Paper Citation Record · LEDGER

Consistency of variational approximations under bounded Kullback--Leibler divergence

As of 25 July 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2606.13230.

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

pith.paper-citation-record.v1
2606.13230 v1

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-27T05:12:37.902286Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-07-24T06:31:00.690269+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

13 of 13 outbound references displayed

verified exact0
verified fuzzy0
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ae0b4755-fd0c-4c66-992f-250fc060ef52 · outbound

This paper cites and Ridgway, J.

Consistency of variational approximations under bounded Kullback--Leibler divergence and Ridgway, J

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-27T05:12:37.902286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e0e9ff7-5b4d-4308-a227-0b607dcbb92f · outbound

This paper cites Sinceω∈Ω ∇, there existsn2(ω)∈Nsuch that ∥∇zgn(0)∥ ≤1for alln≥n 2(ω).

Consistency of variational approximations under bounded Kullback--Leibler divergence Sinceω∈Ω ∇, there existsn2(ω)∈Nsuch that ∥∇zgn(0)∥ ≤1for alln≥n 2(ω)

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-27T05:12:37.902286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d3d008ac-6b60-4217-8289-76dd85fee5da · outbound

This paper cites an unresolved cited work.

Consistency of variational approximations under bounded Kullback--Leibler divergence Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-27T05:12:37.902286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2591ffbf-8b32-49e8-b1d9-d8bb1ef271cd · outbound

This paper cites sup θ∈B(θ0,r0) |b′′′(θ⊤W1)| |W1jW1kW1ℓ| # ≤E.

Consistency of variational approximations under bounded Kullback--Leibler divergence sup θ∈B(θ0,r0) |b′′′(θ⊤W1)| |W1jW1kW1ℓ| # ≤E

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-27T05:12:37.902286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a496a57f-84e3-484c-89b6-76fd325548a9 · outbound

This paper cites an unresolved cited work.

Consistency of variational approximations under bounded Kullback--Leibler divergence Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-27T05:12:37.902286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 38aa310e-edca-4201-b078-88e0e487efb6 · outbound

This paper cites Sinceη n →η ∗ ∈(0,∞), it follows that, for everyω∈Ω M, the sequence(˜gn(ω,·)) n≥1 also satisfies the hypotheses of case (2) of Miller (2021, Thm.

Consistency of variational approximations under bounded Kullback--Leibler divergence Sinceη n →η ∗ ∈(0,∞), it follows that, for everyω∈Ω M, the sequence(˜gn(ω,·)) n≥1 also satisfies the hypotheses of case (2) of Miller (2021, Thm

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-27T05:12:37.902286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 66eaa795-9540-4bdc-bca7-83ba11b9b29f · outbound

This paper cites an unresolved cited work.

Consistency of variational approximations under bounded Kullback--Leibler divergence Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-27T05:12:37.902286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 452cf279-3298-472c-ac76-2005a1297e52 · outbound

This paper cites an unresolved cited work.

Consistency of variational approximations under bounded Kullback--Leibler divergence Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-27T05:12:37.902286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e3e1fce0-8eda-402b-bc7a-ce52f41bd6a3 · outbound

This paper cites Consequently, Assumption (1) of Miller (2021, Thm.

Consistency of variational approximations under bounded Kullback--Leibler divergence Consequently, Assumption (1) of Miller (2021, Thm

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-27T05:12:37.902286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9d1db70-18b0-4095-b1a8-552b6784f805 · outbound

This paper cites To verify Assumption (2) of Miller (2021, Thm.

Consistency of variational approximations under bounded Kullback--Leibler divergence To verify Assumption (2) of Miller (2021, Thm

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-27T05:12:37.902286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2bd5830d-501e-434f-88b2-108e42174864 · outbound

This paper cites Therefore, for all sufficiently largen, inf θ∈B( ˆθn,ε)c {˜gn(θ)−˜gn(ˆθn)} ≥inf θ∈B(θ 0,ε/2)c {˜gn(θ)−˜gn(ˆθn)} ≥inf θ∈B(θ 0,ε/2)c {˜gn(θ)−˜gn(θ0)}, since ˆθn minimises˜gn.

Consistency of variational approximations under bounded Kullback--Leibler divergence Therefore, for all sufficiently largen, inf θ∈B( ˆθn,ε)c {˜gn(θ)−˜gn(ˆθn)} ≥inf θ∈B(θ 0,ε/2)c {˜gn(θ)−˜gn(ˆθn)} ≥inf θ∈B(θ 0,ε/2)c {˜gn(θ)−˜gn(θ0)}, since ˆθn minimises˜gn

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-27T05:12:37.902286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5c10de49-5bb1-426c-8b08-22e6aa0aab2b · outbound

This paper cites Sinceπis strictly positive and twice continuously differentiable by (C2), the prior assumptions in Miller (2021, Thm.

Consistency of variational approximations under bounded Kullback--Leibler divergence Sinceπis strictly positive and twice continuously differentiable by (C2), the prior assumptions in Miller (2021, Thm

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-27T05:12:37.902286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 105ee58e-4d03-45fa-b92f-0f4111710c4e · outbound

This paper cites Finally, µn(dθ)∝exp{−n˜g n(θ)}π(θ) dθ.

Consistency of variational approximations under bounded Kullback--Leibler divergence Finally, µn(dθ)∝exp{−n˜g n(θ)}π(θ) dθ

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-27T05:12:37.902286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.