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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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:09.735356Z digest=sha256:d91b92cef9ad9074f6ea67db0fff940585527cf5a0170f5d6793a2a759e19c7f

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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raw_fallback, observed 2026-08-06T16:37:25.029995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:09.804817Z digest=sha256:c744e101d955d4d32642f7f8ca5611bb2b18c775cb9feb2e6cb804f47b63c7e3

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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:09.985066Z digest=sha256:69b8c04eb92e0d9a4d8dfb083f86fb2217f56d0d462667e2c400a54732553ea2

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 2026-08-15T06:32:42.880941+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
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+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
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:10.133912Z digest=sha256:6a7e2f193a0932a8eb4130992a15248a9b12a3b4a09dd1a7f9e45a78603213aa

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
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+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
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:10.378120Z digest=sha256:37cbf2248a0cb78d0d55eb257cc11ed7a6b5bd54d57f3bc3fc807e27278e05c3

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:10.445003Z digest=sha256:3e2338e860c7d4f6f8a33f2c6410904f8d18c2d252fc4efd1f188b898f323ca2

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:10.493471Z digest=sha256:06ca064845741bd54af5bfb3383242c4469a5f551017fccdca483e2c18c5306c

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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:10.881257Z digest=sha256:27ff776eb12bd80325c34cd7245d6fe2e418b342ceaea20de35cb05f4e11aecd

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

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:10.930348Z digest=sha256:2288463ad78aa2cadb7a1cbeec3f9167b7f6b7f8da5d7f4a70ca3d8ef6516081

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 2026-08-15T06:32:42.880941+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

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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
raw_fallback, observed 2026-08-06T16:37:20.715070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:11.408064Z digest=sha256:4d6c753badd4eaf0a091f6b5fd1bf88dc6d13de678227a17d743d8836011e41f

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
raw_fallback, observed 2026-08-06T16:37:20.055127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:11.500212Z digest=sha256:f423311c803470cc770df5d8c17fbae2b0e96a3916bab03d17b0054153724731

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:11.614616Z digest=sha256:b4ed78f60e1d712bbbd8a06af1cbe183f4cdf1b63f20f4eb65289152dd1bc864

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:11.679945Z digest=sha256:88746e5cfbe89458806ab67b664a8199aa48868c65fb2573eea6f171ce42ed21

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:11.682506Z digest=sha256:61d43522c07c42f3b0922cc71e6e048ff67c897d514c85d609cca0a61c81caf4

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:11.686335Z digest=sha256:075654636169f0df23e96ff3ae70c20b3305fdaeb6988c71083064ae7365fbf1

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:11.739215Z digest=sha256:4e04927824a048181cae3a50302f8f1fe639743707fc3cd60854f911f60727f8

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:11.819702Z digest=sha256:3f61689c2ed0e800dec1ed76b6200fb26c7cdfe044e0ed327c7d44cc0220dd3f

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:11.894728Z digest=sha256:1bad3f3026b13c069de9e26885f3f7b3e08163e91a2eba3d7272dc45d1cb12b4

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:11.979928Z digest=sha256:ba8f0543294002a16b3de529b115f9dcbd8e697b7943c508753c71d23bc848a4

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:12.127558Z digest=sha256:44373fc78905172446937eb76441e490cee6a944808a86d70ca79a9751e637d2

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:12.237153Z digest=sha256:a9952697608dc9722085ad2148a5f879b7a42143d069a75142e9e529986828bf

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:12.664489Z digest=sha256:078acabcaf80d4a3c3ed684d3e8eb0646cf00b386aede523e9363aad3ddc0896

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:12.870081Z digest=sha256:b8ce572715ba5830ee1a7274261b33b1911ad62e6b3103d3fe4a24a3c14b26ce

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:13.003431Z digest=sha256:25b6c25229af184b03dc36ebb9bd141bfdb1d1b4e1d664e815ef309762825daf

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:13.138512Z digest=sha256:a7d50cb4f2afb8ef0196bb7ace21b8392aab327a6ae0a28dbaa501bc9645d2f6

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:13.219890Z digest=sha256:871f996a42d3bb6d834e4f4a70e81a32a795aa2599e4b194fdf5e25b6c4b0360

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:13.290335Z digest=sha256:111c3925cc268e42027c1efc5f0ca5a8ff352c20f440e7b0cec6504f5d4f6aa3

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:13.401019Z digest=sha256:6c93d5fc6e48a7767e6828c6e6e5d8baab266c5a307d55acda19af7eef4ab940

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:13.494799Z digest=sha256:6bd0e95425d5e080cd45166de0239f12977585c0430a3e8d5cd2fdfd5971fa7b

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:13.614175Z digest=sha256:7ad1d8611625f6cf9e26d322b4f7c1848817beff30735dff681beca29005b943

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:13.753745Z digest=sha256:78859d120ee7972702191714a6e2e9cdea33539c3e7c6eda6a2e5db4b468fb35

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:13.840142Z digest=sha256:fed53f7964f578660a758581a1812b4a455cbe1533d2f90401bedbcffd66dd9b

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:13.909057Z digest=sha256:bbca68e08174e89cc9bd4b4d5bcf78731d36a2df4d08eca848871abf99951101

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:13.982095Z digest=sha256:c2458398130f2707695552a6b637292f4233e3e75ad62487ae5441dd15d45843

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:14.048696Z digest=sha256:480c270294b1fdcf599a10c6f83639578272673a387205c27050436462d79b42

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:14.145367Z digest=sha256:49475c2eda8e766469ec313b85c0bc750aed87f64d9feeff85e806617c406542

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-06T16:37:14.304295Z digest=sha256:57185361377190460da7c2551c08a6631285b4baf0574d1ea16e72b86580bd9c

Pith citing papers

No inbound Pith citation observations are available.