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Paper Citation Record · LEDGER

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory

As of 16 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 0 inbound Pith citation observations for arXiv:2507.13418.

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

pith.paper-citation-record.v1
2507.13418 v1

Coverage vector

measured 55 of 55 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:37:14.304295Z

measured 55 of 55 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 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

55 of 55 outbound references displayed

  • verified exact3
  • verified fuzzy30
  • unresolved20
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 879a3b77-6ab1-417e-8b85-3545cc7063b5 · outbound

This paper cites , Science 156, 636–638 (1967). B. B. Mandelbrot ``The Fractal Geometry of Nature.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory , Science 156, 636–638 (1967). B. B. Mandelbrot ``The Fractal Geometry of Nature

Reference 1

Resolution
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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=arxiv_source observed=2026-08-06T16:37:09.735356Z digest=sha256:46f07e29b39fe794335e3da7dcf701dae4423199314df877907d890cd594f618

Observation c264c222-4108-4f97-89be-f2ab7c30701b · outbound

This paper cites Hofstadter, Phys.Rev.B , 14 , (1976) 2239-49.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Hofstadter, Phys.Rev.B , 14 , (1976) 2239-49

Reference 2

Resolution
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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=arxiv_source observed=2026-08-06T16:37:09.804817Z digest=sha256:958f89a2295e708ef0d75ca2293751eafbdffef3bac19362ce767be3a0666a2a

Observation fb57f347-189a-4d8b-9c8d-7eb834b8d021 · outbound

This paper cites , G.H.Wannier, phys. stat. sol. (b) 88, 767 (1978).

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory , G.H.Wannier, phys. stat. sol. (b) 88, 767 (1978)

Reference 3

Resolution
verified fuzzy
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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.

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Observation 43e21d74-785d-4003-8421-13e7d41186a7 · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-06T16:37:24.466419Z

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.

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Observation 556af900-6888-4c60-9504-26738519aeec · outbound

This paper cites Streda, J.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Streda, J

Reference 5

Resolution
verified fuzzy
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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.

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Observation bb3d583c-56ca-4be9-abae-1e5e53d3fd54 · outbound

This paper cites Thouless , M.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Thouless , M

Reference 6

Resolution
verified fuzzy
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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.

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Observation 3816a86f-a128-4c54-ab5d-6e3361340dd8 · outbound

This paper cites Developments in the quantum Hall effect.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Developments in the quantum Hall effect

Reference 7

Resolution
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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.

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Observation 9d480b34-469f-472f-88f7-024253595ed9 · outbound

This paper cites Today January 33–8; I.I.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Today January 33–8; I.I

Reference 8

Resolution
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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.

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Observation 1cc5ad01-bc73-48cf-b76e-444295af0632 · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 9

Resolution
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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.

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Observation 73d2f233-f06a-4970-86d1-a300895b7e0e · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 10

Resolution
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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.

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Observation 5f7cc51e-968a-48d7-a350-617eccd59650 · outbound

This paper cites Satija and M.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Satija and M

Reference 11

Resolution
verified fuzzy
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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.

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Observation ff24bd83-1c58-4f8b-bca0-e4a8bb9ce362 · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 12

Resolution
unresolved
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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=arxiv_source observed=2026-08-06T16:37:10.378120Z digest=sha256:5f7664f23701ba23512d2f1aa153e1e1415d6e48e102349d81b5d0406971ae9f

Observation 2aa02187-015c-4fff-9999-52b760b02774 · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 13

Resolution
unresolved
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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=arxiv_source observed=2026-08-06T16:37:10.445003Z digest=sha256:634427cdb4b59c9fc7b6307186148ebadfdba1531c2fbbd6db12ca3f39aebf9e

Observation 0799fcfd-7ca8-46e4-8562-81cd75c663d9 · outbound

This paper cites Phys, JETP 19 634, 1964.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Phys, JETP 19 634, 1964

Reference 14

Resolution
verified fuzzy
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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.

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Observation e7851231-78a6-4e77-a9f7-752a57115aec · outbound

This paper cites Langbein D, `` The tight-binding and the nearly-free-electron approach to lattice electrons in external magnetic fields Phys.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Langbein D, `` The tight-binding and the nearly-free-electron approach to lattice electrons in external magnetic fields Phys

Reference 15

Resolution
verified fuzzy
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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.

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Observation 2d464627-f435-4e3e-93c7-2c0a5760dc5b · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 16

Resolution
unresolved
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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.

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Observation 6c5ce342-7f56-4b03-897c-9fd949a0b62c · outbound

This paper cites , Armelle Barelli, Jean Bellissard and Robert Fleckinger, ( unpublished ); ``Bloch electrons in a magnetic field.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory , Armelle Barelli, Jean Bellissard and Robert Fleckinger, ( unpublished ); ``Bloch electrons in a magnetic field

Reference 17

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

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Observation d58995bb-5897-4fa7-960c-4e15349ded3b · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 18

Resolution
unresolved
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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.

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Observation 9870636b-d494-4cbb-8c49-d7635b61367a · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 19

Resolution
unresolved
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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.

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Observation 317ec743-c9d4-4eb1-9189-bef612f6255a · outbound

This paper cites Harper, Proc.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Harper, Proc

Reference 20

Resolution
verified fuzzy
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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.

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Observation 0945cd8d-ccc0-4375-8bdf-fe98c45c4657 · outbound

This paper cites & André, G.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory & André, G

Reference 21

Resolution
verified fuzzy
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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.

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Observation 40aeaee8-b382-4733-937d-1564e1072669 · outbound

This paper cites , J. Ketoja and I. Satija, 75 , (1995).

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory , J. Ketoja and I. Satija, 75 , (1995)

Reference 22

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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=arxiv_source observed=2026-08-06T16:37:10.930348Z digest=sha256:698893a795b6c4c7cfded510a889eae5178d4f1a0fb6f5f864985b41ca018d1e

Observation c0f51cc6-f986-463f-9e5b-6511cf3f6899 · outbound

This paper cites RAY,Thesis, University of Oregon, 1978.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory RAY,Thesis, University of Oregon, 1978

Reference 23

Resolution
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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.

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Observation 3449f5ce-f6ad-4f7b-8fa5-e2806b3af340 · outbound

This paper cites Danna, Y Avron and J.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Danna, Y Avron and J

Reference 24

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

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Observation 11cfa9ac-1a91-492f-abf6-9ee84756db3f · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 25

Resolution
unresolved
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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.

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Observation bac9c140-2499-4501-b7ae-33cfc5a60478 · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 26

Resolution
unresolved
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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.

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Observation b83c9d66-5df4-48da-8131-9380bde2464a · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-06T16:37:20.548509Z

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.

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Observation 4610e5c6-917a-4322-8e27-1fbdbdbf830b · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-06T16:37:20.277752Z

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.

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Observation bf2d93b8-513c-4766-bbe2-90d39562cb75 · outbound

This paper cites Wilkinson, J.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Wilkinson, J

Reference 29

Resolution
verified fuzzy
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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.

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Observation e41094d5-a8f0-4b33-b1ba-f44eea3fa7f9 · outbound

This paper cites Satija, J.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Satija, J

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T16:37:19.805566Z

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.

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Observation 724898fa-005d-4152-8e25-6d60456337c4 · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-06T16:37:19.507338Z

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=arxiv_source observed=2026-08-06T16:37:11.679945Z digest=sha256:fb6aea1a18294bf6d42726e88c7fd61b3448243cec16a8cf2b47f444516a9c5f

Observation 03e7f099-fa1e-446b-9c57-a6851b10062f · outbound

This paper cites Wilkinson, Proc.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Wilkinson, Proc

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T16:37:19.344897Z

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=arxiv_source observed=2026-08-06T16:37:11.682506Z digest=sha256:0a6b99908489bbfb6f24b07c4d1be4ba040c873ffc6e19d7d37f2dc8ebef0400

Observation 8c93ca43-ed06-4d89-9c23-1f7b25c89463 · outbound

This paper cites Wilkinson J.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Wilkinson J

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T16:37:19.089154Z

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=arxiv_source observed=2026-08-06T16:37:11.686335Z digest=sha256:8871605964922a906017b8bff60078d068884a20316f8831c6be1fc9e3f45209

Observation 5e0f184e-bc05-41f8-9283-4db5280019dd · outbound

This paper cites Simon, Adv.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Simon, Adv

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T16:37:18.856182Z

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.

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Observation 7adf3898-03b9-4aa4-b229-62eeca7412f1 · outbound

This paper cites A theorem on circle configurations.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory A theorem on circle configurations

Reference 35

Resolution
verified exact
local_arxiv, observed 2026-08-06T16:37:15.349641Z

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=arxiv_source observed=2026-08-06T16:37:11.819702Z digest=sha256:0087b7234fe4be2ed8e692e2eaea81631c6c8a4b8f1b69ab3d54903810244af6

Observation 4f0e5637-0181-4edd-ba30-8e5a68f7a108 · outbound

This paper cites Pythagorean Triplets, Integral Apollonians and The Hofstadter Butterfly.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Pythagorean Triplets, Integral Apollonians and The Hofstadter Butterfly

Reference 36

Resolution
verified exact
local_arxiv, observed 2026-08-06T16:37:15.166007Z

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=arxiv_source observed=2026-08-06T16:37:11.894728Z digest=sha256:28b74068d7209f53367213fa3c73466b4cd65be8f2e5eec9c5636f854f92ff02

Observation 9429ba11-1107-4b39-8f86-66ebf1559a8d · outbound

This paper cites Berggren, ”Pytagoreiska triangular” (in Swedish), Elementa: Tidskrift fr elementŁr matematik, fysik och kemi 17 (1934), 129139.; ``Geneology of Pythagorean Triads" A.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Berggren, ”Pytagoreiska triangular” (in Swedish), Elementa: Tidskrift fr elementŁr matematik, fysik och kemi 17 (1934), 129139.; ``Geneology of Pythagorean Triads" A

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T16:37:18.655891Z

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=arxiv_source observed=2026-08-06T16:37:11.979928Z digest=sha256:223f96d4b4672d9d5fc4836475a3068832652b0b51e3d4540c2a17c66a573056

Observation fd70647e-3916-4554-924f-0b5737d73d1a · outbound

This paper cites Kaleidoscopic Symmetries and Self-Similarity of Integral Apollonian Gaskets.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Kaleidoscopic Symmetries and Self-Similarity of Integral Apollonian Gaskets

Reference 38

Resolution
metadata mismatch
local_arxiv, observed 2026-08-06T16:37:14.947316Z

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=arxiv_source observed=2026-08-06T16:37:12.127558Z digest=sha256:aa633d7324a3edd6a32f309923a9a1e3c98158377963f03df8b0e93f7815e3bc

Observation 316c8946-c939-4a82-b542-335b608751c8 · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-08-06T16:37:18.526181Z

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=arxiv_source observed=2026-08-06T16:37:12.237153Z digest=sha256:0fa276f1448d3d9621e5b9fb7ec8672aac3d3efa6bef6e3df525c032650404ca

Observation 8b694013-6a5f-486e-9aba-5389ba244d8b · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 40

Resolution
unresolved
raw_fallback, observed 2026-08-06T16:37:18.272331Z

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=arxiv_source observed=2026-08-06T16:37:12.664489Z digest=sha256:06ed581b16c5462dca1204abc006f73fbe5f858b4bd0501234b6cb653c14fbfd

Observation 43389499-cd71-44a3-b100-67eb954a425c · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-06T16:37:18.098660Z

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=arxiv_source observed=2026-08-06T16:37:12.870081Z digest=sha256:910d6440ffa1ed143d29b27dac007b5a7a28af8f8c2b2c69e4aa087427c89179

Observation e6e7026d-d2a7-4c05-b646-ceb80a1b4c7f · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 42

Resolution
unresolved
raw_fallback, observed 2026-08-06T16:37:17.938224Z

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=arxiv_source observed=2026-08-06T16:37:13.003431Z digest=sha256:b7b0e8b953a9ab1cfb37fb5020de495e5e8334844b90d1417a4777f4659e45d9

Observation 0a504d0c-cfcf-4f3a-bc4c-8bce42eac4d4 · outbound

This paper cites Nuckolls, Michael G.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Nuckolls, Michael G

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T16:37:17.695634Z

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=arxiv_source observed=2026-08-06T16:37:13.138512Z digest=sha256:28272e0c35e2b3776ee9b3d9bf318b4799475c7154b50ebeed8ed300f77c6402

Observation c13e1f85-d6b4-45b1-8235-1afa201c4f4d · outbound

This paper cites MacDonald, Phys.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory MacDonald, Phys

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T16:37:17.518755Z

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=arxiv_source observed=2026-08-06T16:37:13.219890Z digest=sha256:7736c0225481504815fff7e67b3fa2389bb78e7c4c387de415ccaef21c6913db

Observation a5a912da-32f9-4fa0-8168-72c36728139d · outbound

This paper cites Faddeev and R.M.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Faddeev and R.M

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T16:37:17.358161Z

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=arxiv_source observed=2026-08-06T16:37:13.290335Z digest=sha256:a5a46ec09ae213856ee798051f798952c365a4dfaf5d59b05ac98bef581c17bd

Observation 760d6746-277a-432a-a8f2-ae3ba115413d · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 46

Resolution
unresolved
raw_fallback, observed 2026-08-06T16:37:17.068655Z

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=arxiv_source observed=2026-08-06T16:37:13.401019Z digest=sha256:548ebe7bf19f23a90a39b8ca752460100d008d4d6e2eabbac96c54a2080e0baa

Observation 2e279c70-84a0-4a5f-8a62-c710e6467a5c · outbound

This paper cites ATHREYA, CRISTIAN COBELI, AND ALEXANDRU ZAHARESCU, International Mathematics Research Notices, Volume 2015, Issue 20, 2015, Pages 9991–10011.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory ATHREYA, CRISTIAN COBELI, AND ALEXANDRU ZAHARESCU, International Mathematics Research Notices, Volume 2015, Issue 20, 2015, Pages 9991–10011

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T16:37:16.893969Z

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=arxiv_source observed=2026-08-06T16:37:13.494799Z digest=sha256:bdefd6dc65e30ebf0486c7c97e9970745c0ece73352252c0404cd5a110505121

Observation c8ff0e67-f19f-4d6d-8525-ec663e1c8eda · outbound

This paper cites Spectral theory of extended Harper's model and a question by Erd\H{o}s and Szekeres.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Spectral theory of extended Harper's model and a question by Erd\H{o}s and Szekeres

Reference 48

Resolution
verified exact
local_arxiv, observed 2026-08-06T16:37:14.649612Z

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=arxiv_source observed=2026-08-06T16:37:13.614175Z digest=sha256:8c6875e535ff7c90088c03b47513c640da371d25354ad6be2b88c9f57dd203cb

Observation 3ed654c2-15ce-4801-bef9-4e5e51def449 · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 49

Resolution
unresolved
raw_fallback, observed 2026-08-06T16:37:16.731402Z

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=arxiv_source observed=2026-08-06T16:37:13.753745Z digest=sha256:2fc4083ab0007f0c7bf3013bcc94149ecd82709441db2720456b5e05e762d553

Observation 828a30f2-bb27-4b80-acb2-41ce985a7247 · outbound

This paper cites & Santos, L.H.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory & Santos, L.H

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T16:37:16.457451Z

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=arxiv_source observed=2026-08-06T16:37:13.840142Z digest=sha256:3156ebc7dc9bebebcad0df7542d66ad55a79a592f9ef6e550d4bdbcf0b40bde4

Observation e87ff17a-cd3d-40cf-8165-1be353fb6108 · outbound

This paper cites Satija and Erhai Zhao, Phys Rev B, 94 , 245128 (2016).

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Satija and Erhai Zhao, Phys Rev B, 94 , 245128 (2016)

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T16:37:16.296197Z

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=arxiv_source observed=2026-08-06T16:37:13.909057Z digest=sha256:cab53f114189d08ae06425e2251d1c3fa67f0c615543f3ca9e58bc8789132c7a

Observation 1319cb03-81f3-4f30-81e1-7a519e1f273f · outbound

This paper cites Anatomy of a periodically driven p-wave superconductor.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Anatomy of a periodically driven p-wave superconductor

Reference 52

Resolution
metadata mismatch
local_arxiv, observed 2026-08-06T16:37:14.467467Z

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=arxiv_source observed=2026-08-06T16:37:13.982095Z digest=sha256:c722c9b8e450b46491584f9af2c2eeff1f2a7e03e133ed699b162580d6bf8b3d

Observation cecf6309-72be-4adf-9752-753f537be160 · outbound

This paper cites Galitski, G.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Galitski, G

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T16:37:16.148347Z

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=arxiv_source observed=2026-08-06T16:37:14.048696Z digest=sha256:869455332e40684fa240eba0535c85da5dbe6da5bb5e94d7f956f2fa7b9fa8a6

Observation 5ada19e3-4f74-4089-9f37-9ff3952a05de · outbound

This paper cites Linear-network model for magnetic breakdown in two dimensions.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Linear-network model for magnetic breakdown in two dimensions

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T16:37:15.884765Z

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=arxiv_source observed=2026-08-06T16:37:14.145367Z digest=sha256:dd61eb5e6bdafefd7fc33ddebf7dbe585ec15fa53bb81b1c4152599d7cdbb58b

Observation 63c2ae3e-0da6-4c50-ba3d-812bcfe3f660 · outbound

This paper cites an unresolved cited work.

The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work

Reference 55

Resolution
unresolved
raw_fallback, observed 2026-08-06T16:37:15.649706Z

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=arxiv_source observed=2026-08-06T16:37:14.304295Z digest=sha256:0d9412ace8ac9c63896f47984cfda2567fd2ce6d9117135017a6f73a365a8572

Pith citing papers

No inbound Pith citation observations are available.