Paper Citation Record · LEDGER

Instance-Optimality for Private KL Distribution Estimation

As of 15 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2505.23620.

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

pith.paper-citation-record.v1
2505.23620 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:50:22.549729Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+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

27 of 27 outbound references displayed

verified exact0
verified fuzzy16
unresolved11
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d8b66239-63c7-4194-8937-1914d5c61afc · outbound

This paper cites an unresolved cited work.

Instance-Optimality for Private KL Distribution Estimation Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:27.137311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 4d6dcd2a-4bb1-43cb-90bc-f84c20ede1c3 · outbound

This paper cites Then for any fixedε >0, δ ≤ ε, min A is (ε, δ)-DP max p∈P E x∼S(n,p) [dist(p, A(x))] ≥ 1 2 kX i=1 wi · τi · f (Pi) (17) Proof.

Instance-Optimality for Private KL Distribution Estimation Then for any fixedε >0, δ ≤ ε, min A is (ε, δ)-DP max p∈P E x∼S(n,p) [dist(p, A(x))] ≥ 1 2 kX i=1 wi · τi · f (Pi) (17) Proof

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:26.973689Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 66757c62-36a9-4353-98bf-d30910c265b7 · outbound

This paper cites For brevity, denoteˆd = ⌊ dsmall(L′) 2 ⌋ ≥2 and ˆp = P ˆd i=1 pi.

Instance-Optimality for Private KL Distribution Estimation For brevity, denoteˆd = ⌊ dsmall(L′) 2 ⌋ ≥2 and ˆp = P ˆd i=1 pi

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:24.208364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 28c2a691-b4f1-4ac1-b66e-df9fa38c8819 · outbound

This paper cites an unresolved cited work.

Instance-Optimality for Private KL Distribution Estimation Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:26.753976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation eb490b62-7053-4bbc-9284-617d5113219e · outbound

This paper cites Then for any fixedε >0, δ ≤ ε, min A is (ε, δ)-DP max p∈P E x∼S(n,p) [dist(p, A(x))] ≥ kX i=1 wi · 1 10 − 4ε · τi · f (Pi) (30) Proof.

Instance-Optimality for Private KL Distribution Estimation Then for any fixedε >0, δ ≤ ε, min A is (ε, δ)-DP max p∈P E x∼S(n,p) [dist(p, A(x))] ≥ kX i=1 wi · 1 10 − 4ε · τi · f (Pi) (30) Proof

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:26.481546Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3b205121-cf1d-4edd-bb5f-cc161884ea9f · outbound

This paper cites an unresolved cited work.

Instance-Optimality for Private KL Distribution Estimation Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:26.324261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 7603dba6-4dcc-467d-926e-2941c6478227 · outbound

This paper cites 24 Lemma A.6 (Dirac Distribution Packing over κ Symbols).

Instance-Optimality for Private KL Distribution Estimation 24 Lemma A.6 (Dirac Distribution Packing over κ Symbols)

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:26.128958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ddd76f34-84cf-474e-9b42-64f9b1d1df14 · outbound

This paper cites an unresolved cited work.

Instance-Optimality for Private KL Distribution Estimation Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:25.887119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6e46f6fd-37a7-4c35-a810-2edfec67812e · outbound

This paper cites 1 c + PK k=1 sk # ≤ 1PK k=1 pk (110) Proof. Conditioned on any fixed value fors3, · · ·, sK, denote c′ = c + PK k=3 sk we have that E.

Instance-Optimality for Private KL Distribution Estimation 1 c + PK k=1 sk # ≤ 1PK k=1 pk (110) Proof. Conditioned on any fixed value fors3, · · ·, sK, denote c′ = c + PK k=3 sk we have that E

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:25.643054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6cec2878-7e1a-460d-81d0-cca2329733a6 · outbound

This paper cites an unresolved cited work.

Instance-Optimality for Private KL Distribution Estimation Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:25.446423Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 72cf196e-89fd-4ad3-b041-475db19a5785 · outbound

This paper cites By the coupling lemma Lemma D.1, there exists(Z1, Z′.

Instance-Optimality for Private KL Distribution Estimation By the coupling lemma Lemma D.1, there exists(Z1, Z′

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:25.320666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3e0ca429-32ee-454d-99f3-23273e765c4c · outbound

This paper cites Similarly, there exists (Z2, Z′.

Instance-Optimality for Private KL Distribution Estimation Similarly, there exists (Z2, Z′

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:25.203084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation bf868323-cb47-416a-bb96-a8fa8a9bbcee · outbound

This paper cites Let Z = (Z1, Z′.

Instance-Optimality for Private KL Distribution Estimation Let Z = (Z1, Z′

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:25.071179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation eebf63af-bbf5-493f-9d4d-44c9cc35501b · outbound

This paper cites Then Z ∼ µ1 × µ′ 1 and Z′ ∼ µ2 × µ′ 2.

Instance-Optimality for Private KL Distribution Estimation Then Z ∼ µ1 × µ′ 1 and Z′ ∼ µ2 × µ′ 2

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:24.935121Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 98e0b7ea-45ef-47b1-aa72-5a05b6a4c508 · outbound

This paper cites D.2 Non-DP Per-Instance Lower Bound under N≤ t n (p) We now prove the per-instance lower bound in Table 4 under additive neighborhoodN≤ t n (p) for low-probability symbols.

Instance-Optimality for Private KL Distribution Estimation D.2 Non-DP Per-Instance Lower Bound under N≤ t n (p) We now prove the per-instance lower bound in Table 4 under additive neighborhoodN≤ t n (p) for low-probability symbols

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:24.773013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 92c3b799-84a3-4b68-8101-3c4eabffb700 · outbound

This paper cites an unresolved cited work.

Instance-Optimality for Private KL Distribution Estimation Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:24.608305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 462ae3ca-797c-45fb-b900-8c0625b6eeb8 · outbound

This paper cites (a) If maxi∈[d]\[dsmall(L′)] pi ≤ 1 n: Then the neighborhood Nstat defined in (137) is a subset of N≤ t n defined in (142), i.e., Nstat ⊆ N≤ t n.

Instance-Optimality for Private KL Distribution Estimation (a) If maxi∈[d]\[dsmall(L′)] pi ≤ 1 n: Then the neighborhood Nstat defined in (137) is a subset of N≤ t n defined in (142), i.e., Nstat ⊆ N≤ t n

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:24.420153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation de0bba31-745a-4e3d-8e1d-83dec3d06493 · outbound

This paper cites an unresolved cited work.

Instance-Optimality for Private KL Distribution Estimation Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:24.087419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 776c0243-6aba-4acc-91df-03d1a64e2336 · outbound

This paper cites X i∈L pi · ln npi/2 ˜xi # | {z } 1 + E.

Instance-Optimality for Private KL Distribution Estimation X i∈L pi · ln npi/2 ˜xi # | {z } 1 + E

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:23.814199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a35e66d3-c1da-4000-b6ef-0f74cf16fd53 · outbound

This paper cites sampling twice.

Instance-Optimality for Private KL Distribution Estimation sampling twice

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:23.645035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 440bfc40-9518-4181-b9a0-5f21a5a8000a · outbound

This paper cites We construct a packing set of distributionsP = {p+, p−} that contains the following two distributions.

Instance-Optimality for Private KL Distribution Estimation We construct a packing set of distributionsP = {p+, p−} that contains the following two distributions

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:23.489788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 04f36ffa-6ec3-4d8a-9833-88f717443212 · outbound

This paper cites X i∈L pi · ln piP i∈L pi ¯xiP i∈L ¯xi !# = E.

Instance-Optimality for Private KL Distribution Estimation X i∈L pi · ln piP i∈L pi ¯xiP i∈L ¯xi !# = E

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:23.359915Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c6cb1552-70c4-42a5-b778-cc97bfe532d5 · outbound

This paper cites an unresolved cited work.

Instance-Optimality for Private KL Distribution Estimation Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:23.227746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 30c7be6b-4c97-4495-9228-d649d451dc5d · outbound

This paper cites We will prove the lemma by contradiction.

Instance-Optimality for Private KL Distribution Estimation We will prove the lemma by contradiction

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:23.088541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 4ee7f9ef-30b4-44f5-8739-ea56b8461683 · outbound

This paper cites an unresolved cited work.

Instance-Optimality for Private KL Distribution Estimation Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:22.945602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e166664f-5eaa-44d8-93a2-2f65cec2c260 · outbound

This paper cites an unresolved cited work.

Instance-Optimality for Private KL Distribution Estimation Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:22.768155Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 875cd6b5-4a05-48e0-b6f4-c2bbbff1123f · outbound

This paper cites Large Language Models Can Be Strong Differentially Private Learners.

Instance-Optimality for Private KL Distribution Estimation Large Language Models Can Be Strong Differentially Private Learners

Reference 2444

Resolution: unresolved; no resolver link, observed 2026-08-07T12:50:20.230178Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.