Paper Citation Record · LEDGER

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families

As of 11 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 2 inbound Pith citation observations for arXiv:2606.28797.

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

pith.paper-citation-record.v1
2606.28797 v2

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-12T11:17:11.251985Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T18:27:46.410410Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

19 of 19 outbound references displayed

verified exact0
verified fuzzy0
unresolved19
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e92962b1-f087-4da7-a1f1-9726d3569ec0 · outbound

This paper cites an unresolved cited work.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6aab3997-0193-42ef-ad34-0b107bc92198 · outbound

This paper cites Bownik,The Kadison–Singer problem, Frames and Harmonic Analysis, 63–92, Contemp.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Bownik,The Kadison–Singer problem, Frames and Harmonic Analysis, 63–92, Contemp

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation be955dc2-6843-4acc-8948-ebefc459ccca · outbound

This paper cites Selector form of Weaver's conjecture, Feichtinger's conjecture, and frame sparsification.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Selector form of Weaver's conjecture, Feichtinger's conjecture, and frame sparsification

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ecb35dbe-5f5b-4fd9-ad80-369c9d2d37f2 · outbound

This paper cites Bownik,On akemann–weaver conjecture, Adv.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Bownik,On akemann–weaver conjecture, Adv

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f752e22-28eb-4b12-82d7-14110551c364 · outbound

This paper cites Hyperbolic polynomials and the Kadison-Singer problem.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Hyperbolic polynomials and the Kadison-Singer problem

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 75ec061a-dfd7-4cf7-81cb-ca868338576d · outbound

This paper cites an unresolved cited work.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 196f3292-291f-45a3-8cd7-acfeb7109f09 · outbound

This paper cites an unresolved cited work.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8efd3db6-a83b-4153-99b8-5ff2c73703e7 · outbound

This paper cites Chartrand, P.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Chartrand, P

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 598aa538-008b-49e7-a593-8d2a9582b1e0 · outbound

This paper cites an unresolved cited work.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d525e53-3d71-4225-a312-3f8d9cf76dc4 · outbound

This paper cites an unresolved cited work.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7095b771-e5da-47da-9791-ed38fd4e5699 · outbound

This paper cites an unresolved cited work.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8adb34b4-1f1b-4d4b-8826-0cb5a4585168 · outbound

This paper cites an unresolved cited work.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ad16f8a3-9f9e-419c-8d4b-4a06345d8912 · outbound

This paper cites Lubotzky, R.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Lubotzky, R

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b3c76efb-cfb0-45c6-bdec-3fa075507f89 · outbound

This paper cites König,Theorie der endlichen und unendlichen Graphen, Akademische Verlagsgesellschaft, Leipzig, 1936.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families König,Theorie der endlichen und unendlichen Graphen, Akademische Verlagsgesellschaft, Leipzig, 1936

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f7978c1-7921-4c1c-9497-c025c618bf1b · outbound

This paper cites an unresolved cited work.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e02b929-0b65-4654-9c81-f9c9f0895499 · outbound

This paper cites an unresolved cited work.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9e7f155e-e019-488b-890e-80ecae9f74d6 · outbound

This paper cites an unresolved cited work.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 26128ff4-ca1e-47f8-941b-b0e2e1330ce8 · outbound

This paper cites an unresolved cited work.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b316a045-4942-41b9-8c7c-73a66fd47865 · outbound

This paper cites an unresolved cited work.

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-12T11:17:11.251985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 76b24eda-50ba-4fd6-90bb-dbcdc4168cb0 · inbound

Parity families and a kernel-averaged L-function for near-Ramanujan signings cites this paper.

Parity families and a kernel-averaged L-function for near-Ramanujan signings An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T18:27:46.410410Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 28e7f388-5828-460e-9e0b-3e7cce084513 · inbound

Signed circulants at the Ramanujan bound cites this paper.

Signed circulants at the Ramanujan bound An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T18:25:42.979330Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.