Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T11:53:08.187486Z
Paper Citation Record · LEDGER
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization
As of 17 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:1908.08394.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
24 of 24 outbound references displayed
- verified exact0
- verified fuzzy10
- unresolved14
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 6fe1ccc5-0a46-4e25-abf2-ced9f523959e · outbound
This paper cites Let ∇FSC(x) = 0, that is ( L − µ 2n A (√ 2 α + 1 ) + µ I ) x = L − µ n(α + 1) ξem, or ω 2 + 1 + 2nµ L−µ −1 −1 2 + 2nµ L−µ −1.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Let ∇FSC(x) = 0, that is ( L − µ 2n A (√ 2 α + 1 ) + µ I ) x = L − µ n(α + 1) ξem, or ω 2 + 1 + 2nµ L−µ −1 −1 2 + 2nµ L−µ −1
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:53:08.571283Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation bbfbf7b7-b404-4e83-9a72-ec0f7ee56acb · outbound
This paper cites Let y = xm−k+1:m ∈ Rk and Ak be last k rows and columns of the matrix in Equation (22).
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Let y = xm−k+1:m ∈ Rk and Ak be last k rows and columns of the matrix in Equation (22)
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:53:08.555397Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4cecb75d-21d6-4a83-a02b-f2ad16704389 · outbound
This paper cites an unresolved cited work.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:53:08.587315Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ee18b3ba-2f76-412f-869d-df574513ec9d · outbound
This paper cites Let ∇FC(x) = 0, that is L 2n A(1)x = ξ n em, or 2 −1 −1 2 −1.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Let ∇FC(x) = 0, that is L 2n A(1)x = ξ n em, or 2 −1 −1 2 −1
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:53:08.539423Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f13ed542-7ca9-4dc1-8a75-bf551411d25d · outbound
This paper cites Thus min x∈Fk FC(x) − FC(x∗) = ξ2 nL (m − k).
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Thus min x∈Fk FC(x) − FC(x∗) = ξ2 nL (m − k)
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:53:08.523560Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8c6c009f-dc48-4c06-b072-986cd2bd315c · outbound
This paper cites an unresolved cited work.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:53:08.508013Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4549b600-5504-494a-b6eb-d370ff47c180 · outbound
This paper cites an unresolved cited work.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:53:08.492813Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5412a292-5656-4130-a4b8-aa392a183fa3 · outbound
This paper cites 29 E.2 Our Result Theorem E.3.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization 29 E.2 Our Result Theorem E.3
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:53:08.477602Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e22b7104-1f78-4fd3-991e-ddeb823c8674 · outbound
This paper cites an unresolved cited work.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:53:08.462405Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5b8ef85a-1363-493b-8052-3f29e268c46e · outbound
This paper cites an unresolved cited work.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:53:08.447116Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8ba7bf39-2795-47c5-84f0-5e8f995de837 · outbound
This paper cites Similar to Lemma 2.6, similar conclusion hosts for {fi(x; α, m, λ, β )}n i=1.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Similar to Lemma 2.6, similar conclusion hosts for {fi(x; α, m, λ, β )}n i=1
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:53:08.431572Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 922835ff-187e-44a9-abf5-27318e542f8a · outbound
This paper cites an unresolved cited work.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:53:08.415380Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9d7c427b-68b3-42fc-af9c-4bb597f536d2 · outbound
This paper cites For s which satisfies (31), if m − s ⁄∈ Lj and m − s + 1 ⁄∈ Lj, then the s-th element of Au is (β/γ u s).
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization For s which satisfies (31), if m − s ⁄∈ Lj and m − s + 1 ⁄∈ Lj, then the s-th element of Au is (β/γ u s)
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:53:08.399840Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0b04fe5d-8dfe-4d33-97b3-341f66f64945 · outbound
This paper cites an unresolved cited work.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:53:08.383463Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5f17672d-ca48-432a-b095-b23906a193c2 · outbound
This paper cites Moreover, we have that.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Moreover, we have that
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:53:08.368243Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4521de40-9455-4df2-86d1-482afc5cf926 · outbound
This paper cites an unresolved cited work.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:53:08.353320Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ef2f5f6f-0ec9-49d8-b227-96d02e3c0a24 · outbound
This paper cites an unresolved cited work.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:53:08.337519Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 846d6c29-4d09-41b9-aafa-0a769df2ef49 · outbound
This paper cites an unresolved cited work.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:53:08.322424Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 12ec9b02-8a84-42d6-8d2b-dfc981f994bd · outbound
This paper cites an unresolved cited work.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:53:08.306723Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c08ba104-0754-43e1-83e9-3c4b4e543a41 · outbound
This paper cites In short,.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization In short,
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:53:08.289095Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c862f725-bba4-4b3c-b28f-10bb1359035d · outbound
This paper cites an unresolved cited work.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:53:08.273460Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation fa8da37a-fb73-4dfb-90dd-a3a03dffc614 · outbound
This paper cites an unresolved cited work.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:53:08.257123Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 96837c36-a91a-4a26-afb0-75431f371bc3 · outbound
This paper cites an unresolved cited work.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:53:08.241007Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6920c182-1d07-465a-9419-89f8ae912bee · outbound
This paper cites Remark E.7.
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization Remark E.7
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:53:08.224852Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
No inbound Pith citation observations are available.