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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=sha256:487741c068b7cca78895bd27af9e79000cbc73e094d8156ca0e6fc2ea0cc7b8a

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:ba3eb7b898105a96fc482f3cfcebf0438668c34b4609f386360c259e767198a1

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=sha256:4fca0dd3ed756f16491c8475c02cfd949c0429693c71112adb8c46ec93db994c

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=sha256:4e99a8911e7dee6bb210292354bc888ac104c2f6ea8c722c0340011d115bb2ff

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:c7b28306bebc1098d91083b849f06bcaacac5adde1062805be9fe0fd423515d3

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:a218c7015628d809d32353d60d9dc896e7129901e0e056f4698da3f93a92ba1b

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:c330b2b0221fb473559834a5a9ac9f2e6e8ebced8922b13e8bbc24d808357422

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:b67f5e098ee77944cef2054ee165284a1624c568d4792f663cf08518511d9629

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=sha256:12e954aa37ad6de4c802652572ef2ee4174237248f1bda1f71e6eab53926575c

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=sha256:6c320dedc5991acf6d9a2643297017edc3959f53e73a400a300b4a0836a603c0

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=sha256:18aab3fceacf8bfe53801dcb2a3cf5f564098f222bc7ca9f1c3ca0ad6aaf5262

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=sha256:51f9a3daa3bf2fbfa81e6ccfc517ca2b6bad76c7b52c74ae5f378c2e9816ff07

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=sha256:823ba0443d99e2b21a220dbe61a7a6b832e2a581579fa92b42e8b10181b79cd9

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=sha256:78f4f33ea2e83cf866e4b8e79d4d7fd600bda665478086b1e0664f287ba84339

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:f4374a830e49876a396a3aa773f5306cff8afde575ce7bff6f11e25392d1f2bc

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=sha256:78bc1332e8ab564e532c2a333d00550e039d5f31a8d37844cf17e2061bb797b5

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=sha256:7b35fa3f9b03655b3bbb1aece49cf7bbdc6302aeb7a4e9bde5b5fe58370b4c34

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=sha256:41969176e4e75175ce3bc5f3ca508f6ceeba825d6c2678c21a09912210298f72

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=sha256:1c32381a0fa5be665bff7567396dc62ed2ccccb309d2b3cf1b7106c0a766ed79

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=sha256:1ee6749f205162760e47f92c81723a118a6375c8df68b25bcb5149dc8d82c514

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=sha256:539865274c7532ede4a63f9e5cec229f35ddac1d8c54c9d60fcd611bc5447fd7

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:ba1a81067597ae330fd9aa57767dfd320f3a7d364ceb1f1cccf1296fb3a5fa31