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Paper Citation Record · LEDGER

On the convergence rate of the Douglas-Rachford splitting algorithm

As of 8 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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-04T23:25:19.670814Z digest=sha256:22c7cdeef6caace260cf078bf763710696b9dfe8731996ecc69b62b00090b75e

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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-04T23:25:19.678496Z digest=sha256:9fc2e3e32bc1c9638f462caf358b1f9ad6d06faf2434948f6947eaab86b865cb

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 2026-08-08T06:32:00.761636+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=sha256:62bfc228db643f33a7dbd7af4fa5d4648ec001a0cade8a799f0c7f1a1c9b0a48

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 2026-08-08T06:32:00.761636+00:00.

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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 2026-08-08T06:32:00.761636+00:00.

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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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-04T23:25:19.696515Z digest=sha256:be7ead6ca3e075c6f57a34bfb366d99071d86a449103dcdf5eff08cc1d46df3d

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 2026-08-08T06:32:00.761636+00:00.

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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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-04T23:25:19.702789Z digest=sha256:a88b4392edc4851079d7bc6ae0603b7130e7690957c609610f3e7e9685ec974f

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-04T23:25:19.706127Z digest=sha256:c05562cf8eeae035005535e486ce670ff938980f9b76bafefb5241d7748b0c88

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-04T23:25:19.710313Z digest=sha256:784c459ce8436c3c3d0fc55e6770c5c7ddb7daf6335d9352ddd56b81c2a920ef

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
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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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+00:00.

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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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-04T23:25:19.729907Z digest=sha256:d6f3f2a2e0b129ee962baca504b06713360eafd7f65bf7da0d44615bdeff0f2a

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 2026-08-08T06:32:00.761636+00:00.

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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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-04T23:25:19.746222Z digest=sha256:4e1f721ee9930bfe5c18e93d6c48e039f4221a8dc5f070d66a3af3775e07ec97

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-04T23:25:19.749285Z digest=sha256:16ddc59280de43373fa3c0519dbf19b510b75978858b6ae40f7a8ad5ed39b6c6

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-04T23:25:19.752327Z digest=sha256:ab694c7a44d0d43f3b5d1da70b1705ddbaa2aac7cc66a9465a66f97002a29437

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-04T23:25:19.755221Z digest=sha256:0a2b8b47fbf3a7bd236db341cb8453f7477d39e1067a2472a8600ab132190600

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-04T23:25:19.758471Z digest=sha256:879ffc9667786b51a30db535cbc76af6f81c37716a7635bbf355f31fe73cb361

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-04T23:25:19.762157Z digest=sha256:10f9b9cbbca7880676d6c0a89b5d6ba951a702cbf10e292968aba036585d126a

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:c40385dc4160d3a30c131ad337ea20aaab0dea07c207ae5d9776ad278c109fb0

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-06-28T21:43:17.135025Z digest=sha256:29384b284e1a5191d5d8a816a56943d932161b157443fe845b73c71dbcd46759