references displayed

verified exact1
verified fuzzy13
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation cc9bcf91-bb07-4c88-9f6d-19b24ebbdb48 · outbound

This paper cites Exact closed-form recurrence probabilities for biased random walks at any step number.

Exact closed-form recurrence probabilities for biased random walks at any step number Exact closed-form recurrence probabilities for biased random walks at any step number

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-11T05:17:35.476467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f7a681f9-01b6-47f8-a52f-09ce4bdf9551 · outbound

This paper cites This is in agreement with the fact that return can occur only at even step numbers.

Exact closed-form recurrence probabilities for biased random walks at any step number This is in agreement with the fact that return can occur only at even step numbers

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:17:35.612210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4d6901e0-4de8-4ae9-8c2f-dab8cf49abb5 · outbound

This paper cites Ann., 84 (1921).

Exact closed-form recurrence probabilities for biased random walks at any step number Ann., 84 (1921)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:17:35.604263Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation fb16ec22-3435-40ba-9c42-94d4dba7fb54 · outbound

This paper cites and Snell, J.L.

Exact closed-form recurrence probabilities for biased random walks at any step number and Snell, J.L

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:17:35.596226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 83a56f9c-3461-44c2-bc8f-f5ab079cbe9d · outbound

This paper cites and Sokolov, I.M., First Steps in Random Walks: From Tools to Applications (Oxford University Press Inc., New York) 2011.

Exact closed-form recurrence probabilities for biased random walks at any step number and Sokolov, I.M., First Steps in Random Walks: From Tools to Applications (Oxford University Press Inc., New York) 2011

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:17:35.588486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b88c8849-6c07-4fed-a4c5-8e2fbca28a5c · outbound

This paper cites an unresolved cited work.

Exact closed-form recurrence probabilities for biased random walks at any step number Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-11T05:17:35.580932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3b6fb2e2-c4a1-40af-a53a-f815cb8df979 · outbound

This paper cites and Majumdar, S., Phys.

Exact closed-form recurrence probabilities for biased random walks at any step number and Majumdar, S., Phys

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:17:35.571685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 992b3bf5-56d5-4705-899e-5d259f7f770c · outbound

This paper cites and Wordeman, L., Curr.

Exact closed-form recurrence probabilities for biased random walks at any step number and Wordeman, L., Curr

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:17:35.563819Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4a9b11a5-c73f-4f89-bc60-96e55cc94afb · outbound

This paper cites an unresolved cited work.

Exact closed-form recurrence probabilities for biased random walks at any step number Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-11T05:17:35.554973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 54fd8ae0-65f1-414d-bd56-9479f6f157bf · outbound

This paper cites Mag., 80 (2007) 5.

Exact closed-form recurrence probabilities for biased random walks at any step number Mag., 80 (2007) 5

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:17:35.546422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 49e461b8-bd5c-47c0-a1ac-b4bcac50eb61 · outbound

This paper cites and Amir, A.

Exact closed-form recurrence probabilities for biased random walks at any step number and Amir, A

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:17:35.539316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0687aa99-cd95-4713-bcb9-1dbb739d83ac · outbound

This paper cites an unresolved cited work.

Exact closed-form recurrence probabilities for biased random walks at any step number Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-11T05:17:35.435944Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0eca56c0-9411-423e-9b83-4b188f7933f3 · outbound

This paper cites and Stegun I.A., Handbook of Mathematical Functions with F ormulas, Graphs, and Mathematical Tables, 9th ed.

Exact closed-form recurrence probabilities for biased random walks at any step number and Stegun I.A., Handbook of Mathematical Functions with F ormulas, Graphs, and Mathematical Tables, 9th ed

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:17:35.527787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8c7d7430-de4a-45e5-bd89-ca49b9c111fd · outbound

This paper cites an unresolved cited work.

Exact closed-form recurrence probabilities for biased random walks at any step number Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-11T05:17:35.519327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation eca0fce2-7ae7-46c8-9328-f96b31d4eae2 · outbound

This paper cites and Vale, R.D., Curr.

Exact closed-form recurrence probabilities for biased random walks at any step number and Vale, R.D., Curr

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:17:35.510893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 00ea272a-4ad8-4d96-b711-795e495e6561 · outbound

This paper cites and Grill, S.W., Phys.

Exact closed-form recurrence probabilities for biased random walks at any step number and Grill, S.W., Phys

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:17:35.502868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a06741f9-74ad-4086-9718-314258a26ed7 · outbound

This paper cites and John, K., PRX Life, 1 (2023) 1.

Exact closed-form recurrence probabilities for biased random walks at any step number and John, K., PRX Life, 1 (2023) 1

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:17:35.494558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 30907063-df47-4564-a22d-9c360b0783a0 · outbound

This paper cites and Vale, R.D.

Exact closed-form recurrence probabilities for biased random walks at any step number and Vale, R.D

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:17:35.485924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

Observation cc9bcf91-bb07-4c88-9f6d-19b24ebbdb48 · inbound