Paper Citation Record · LEDGER

Exact detection threshold of the packing test

As of 23 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2608.00445.

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

pith.paper-citation-record.v1
2608.00445 v1

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:31:17.623227Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+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 fuzzy9
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3eb7a2cc-c807-42af-9cbd-69d8df73a0aa · outbound

This paper cites Hereκ∈R + is the concentration parameter,µis the unknown location (nuisance) parameter, andc FvML p,κ ,c Wat p,κ are normalizing constants.

Exact detection threshold of the packing test Hereκ∈R + is the concentration parameter,µis the unknown location (nuisance) parameter, andc FvML p,κ ,c Wat p,κ are normalizing constants

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:31:17.789068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f6ec7d3b-0da3-41c1-97b2-214b3bad4d23 · outbound

This paper cites This scaling is also the same as under the null (uniformity).

Exact detection threshold of the packing test This scaling is also the same as under the null (uniformity)

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:31:17.755090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 60d48c49-ced9-4e63-96d4-05ccefbaa87c · outbound

This paper cites Indeed, conditionally on eT1, eT2, the event n X⊤ 1 X2 >t◦ n o is equivalent to √ d·Z> √ d· t◦ n− eT1eT2 q 1− eT 2 1 q 1− eT 2 2.

Exact detection threshold of the packing test Indeed, conditionally on eT1, eT2, the event n X⊤ 1 X2 >t◦ n o is equivalent to √ d·Z> √ d· t◦ n− eT1eT2 q 1− eT 2 1 q 1− eT 2 2

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:31:17.731677Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 8856daf8-e401-4ec0-bd21-a01deceebe07 · outbound

This paper cites u2 2 +v 2 + u4 8 + v4 4 # + 1 2 (2−uv−ε )2 + ≥(1−3ε).

Exact detection threshold of the packing test u2 2 +v 2 + u4 8 + v4 4 # + 1 2 (2−uv−ε )2 + ≥(1−3ε)

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:31:17.720559Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 074139f4-4da3-4a84-aba0-8893eb41c40c · outbound

This paper cites √ 2q+ q2 2 √ 2 # + 1 2 (2−q−ε )2 + ) > 3+c 2 . Proof of Lemma 6.Fixε∈[0,1/10]. Consider the caseq≥2−ε. Then inf q≥0 ( (1−2ε ).

Exact detection threshold of the packing test √ 2q+ q2 2 √ 2 # + 1 2 (2−q−ε )2 + ) > 3+c 2 . Proof of Lemma 6.Fixε∈[0,1/10]. Consider the caseq≥2−ε. Then inf q≥0 ( (1−2ε )

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:31:17.709528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation bd49a128-5af9-4c7d-97f1-93695ccaefc8 · outbound

This paper cites [2026]; Jammalamadaka and Janson.

Exact detection threshold of the packing test [2026]; Jammalamadaka and Janson

Reference 1989

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:31:17.766429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 959b90a1-8c60-4fbd-802b-b102adcd4652 · outbound

This paper cites Understanding Dimensional Collapse in Contrastive Self-supervised Learning.

Exact detection threshold of the packing test Understanding Dimensional Collapse in Contrastive Self-supervised Learning

Reference 2003

Resolution: unresolved; no resolver link, observed 2026-08-15T15:31:17.614516Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0886d71-cf79-4444-90ef-364eaba83f67 · outbound

This paper cites This proves the second claim in (17).

Exact detection threshold of the packing test This proves the second claim in (17)

Reference 2014

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:31:17.743063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 49786e32-50f7-4291-a922-081dfeca91a3 · outbound

This paper cites Asymptotic analysis of high-dimensional uniformity tests under heavy-tailed alternatives.

Exact detection threshold of the packing test Asymptotic analysis of high-dimensional uniformity tests under heavy-tailed alternatives

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-08-15T15:31:17.610094Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a6b0a9bf-0064-461a-9e5d-b10081f4e70c · outbound

This paper cites Learning with hyperspherical uniformity.

Exact detection threshold of the packing test Learning with hyperspherical uniformity

Reference 2018

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:31:17.697837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a5c73ef1-d958-40a7-836d-a7e0509937c9 · outbound

This paper cites An overview of uniformity tests on the hypersphere.

Exact detection threshold of the packing test An overview of uniformity tests on the hypersphere

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-15T15:31:17.623227Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2cb7bd0-8bc4-4490-8c41-200832842e2d · outbound

This paper cites High-dimensional Sobolev tests on hyperspheres.

Exact detection threshold of the packing test High-dimensional Sobolev tests on hyperspheres

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-15T15:31:17.605647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68c9bfb5-8fb7-438c-90e8-30837803398b · outbound

This paper cites In particular, any linear combination ofR n andB n in (2) and (3), respectively, that is not proportional toR n fails to achieve the optimal detection rate.

Exact detection threshold of the packing test In particular, any linear combination ofR n andB n in (2) and (3), respectively, that is not proportional toR n fails to achieve the optimal detection rate

Reference 2025

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:31:17.777710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

No inbound Pith citation observations are available.