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Paper Citation Record · LEDGER

On the convergence rate of the Douglas-Rachford splitting algorithm

As of 19 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2509.06676.

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

pith.paper-citation-record.v1
2509.06676 v2

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T23:25:19.765126Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T21:43:17.135025Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T20:06:11.724154Z

Reference resolution

30 of 30 outbound references displayed

  • verified exact2
  • verified fuzzy5
  • unresolved23
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5ef42373-8659-420d-bd19-e86a1fc3f773 · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:20.103723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 534bf364-503f-43e3-8431-8cde969b9a46 · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:20.094552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-04T23:25:19.670814Z digest=sha256:f9f73f7f38a85b4d1464b7be6b2a2f9dded1b2f78913e80d04f4037ff0cb1585

Observation 6a30f767-84ed-4ea4-9900-df218f74fb7a · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:20.084522Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation dfcb43da-53c7-42d2-80f3-71d156978f47 · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:20.073682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-04T23:25:19.678496Z digest=sha256:7213dcf465f9420c9dc4920b942b2a6f1e596247f565475fd2de0a774c9aa1cb

Observation 39eaab16-e4a6-419c-a62d-46a5383b3761 · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:20.064134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 90d69565-72d2-494d-8904-e5038aefbda2 · outbound

This paper cites Optimized methods for composite optimization: a reduction perspective.

On the convergence rate of the Douglas-Rachford splitting algorithm Optimized methods for composite optimization: a reduction perspective

Reference 6

Resolution
unresolved
no resolver link, observed 2026-08-04T23:25:19.685884Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T23:25:19.685884Z digest=sha256:e8b0297d0bef11cf5a2e31013fdcade53614fbaaaa55d9d9616f655f3d8b290d

Observation 9d57e266-9cc3-4eab-aefa-73f2fcb39f0a · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:20.052932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-04T23:25:19.690239Z digest=sha256:6129cc2d35509e004395b09704f9ecc5d3c76a48240e00f566b010cfbd5023c4

Observation 7a438b28-3dc4-4a0b-88a0-723daa072501 · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:20.042089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-04T23:25:19.693384Z digest=sha256:6d8fd2f7d6136bf6443943d409d3c934776b568069fffd0fdc1e4c10ccf571f1

Observation 7013c328-eb83-461d-9bab-cc426ccd9dc7 · outbound

This paper cites Mathematical Programming145(1):451–482.

On the convergence rate of the Douglas-Rachford splitting algorithm Mathematical Programming145(1):451–482

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:25:20.030468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-04T23:25:19.696515Z digest=sha256:012caa20b10f8d62bb3dd67315b8840b99d041ebccdb8a7d47090be152a2c8e0

Observation 80a4e86f-3f2c-4d68-92ce-aded61872f5f · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:20.019747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-04T23:25:19.699572Z digest=sha256:f9839c5f0b55bd6fa461bcee39d7f02b78bcb16324592eb48b3deb60ce4c1165

Observation 31635df0-2132-4926-bacf-f7d5964ed244 · outbound

This paper cites 16 Convergence rate of the DRS algorithm.

On the convergence rate of the Douglas-Rachford splitting algorithm 16 Convergence rate of the DRS algorithm

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:25:20.008474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-04T23:25:19.702789Z digest=sha256:fbbb82b76d54c0ac2f96485807e524260651224f2e4d74f2888f8c9628d6cdc9

Observation 589e819a-bddc-4dd9-8278-6bfa6a2fa29a · outbound

This paper cites IEEE Transactions on Automatic Control62(2):532–544.

On the convergence rate of the Douglas-Rachford splitting algorithm IEEE Transactions on Automatic Control62(2):532–544

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:25:19.998009Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 2f4cee30-66f4-4320-933f-375ec3c502c2 · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:19.988469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-04T23:25:19.710313Z digest=sha256:32f1e7fc9425d4e4559ea3ae6678a07bce773585bf1b0cde12500bb2bf5f12c9

Observation 9315fc60-71bb-47a4-8592-d5a8ecba7697 · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:19.979799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation e681ef50-43b4-45fa-a6d1-f6222693a354 · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:19.970378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 26f2851b-b5b8-438a-bbd3-c0b15170d876 · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:19.961239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-04T23:25:19.719703Z digest=sha256:9fbeae8ad84a9eeccb8575c2b296d2cdc37b4d687cac9329dbac52c6d8c8d3ec

Observation 926f63e5-c052-4cf8-8d2c-0736da0b0b53 · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:19.951192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation f6bf2885-c995-4d3c-a35b-dfa322528e2c · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:19.940931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 7fae3a6f-0f68-4abe-ba24-26a446f11e26 · outbound

This paper cites SIAM Journal on Control and Optimization30(2):408–425.

On the convergence rate of the Douglas-Rachford splitting algorithm SIAM Journal on Control and Optimization30(2):408–425

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:25:19.930114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-04T23:25:19.729907Z digest=sha256:6f62b94ee6d6672aedc5bba4e64f6e4e69f2fcc71102825a0de1e44b3af42dc5

Observation 1cf56bc4-a369-47ac-9afc-f6d2e60b0323 · outbound

This paper cites (2018)Lectures on convex optimization, volume 137 (Springer).

On the convergence rate of the Douglas-Rachford splitting algorithm (2018)Lectures on convex optimization, volume 137 (Springer)

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:25:19.919982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-04T23:25:19.732991Z digest=sha256:d303ad17bf601a2d0318c2b3267f6bfa3e4f6a3cb01b3b97dbabf6e7e7f389c8

Observation deb45954-2a67-471a-99b9-9906f64c6e73 · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:19.908869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 387358f9-06e9-43a6-89f5-d063e17933e4 · outbound

This paper cites Linear convergence of the Douglas-Rachford algorithm via a generic error bound condition.

On the convergence rate of the Douglas-Rachford splitting algorithm Linear convergence of the Douglas-Rachford algorithm via a generic error bound condition

Reference 22

Resolution
verified exact
local_arxiv, observed 2026-08-04T23:25:19.824775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 76cbbff3-83b1-4da8-8cdf-470fc9c5d952 · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:19.898645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 1db00ccc-6cfd-46c5-aba3-298a731bcfb1 · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:19.887465Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 7e84afc9-fad3-49d4-ba5b-2f0f8f6cdbbb · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:19.876597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 6f2bef9c-911a-4a1d-9c00-83216443602a · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:19.866154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 9c123e69-c5be-42d3-bba0-65c7c3ce43c4 · outbound

This paper cites Relaxed Proximal Point Algorithm: Tight Complexity Bounds and Acceleration without Momentum.

On the convergence rate of the Douglas-Rachford splitting algorithm Relaxed Proximal Point Algorithm: Tight Complexity Bounds and Acceleration without Momentum

Reference 27

Resolution
verified exact
local_arxiv, observed 2026-08-04T23:25:19.810648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-04T23:25:19.755221Z digest=sha256:fd81e76eab5f41aa7e2d13f897749634b91b314e0a2fb74661a144a7824a81ac

Observation ed5091ba-e427-4352-8476-c0830828df8e · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:19.856027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-04T23:25:19.758471Z digest=sha256:96046843112b1afa5f1f868fbd132bee170c6a2ff65f8115222589099bb37bbe

Observation 33804e92-fed1-4993-944f-11af2e14922b · outbound

This paper cites an unresolved cited work.

On the convergence rate of the Douglas-Rachford splitting algorithm Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:25:19.845454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-04T23:25:19.762157Z digest=sha256:afe097306a157454a8b4ea636b31ad20269b0550d18b6e427e79f42a2844f32c

Observation d3059cc5-fa47-47f6-86b8-9b016d440807 · outbound

This paper cites Exact Convergence rate of the subgradient method by using Polyak step size.

On the convergence rate of the Douglas-Rachford splitting algorithm Exact Convergence rate of the subgradient method by using Polyak step size

Reference 30

Resolution
unresolved
no resolver link, observed 2026-08-04T23:25:19.765126Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T23:25:19.765126Z digest=sha256:aeab64b73404537f91fcf851092f4d9e815dad98f84022ff752bcc7f360f34db

Pith citing papers

Observation a9e056e5-a4ca-44c8-aeb5-07aa7447890e · inbound

Stepsize Hedging: an Alternative Mechanism for Accelerating Gradient Descent cites this paper.

Stepsize Hedging: an Alternative Mechanism for Accelerating Gradient Descent On the convergence rate of the Douglas-Rachford splitting algorithm

Reference 1

Resolution
verified exact
arxiv_id, observed 2026-07-01T20:06:11.725524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-06-28T21:43:17.135025Z digest=sha256:74fd097b20180ff7ec0b791e21c2259cb496652aea272e60be9fa5f567262933