Paper Citation Record · LEDGER

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis

As of 6 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2501.10806.

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

pith.paper-citation-record.v1
2501.10806 v4

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-23T05:26:37.263966Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-06T06:34:29.942622+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T05:23:28.760890Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

30 of 30 outbound references displayed

verified exact6
verified fuzzy14
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 67ab41f5-51a0-49e2-ad27-6e42480cad87 · outbound

This paper cites an unresolved cited work.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-05-23T05:27:36.376070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation ce044a14-f0aa-43e6-a2a2-456553be58a8 · outbound

This paper cites Borkar , Stochastic Approximation: A Dynamical Systems Viewpoint: Second Edition , Texts and Readings in Mathematics, Hindustan Book Agency.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Borkar , Stochastic Approximation: A Dynamical Systems Viewpoint: Second Edition , Texts and Readings in Mathematics, Hindustan Book Agency

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:27:36.384771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 8fad1c5d-59cb-4bc5-b154-a2461835e955 · outbound

This paper cites Bravo and R.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Bravo and R

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:27:36.332122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation e1e14bf0-2a02-49ac-8c69-9adc6ea5c139 · outbound

This paper cites Bravo, R.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Bravo, R

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:27:36.334758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation a119243c-e505-44f5-bb24-841de7d902b7 · outbound

This paper cites Chandak, o(1/k) finite-time bound for non-linear two-time-scale stochastic approximation , 2025, https://arxiv.org/abs/2504.19375.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Chandak, o(1/k) finite-time bound for non-linear two-time-scale stochastic approximation , 2025, https://arxiv.org/abs/2504.19375

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-23T05:27:36.025949Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 58378cdf-9044-4fc4-a621-a734d110c701 · outbound

This paper cites Chandak, I.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Chandak, I

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-23T05:27:36.035978Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 0f22443d-17e0-4a5f-a230-a668c1d77134 · outbound

This paper cites Chandak, V.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Chandak, V

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:27:36.329162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation a04c7e4f-70e5-4e0f-b469-281e7e359355 · outbound

This paper cites Chandak, S.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Chandak, S

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-05-23T05:27:36.020311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 94b73246-f973-40fb-b1cf-5e944e368865 · outbound

This paper cites an unresolved cited work.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-05-23T05:27:36.378902Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 2b9dbc19-93b1-4844-9873-4b80866931d3 · outbound

This paper cites Concentration of Contractive Stochastic Approximation: Additive and Multiplicative Noise.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Concentration of Contractive Stochastic Approximation: Additive and Multiplicative Noise

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-23T05:27:36.040325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 07f72026-e0c4-4c11-8dba-589747ee88d6 · outbound

This paper cites Davis and W.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Davis and W

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:27:36.323505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation a6388ff5-b8a5-4059-ba26-f1b4d33108df · outbound

This paper cites an unresolved cited work.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-05-23T05:27:36.306027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation a0d6563a-9313-48c0-9d41-e68444fea051 · outbound

This paper cites an unresolved cited work.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-05-23T05:27:36.320781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation e8797504-50e4-4023-863c-cadcbb8942f6 · outbound

This paper cites Facchinei and C.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Facchinei and C

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:27:36.302883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation e0883880-2b1f-46ae-ae60-7304063a6c6d · outbound

This paper cites Facchinei and J.-S.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Facchinei and J.-S

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:27:36.309183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation aef51157-2292-4b1a-b4c1-7e6fc6bfe2f8 · outbound

This paper cites Tight Finite Time Bounds of Two-Time-Scale Linear Stochastic Approximation with Markovian Noise.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Tight Finite Time Bounds of Two-Time-Scale Linear Stochastic Approximation with Markovian Noise

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-23T05:27:36.031054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 42e0ac0c-4852-41c0-b698-a394eba2a742 · outbound

This paper cites Kaledin, E.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Kaledin, E

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:27:36.373170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation bdcb5bd8-647a-412a-9e94-cfaacd293f9b · outbound

This paper cites an unresolved cited work.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-05-23T05:27:36.363392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation c6e41987-27ee-4ee3-a5d6-c6566daacb44 · outbound

This paper cites Liang, J.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Liang, J

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:27:36.366463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation c04e86ab-1520-468d-8aa0-b7caae2b88d5 · outbound

This paper cites Two-Timescale Gradient Descent Ascent Algorithms for Nonconvex Minimax Optimization.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Two-Timescale Gradient Descent Ascent Algorithms for Nonconvex Minimax Optimization

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-23T05:27:36.044145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation e0c64d9e-f3ba-4f53-8e2f-4d6d58397b25 · outbound

This paper cites an unresolved cited work.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-05-23T05:27:36.357575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 2abf81bd-10d8-44c4-9a04-194c83d1a6c7 · outbound

This paper cites Nagurney and D.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Nagurney and D

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:27:36.318089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation e4c1b16f-7d0e-4f24-95f4-763441348b5c · outbound

This paper cites Nesterov et al., Lectures on convex optimization, vol.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Nesterov et al., Lectures on convex optimization, vol

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:27:36.312082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 2894df19-824a-4dd2-9e04-678abc41c30c · outbound

This paper cites Platt and A.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Platt and A

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:27:36.315230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 274f6a6f-afbe-4c19-91b4-15426f9c0153 · outbound

This paper cites Robbins and S.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Robbins and S

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:27:36.300336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation d5e61cc2-a868-46f6-9b81-0ae751d36463 · outbound

This paper cites Srikant and L.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Srikant and L

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:27:36.326341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 93b0309b-5fdc-4dc2-89bf-90f26d58ee1d · outbound

This paper cites an unresolved cited work.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-05-23T05:27:36.354529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation ec0b8c77-8484-4355-8de5-a197b99a2194 · outbound

This paper cites an unresolved cited work.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-05-23T05:27:36.360440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 0addf60b-3e1e-468b-a073-168c9ad6022b · outbound

This paper cites an unresolved cited work.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-05-23T05:27:36.369664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation cf71cf5b-2cf3-4d9f-8658-53b23e270242 · outbound

This paper cites an unresolved cited work.

Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-05-23T05:27:36.381813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Pith citing papers

Observation 63c369d2-6897-4e6a-96a8-3e3a196fccf4 · inbound

Non-Expansive Two-Time-Scale Stochastic Approximation: A Fixed-Schedule One-Quarter Barrier and Bias-Corrected Acceleration cites this paper.

Non-Expansive Two-Time-Scale Stochastic Approximation: A Fixed-Schedule One-Quarter Barrier and Bias-Corrected Acceleration Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T05:23:28.760890Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.