Paper Citation Record · LEDGER

Rank-Based Estimation of U-Shaped Biomarker Risk Curves and Critical Points for Time-to-Event Outcomes

As of 14 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2607.19280.

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

pith.paper-citation-record.v1
2607.19280 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T12:59:25.118745Z

measured 12 of 12 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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 fuzzy0
unresolved11
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7ebd80ea-48b8-4243-a13d-557bdc81120d · outbound

This paper cites an unresolved cited work.

Rank-Based Estimation of U-Shaped Biomarker Risk Curves and Critical Points for Time-to-Event Outcomes Unresolved cited work

Reference 1

Resolution: malformed identifier; no resolver link, observed 2026-08-01T12:59:23.654468Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 02f0367d-9598-4da7-8f93-5dbf2f5e2216 · outbound

This paper cites an unresolved cited work.

Rank-Based Estimation of U-Shaped Biomarker Risk Curves and Critical Points for Time-to-Event Outcomes Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T12:59:23.806753Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 92342dad-2281-472b-b98f-b091d296527a · outbound

This paper cites We next show that Λ(θ) is continuous on Θ.

Rank-Based Estimation of U-Shaped Biomarker Risk Curves and Critical Points for Time-to-Event Outcomes We next show that Λ(θ) is continuous on Θ

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T12:59:23.949295Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c57c6d36-3268-4852-a21c-764ac6f05d07 · outbound

This paper cites Lemma 3:Letθ n be a maximizer ofΓ n(θ), and0a maximizer ofΓ(θ).

Rank-Based Estimation of U-Shaped Biomarker Risk Curves and Critical Points for Time-to-Event Outcomes Lemma 3:Letθ n be a maximizer ofΓ n(θ), and0a maximizer ofΓ(θ)

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T12:59:24.087552Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d8d7aecf-3378-4a3a-aae3-d623731d6d8d · outbound

This paper cites Pakes and Pollard (1989) provide simple criteria for determining the Euclidean property.

Rank-Based Estimation of U-Shaped Biomarker Risk Curves and Critical Points for Time-to-Event Outcomes Pakes and Pollard (1989) provide simple criteria for determining the Euclidean property

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T12:59:24.232881Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3acd6009-ad3e-42a3-aea5-d5653d9394df · outbound

This paper cites an unresolved cited work.

Rank-Based Estimation of U-Shaped Biomarker Risk Curves and Critical Points for Time-to-Event Outcomes Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T12:59:24.324412Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bfd4aaab-e834-4287-ad4c-e25623cd628f · outbound

This paper cites Notice thatGis a (2p+ 7)-dimensional vector space of real-valued functions onS⊗S⊗R.

Rank-Based Estimation of U-Shaped Biomarker Risk Curves and Critical Points for Time-to-Event Outcomes Notice thatGis a (2p+ 7)-dimensional vector space of real-valued functions onS⊗S⊗R

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T12:59:24.443115Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf523147-b44c-45ef-ac9e-a1fdaafb6189 · outbound

This paper cites By Lemma 2.4 of Pakes and Pollard (1989), each of the corresponding sets lies in a VC class.

Rank-Based Estimation of U-Shaped Biomarker Risk Curves and Critical Points for Time-to-Event Outcomes By Lemma 2.4 of Pakes and Pollard (1989), each of the corresponding sets lies in a VC class

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T12:59:24.556612Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 987092ec-4db4-40ac-8e45-342b9207d856 · outbound

This paper cites BecauseH(·,z;θ) is piecewise linear inx, its gradient with respect toθis piecewise constant, with a jump at the critical point: Ψ(x,z) =∇ θH(x,z;θ.

Rank-Based Estimation of U-Shaped Biomarker Risk Curves and Critical Points for Time-to-Event Outcomes BecauseH(·,z;θ) is piecewise linear inx, its gradient with respect toθis piecewise constant, with a jump at the critical point: Ψ(x,z) =∇ θH(x,z;θ

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T12:59:24.720195Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a7cc23d-65f4-4961-816c-8548f691737d · outbound

This paper cites By assumption (4), Pr{X i =x c(Z i;θ 0)}= 0, soΨ(X i,Z i) is defined almost surely.

Rank-Based Estimation of U-Shaped Biomarker Risk Curves and Critical Points for Time-to-Event Outcomes By assumption (4), Pr{X i =x c(Z i;θ 0)}= 0, soΨ(X i,Z i) is defined almost surely

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T12:59:24.854666Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8768d81-e247-4a5c-aedc-e238024b3d57 · outbound

This paper cites an unresolved cited work.

Rank-Based Estimation of U-Shaped Biomarker Risk Curves and Critical Points for Time-to-Event Outcomes Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T12:59:24.949678Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 38f9793e-9fe7-497c-be08-e03ff7b0ebda · outbound

This paper cites These expressions also show that assumption (7)(v) need not be imposed separately.

Rank-Based Estimation of U-Shaped Biomarker Risk Curves and Critical Points for Time-to-Event Outcomes These expressions also show that assumption (7)(v) need not be imposed separately

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T12:59:25.118745Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.