Paper Citation Record · LEDGER

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition

As of 13 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2501.12153.

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

pith.paper-citation-record.v1
2501.12153 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T17:38:29.114324Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+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

34 of 34 outbound references displayed

verified exact1
verified fuzzy21
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1ab0be08-0226-4e40-8688-1ba5ae77d9c3 · outbound

This paper cites The absolutely continuous spectrum of the almost Mathieu operator.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition The absolutely continuous spectrum of the almost Mathieu operator

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-10T17:38:28.529343Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 66861858-2275-4357-9de4-cf5fc50580ed · outbound

This paper cites Avila and S.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Avila and S

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.474866Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 03c6d006-42ed-4d26-b320-499e280c76a2 · outbound

This paper cites Avila, S.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Avila, S

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.455760Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 6ff85633-1f46-4f25-8ca1-a317a8e1fd46 · outbound

This paper cites Avila, J.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Avila, J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.439029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 6759eb7a-b617-466e-a82f-41deabe37815 · outbound

This paper cites Barbaroux, F.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Barbaroux, F

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.421161Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b8092bb5-a728-49ce-ad9c-852b0f12044d · outbound

This paper cites Barbaroux, F.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Barbaroux, F

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.403508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 41de54d6-03c9-4d3b-b320-7c986905b07f · outbound

This paper cites Bourgain.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Bourgain

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.387078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8930e4db-8149-4b7f-8398-cd79b7435737 · outbound

This paper cites Bourgain and S.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Bourgain and S

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.370034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0a21f9e1-6a69-4077-b8f7-f5dd87b8f227 · outbound

This paper cites Damanik and S.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Damanik and S

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.334488Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 53d2543a-cc1e-4b9c-9231-eec58625174d · outbound

This paper cites del Rio, S.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition del Rio, S

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.298177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 14769fae-697e-4bff-838f-771836c9c52d · outbound

This paper cites Ge and S.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Ge and S

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-10T17:38:28.606942Z

Source-reported events for the cited work

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Observation c48f6545-4fa0-4e15-831c-68655b1b9bd6 · outbound

This paper cites an unresolved cited work.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:38:30.243446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c788320d-ddb8-49d3-967e-4f7875d0083e · outbound

This paper cites Guarneri and H.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Guarneri and H

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.144476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b119f971-3e06-48f8-ae14-4f8581fbc9f8 · outbound

This paper cites Jitomirskaya.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Jitomirskaya

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.126657Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 34b9f3ef-75ca-4f06-af93-035e59eac567 · outbound

This paper cites Jitomirskaya.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Jitomirskaya

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.109911Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8d48ce86-afa3-4cbe-b2eb-2dd4362c5341 · outbound

This paper cites Sharp arithmetic delocalization for quasiperiodic operators with potentials of semi-bounded variation.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Sharp arithmetic delocalization for quasiperiodic operators with potentials of semi-bounded variation

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-10T17:38:28.643620Z

Source-reported events for the cited work

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Observation ab43b8bb-570f-46be-96d6-04bb0468faa0 · outbound

This paper cites Sharp arithmetic localization for quasiperiodic operators with monotone potentials.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Sharp arithmetic localization for quasiperiodic operators with monotone potentials

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-10T17:38:28.649992Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f5b1557b-9d6a-4408-b250-5089ffc057c5 · outbound

This paper cites Jitomirskaya and Y.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Jitomirskaya and Y

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.089790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 65d14cf2-af1a-470a-9dd2-56e1cf0763cc · outbound

This paper cites Jitomirskaya and W.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Jitomirskaya and W

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.066859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cb90d70d-4786-4672-847a-95cac8b14ca6 · outbound

This paper cites Jitomirskaya and W.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Jitomirskaya and W

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.044816Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 23b367e8-5b1a-464c-8fb6-7e60b885cb85 · outbound

This paper cites Jitomirskaya and M.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Jitomirskaya and M

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.022731Z

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Observation b2b19875-495f-4d96-a346-1746f53526ca · outbound

This paper cites Jitomirskaya and S.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Jitomirskaya and S

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:29.982489Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cf09ef08-5f37-407b-a464-50349d89927c · outbound

This paper cites an unresolved cited work.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:38:29.929088Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 59901579-362e-4ea5-bfb1-d26ea6070a1c · outbound

This paper cites Killip, A.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Killip, A

Reference 24

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 88b66960-f3a6-45ef-9c33-a28863ef4685 · outbound

This paper cites Last and B.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Last and B

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:29.788320Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 320f7832-f583-4f6a-9504-78c96f406904 · outbound

This paper cites Exact local distribution of the absolutely continuous spectral measure.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Exact local distribution of the absolutely continuous spectral measure

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-10T17:38:29.071142Z

Source-reported events for the cited work

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Observation 43e59a9c-9df2-4847-8a9b-aa9ccf2e7773 · outbound

This paper cites an unresolved cited work.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:38:29.589159Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7986a05f-b8d6-4068-ae25-7bc10e6d5cd7 · outbound

This paper cites an unresolved cited work.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:38:29.474538Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 103b1ee5-0c0a-4e06-b6a9-9a6d8fe45f76 · outbound

This paper cites Quantum dynamical bounds for long-range operators with skew-shift potentials.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Quantum dynamical bounds for long-range operators with skew-shift potentials

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-10T17:38:29.168575Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 1a9f801a-ce5a-4479-8ced-2dfd610b7a89 · outbound

This paper cites Shamis and S.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Shamis and S

Reference 30

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8d9ab491-e799-43e6-93ec-71b2d54cf742 · outbound

This paper cites an unresolved cited work.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:38:29.437404Z

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Observation d573b976-9041-4c95-abfe-76cc6a4ae7bd · outbound

This paper cites an unresolved cited work.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:38:29.420111Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ce02efa8-9922-4b72-9b30-b31c3811a908 · outbound

This paper cites an unresolved cited work.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:38:29.402500Z

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Observation 665d3e51-68f9-445c-b553-dbc927e8da34 · outbound

This paper cites Dedicated to David Ruelle and Yasha Sinai on the occasio n of their 65th birthdays.

Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition Dedicated to David Ruelle and Yasha Sinai on the occasio n of their 65th birthdays

Reference 1218

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:38:30.352915Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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