Paper Citation Record · LEDGER

Semi-supervised inference for treatment heterogeneity

As of 6 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2509.05048.

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

pith.paper-citation-record.v1
2509.05048 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T05:47:57.212622Z

measured 12 of 12 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-06T06:34:29.942622+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

12 of 12 outbound references displayed

verified exact0
verified fuzzy6
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fc928b6a-ace7-4b10-8043-d48fd2e20d45 · outbound

This paper cites an unresolved cited work.

Semi-supervised inference for treatment heterogeneity Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-05T05:47:58.214634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 50201558-ef18-4975-a770-4a17742c6f3a · outbound

This paper cites an unresolved cited work.

Semi-supervised inference for treatment heterogeneity Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-05T05:47:58.925802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 84142b2c-91ee-4caa-a846-f117c0cd0004 · outbound

This paper cites an unresolved cited work.

Semi-supervised inference for treatment heterogeneity Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-05T05:47:57.769404Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 5dfa3dd7-a789-481c-9197-6d66184a1d33 · outbound

This paper cites (S37) It follows that ( ˆQ(k) )2 −θ2 ETH = ( ˆQ(k) +θETH)( ˆQ(k) −θETH) (i) =Op(1)op(1) = op(1), (S38) where (i) holds from ( S36) and ( S37).

Semi-supervised inference for treatment heterogeneity (S37) It follows that ( ˆQ(k) )2 −θ2 ETH = ( ˆQ(k) +θETH)( ˆQ(k) −θETH) (i) =Op(1)op(1) = op(1), (S38) where (i) holds from ( S36) and ( S37)

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:47:58.440408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation cf8ca23b-f171-480a-8b15-e8c163791560 · outbound

This paper cites Finally, ∥ǫ∥ψ2 = ∥ϕ∗(Z) − W ⊤β∗∥ψ2 ≤ ∥ϕ∗(Z)∥ψ2 + ∥ W ⊤β∗∥ψ2 (i) ≤O(1) +σx ∥ β∗∥ 2 =O(1), where (i) holds from ∥ϕ∗(Z)∥ψ2 =O(1) and Assumption 6.

Semi-supervised inference for treatment heterogeneity Finally, ∥ǫ∥ψ2 = ∥ϕ∗(Z) − W ⊤β∗∥ψ2 ≤ ∥ϕ∗(Z)∥ψ2 + ∥ W ⊤β∗∥ψ2 (i) ≤O(1) +σx ∥ β∗∥ 2 =O(1), where (i) holds from ∥ϕ∗(Z)∥ψ2 =O(1) and Assumption 6

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:47:58.771839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation d43d3a7d-adf6-4b56-8360-700fb374853b · outbound

This paper cites an unresolved cited work.

Semi-supervised inference for treatment heterogeneity Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-05T05:47:58.333277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation fec9b933-f78f-4b93-9a16-33311cdeaa98 · outbound

This paper cites Since E(a −b)2 ≤ 2E(a2 +b2), we have EX(∆2.

Semi-supervised inference for treatment heterogeneity Since E(a −b)2 ≤ 2E(a2 +b2), we have EX(∆2

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:47:58.064566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 93006b7f-6173-4865-8d31-e55531dbcaf6 · outbound

This paper cites Hence, EX          1 ∑ k′̸=k |Ik′| ∑ k′̸=k ∑ i∈Ik′ /BD Ai=a∆2iWi       2 ∞    =Op ( sγ log(d) log(p) nN ) =op ( log(p) n ) , since sγ log(d) = o(N).

Semi-supervised inference for treatment heterogeneity Hence, EX          1 ∑ k′̸=k |Ik′| ∑ k′̸=k ∑ i∈Ik′ /BD Ai=a∆2iWi       2 ∞    =Op ( sγ log(d) log(p) nN ) =op ( log(p) n ) , since sγ log(d) = o(N)

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:47:57.918181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation ff8a4c68-ca07-4337-829f-787f6309745f · outbound

This paper cites an unresolved cited work.

Semi-supervised inference for treatment heterogeneity Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-05T05:47:58.621331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation ce359d28-4e18-49b4-a30b-4cd17d8a6f77 · outbound

This paper cites an unresolved cited work.

Semi-supervised inference for treatment heterogeneity Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-05T05:47:57.591731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 873d4f21-40e0-4de1-8f23-7dba613a3f6f · outbound

This paper cites Repeating the steps in the proof of Theorem 2, under Assumption 3, 3∑ l=1       1 ∑ k′̸=k |Ik′| ∑ k′̸=k ∑ i∈Ik′ ∆liWi       ∞ =Op   √ log(p) n + √ EX(∆2.

Semi-supervised inference for treatment heterogeneity Repeating the steps in the proof of Theorem 2, under Assumption 3, 3∑ l=1       1 ∑ k′̸=k |Ik′| ∑ k′̸=k ∑ i∈Ik′ ∆liWi       ∞ =Op   √ log(p) n + √ EX(∆2

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:47:57.486529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 5c9d4435-edfe-405c-8eaf-deb70627bdf3 · outbound

This paper cites This ensures the upper bound ( S61).

Semi-supervised inference for treatment heterogeneity This ensures the upper bound ( S61)

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:47:57.380587Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Pith citing papers

No inbound Pith citation observations are available.