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Paper Citation Record · LEDGER

On the convergence rate of the Douglas-Rachford splitting algorithm

As of 9 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=sha256:4d79e02d4108ab910158e061f204edaef83dfcff75023a3ac3a97f360be9d017

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.

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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=sha256:15260a7daab3033ea744c0a5b2ef6a65153d95e6d6430ecc903aaa4d26e11aab

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.

source=pdf_text observed=2026-08-04T23:25:19.690239Z digest=sha256:90bb9248a86dea88f38e009b391113dd0401b28c4f1b8d74b10af09d34a34076

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.

source=pdf_text observed=2026-08-04T23:25:19.693384Z digest=sha256:f34e7f6e705dcb69f4d89c2c3ead2b92f282aebdca471366e168c966b9371226

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.

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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.

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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=sha256:624cbac3d64b0d0c455aae7b6bbe0157ff4d5917b18af459eb4f64b9960b5601

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.

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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 2026-08-08T06:32:00.761636+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
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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=sha256:0871cce334a81e50d54f07482971c5d7b69204c23ea470ce6e63f269a6927e2e

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
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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.

source=pdf_text observed=2026-08-04T23:25:19.736791Z digest=sha256:b69bbd49fd874cae5dcba9dd8f56e2d1235f0aa5d68a7e99bcc1eaa857614383

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:b53680e9b3a35428497a404a8f6baf1e5b3dfd784db26d11c6fe49ee08f116b1

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:c08b19c26977b37596cc33f1682493db25e2ed527deefd9704ec10d6a4b62f1f

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=sha256:96977c9a5817f24c23d4e7f3a7ece2c0417796bdb1f0e20d7afbc772725ec243

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:d9b879148d524c7037579fe36718aa08580ace29608517193cfe3d7088f57fc6

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:dad1eb39b7fdf6239c5f539c8bc51300efd10538f556c06af474d0a7c42df11e

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:d44b3f54bafe3998887f23e705cbcf61f73672bda59f99b1b346ff29b5bcf44a

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=sha256:68684bc861f06b2b9e7bd0b49c84997e180f2e716d03c6f0ef8fac2e28de5a77

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=sha256:03231f7139462ab16ce1ad940db0249caef3f0b3a16f4942d6aa5c699f40f08f