Paper Citation Record · LEDGER

Optimal e-value testing for properly constrained hypotheses

As of 20 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 5 inbound Pith citation observations for arXiv:2412.21125.

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

pith.paper-citation-record.v1
2412.21125 v3

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:16:10.616850Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T05:47:13.658596Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-23T08:22:44.478626Z

Reference resolution

12 of 12 outbound references displayed

verified exact0
verified fuzzy3
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a9e03529-b255-4fe0-bf3e-ebb22450a764 · outbound

This paper cites an unresolved cited work.

Optimal e-value testing for properly constrained hypotheses Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:16:10.837233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b463450e-a7b8-41ab-806b-3fed17b60bdf · outbound

This paper cites an unresolved cited work.

Optimal e-value testing for properly constrained hypotheses Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:16:10.859141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 4b6d01c0-d1eb-4ae7-b877-6cac1673320a · outbound

This paper cites Admissible anytime-valid sequential inference must rely on nonnegative martingales.

Optimal e-value testing for properly constrained hypotheses Admissible anytime-valid sequential inference must rely on nonnegative martingales

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-10T23:16:10.594651Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fabf7bec-aeba-4f36-a9ed-7013425dfa6c · outbound

This paper cites The only admissible way of merging arbitrary e-values.

Optimal e-value testing for properly constrained hypotheses The only admissible way of merging arbitrary e-values

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-10T23:16:10.598637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 07e893f8-c6bf-4860-8f30-6439eccd0051 · outbound

This paper cites By Lemma 27, we have that ˆE ∈ arg maxE∈EH ⟨ ˆQ, log E⟩.

Optimal e-value testing for properly constrained hypotheses By Lemma 27, we have that ˆE ∈ arg maxE∈EH ⟨ ˆQ, log E⟩

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:16:10.815222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 141cb2f8-39e6-42c0-8184-746a250bad40 · outbound

This paper cites , vr} ⊆Rm be a family of vectors that spans Rm.

Optimal e-value testing for properly constrained hypotheses , vr} ⊆Rm be a family of vectors that spans Rm

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:16:10.848076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 51c0262d-7012-475e-8869-a0db0673ea76 · outbound

This paper cites Then, for any Q ∈ PX , the set arg maxE∈EH ⟨Q, log E⟩ is non-empty.

Optimal e-value testing for properly constrained hypotheses Then, for any Q ∈ PX , the set arg maxE∈EH ⟨Q, log E⟩ is non-empty

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:16:10.826988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation fd01b21e-7359-49fe-a2e5-612ada29272a · outbound

This paper cites The numeraire e-variable and reverse information projection.

Optimal e-value testing for properly constrained hypotheses The numeraire e-variable and reverse information projection

Reference 1976

Resolution: unresolved; no resolver link, observed 2026-08-10T23:16:10.580517Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9be05140-f26f-4938-b93f-d0c3603c972c · outbound

This paper cites On the optimality of coin-betting for mean estimation.

Optimal e-value testing for properly constrained hypotheses On the optimality of coin-betting for mean estimation

Reference 2006

Resolution: unresolved; no resolver link, observed 2026-08-10T23:16:10.576587Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7d27c20d-1466-46b4-99b7-c50b2c2ef7b1 · outbound

This paper cites Online Learning: A Modern Introduction Using Convex Optimization.

Optimal e-value testing for properly constrained hypotheses Online Learning: A Modern Introduction Using Convex Optimization

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-10T23:16:10.587324Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 98795c4e-f406-454c-89aa-082b3f3957e0 · outbound

This paper cites Hypothesis testing with e-values.

Optimal e-value testing for properly constrained hypotheses Hypothesis testing with e-values

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-10T23:16:10.591210Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a015b183-4eea-46a7-9c8d-ad0fcd71c11d · outbound

This paper cites Larsson, A.

Optimal e-value testing for properly constrained hypotheses Larsson, A

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-10T23:16:10.584287Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 2f6f17a6-dd8c-459f-9500-ef95ce1d7ac5 · inbound

On the optimality of coin-betting for mean estimation cites this paper.

On the optimality of coin-betting for mean estimation Optimal e-value testing for properly constrained hypotheses

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-23T08:22:44.482090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 503e8389-fed4-4435-b3f2-ee981518e1a2 · inbound

Uniform mean estimation for monotonic processes cites this paper.

Uniform mean estimation for monotonic processes Optimal e-value testing for properly constrained hypotheses

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-09T16:14:02.309236Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c95e80f2-1102-4f3e-8d92-def6881c307f · inbound

On Stopping Times of Power-one Sequential Tests: Tight Lower and Upper Bounds cites this paper.

On Stopping Times of Power-one Sequential Tests: Tight Lower and Upper Bounds Optimal e-value testing for properly constrained hypotheses

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-16T05:47:13.658596Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1379fc3d-a94b-443c-a143-02637193794c · inbound

Optimal e-values for testing the mean of a bounded random variable against a composite alternative cites this paper.

Optimal e-values for testing the mean of a bounded random variable against a composite alternative Optimal e-value testing for properly constrained hypotheses

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T10:14:29.408773Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation baf19c0f-37e3-41d6-8afb-682ca003c116 · inbound

Time-sensitive anytime-valid testing cites this paper.

Time-sensitive anytime-valid testing Optimal e-value testing for properly constrained hypotheses

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-11T21:46:43.062251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.