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Paper Citation Record · LEDGER

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$

As of 16 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 1 inbound Pith citation observation for arXiv:1908.03805.

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

pith.paper-citation-record.v1
1908.03805 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:11:46.336317Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-14T10:15:30.573465Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-14T10:15:30.611348Z

Reference resolution

21 of 21 outbound references displayed

  • verified exact2
  • verified fuzzy11
  • unresolved8
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0f4993ea-a0bd-45f0-bf5b-931798a9d196 · outbound

This paper cites an unresolved cited work.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:11:46.572245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.259067Z digest=sha256:b2b7f71a82f44a90476e3613d340952179b814e4f6baf46e39b059fc0d99f474

Observation e9b213a5-b339-4af9-bfb8-9c478ef85213 · outbound

This paper cites Avila, J.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Avila, J

Reference 2

Resolution
unresolved
no resolver link, observed 2026-08-14T14:11:46.263332Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T14:11:46.263332Z digest=sha256:008a6ed2ddecc8ea98909673d59c41a97c474bf5d7b3b44cc003902f2539bfdd

Observation 8ee13d7c-c2cc-4794-85b2-0c36f01c920f · outbound

This paper cites Bourgain.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Bourgain

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:46.555375Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.266823Z digest=sha256:f9eb9667f3ad395a2e3a7c1f51b67244f8c84cc73f6129b56db4598c28332f8c

Observation c1e35d86-28c3-4d6f-b6aa-411f24e6394e · outbound

This paper cites Bourgain.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Bourgain

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:46.546057Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.271488Z digest=sha256:db9f2fee6a6c25aae697563c61a3ca103c2bc53dd7ee2d7afbdd8cd72bb84477

Observation 67f87edb-098f-4de1-a31e-907fea54dd36 · outbound

This paper cites Bourgain.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Bourgain

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:46.536102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.275410Z digest=sha256:1133e3e2c6b15d0688fbb145b243c563e6d9c5e71da452b880aa6d444f2aeddc

Observation 6ec2ae90-c902-49ca-94f2-38b7c48141f6 · outbound

This paper cites Bourgain and M.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Bourgain and M

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:46.526676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.280575Z digest=sha256:8420d47e8ae90298f67988efbaa47d81b2bd28a9b91de33f3c24d64b43f904d0

Observation 184a3c60-ac99-4c10-8a4f-edf6b022c950 · outbound

This paper cites Bourgain, M.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Bourgain, M

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:46.517261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.284547Z digest=sha256:10f14613a09e50e1533ee1f60e6016969d5b56bc39edee5f66491ef286d034b5

Observation 37aca39d-b393-48fd-927d-3d9613b2fba6 · outbound

This paper cites Bourgain and S.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Bourgain and S

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:46.507202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.288026Z digest=sha256:240a67400789077ef68b9b45bb460852e368a7150e685e76842db7186108af99

Observation 97d66740-aa22-4c31-898a-236b20caedde · outbound

This paper cites Bourgain, S.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Bourgain, S

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:46.496969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.292144Z digest=sha256:bf99537a92fa1f4cd134ea3560d28655549ccba78cf81522c11d769c0f73f9fa

Observation 89ee564f-8654-419f-982f-954b5fcc9625 · outbound

This paper cites Bourgain and I.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Bourgain and I

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:46.486295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.296590Z digest=sha256:7475fe9fc5e217bea664c4041caa977e236ddddb85f719f216ad6bcea9906ee1

Observation 443ea366-6079-4010-b4fe-57d8ea94a95f · outbound

This paper cites an unresolved cited work.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:11:46.475741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.299980Z digest=sha256:471772f5bfe482f49a9033a1492679b8e2c0e221148c14951cf25e2af0971846

Observation 50388f69-9a92-4c55-882b-1c7d29d6b262 · outbound

This paper cites Fr¨ ohlich and T.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Fr¨ ohlich and T

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:46.466742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.303361Z digest=sha256:ff616fbe7ea1bec5dece4a901a57a996246a940bbef277c935bd76c912efa10b

Observation 19a83ef8-3690-4d75-8aec-266584ba977b · outbound

This paper cites Goldstein and W.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Goldstein and W

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:46.456606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.307040Z digest=sha256:7ef23210d2db231ba6b4b820f91f05bda28e0e707715cc9b33c4947828994319

Observation 45171caf-d3f2-4aa7-9e4b-cf1b2c4d665e · outbound

This paper cites Jitomirskaya and W.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Jitomirskaya and W

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:46.446946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.311000Z digest=sha256:88370f6bdd3d4de8d30f2106da0d4e7f97d975eace7d5f7a150660695ea81950

Observation 9080ccab-9137-492e-8ca4-670f0c220d7f · outbound

This paper cites Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase

Reference 15

Resolution
verified exact
local_arxiv, observed 2026-08-14T14:11:46.385305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.314250Z digest=sha256:39052569c16a4669d87b59a0aa8e7ad36c84a7ec69fe4e93f54c31e9673a9607

Observation 869bde11-200f-4c62-9d2d-ba0e3fe24069 · outbound

This paper cites Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schr\"odinger operators.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schr\"odinger operators

Reference 16

Resolution
verified exact
local_arxiv, observed 2026-08-14T14:11:46.370138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.318045Z digest=sha256:5159ad84f4e4bbe60d7a0d9783d301401c0ce409d95acc87c48bb7534962b0d4

Observation 084a1a1e-d43c-4122-99a8-d2b67ad203f9 · outbound

This paper cites an unresolved cited work.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:11:46.436391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.322103Z digest=sha256:6ba30ecbb74abf784f00f016b76e39e41fc473b8124ec916d79f58d8e97e79dd

Observation f6de16fc-bc75-4f57-8007-a4860c73f3ab · outbound

This paper cites an unresolved cited work.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:11:46.425969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.325529Z digest=sha256:1749dde932d1165f91cec6e77918ad498f10c850b1c1f960b5d321e54b0d6f28

Observation ade8ef19-0438-4e16-adbb-f48da6d02b34 · outbound

This paper cites an unresolved cited work.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:11:46.415556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.328778Z digest=sha256:f14c05b25480cd6a6f9767c784bfd3fbefb04f4bd6fcf243389687766d95abf3

Observation 785fa0a2-2b18-46d1-9784-9c58fb5eabef · outbound

This paper cites an unresolved cited work.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:11:46.405813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.332137Z digest=sha256:7c9e5e61595797d62ba23453cdfaa70b044fbe4d6409670a4dbe038bd3e7f9e5

Observation 17eca0da-75ab-4630-aeb1-740d0e88734b · outbound

This paper cites an unresolved cited work.

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$ Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:11:46.395932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:46.336317Z digest=sha256:5fa235633fa7313b598d27688033d43ec3c68645fb633144905dd8d2df3d6779

Pith citing papers

Observation ffc860d7-af2b-4938-949f-2d330125d902 · inbound

Infinite energy quasi-periodic solutions to nonlinear Schr\"odinger equations on $\mathbb R$ cites this paper.

Infinite energy quasi-periodic solutions to nonlinear Schr\"odinger equations on $\mathbb R$ Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$

Reference 1997

Resolution
verified exact
local_arxiv, observed 2026-08-14T10:15:30.618855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T10:15:30.573465Z digest=sha256:b03a93c67942134359593510724b5016dce01c96c53b3870d341e4cc8ec10395