Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T16:37:14.304295Z
Paper Citation Record · LEDGER
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.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T16:37:14.304295Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
55 of 55 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 879a3b77-6ab1-417e-8b85-3545cc7063b5 · outbound
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
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.
Observation c264c222-4108-4f97-89be-f2ab7c30701b · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Hofstadter, Phys.Rev.B , 14 , (1976) 2239-49
Reference 2
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.
Observation fb57f347-189a-4d8b-9c8d-7eb834b8d021 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory , G.H.Wannier, phys. stat. sol. (b) 88, 767 (1978)
Reference 3
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.
Observation 43e21d74-785d-4003-8421-13e7d41186a7 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 4
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.
Observation 556af900-6888-4c60-9504-26738519aeec · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Streda, J
Reference 5
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.
Observation bb3d583c-56ca-4be9-abae-1e5e53d3fd54 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Thouless , M
Reference 6
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.
Observation 3816a86f-a128-4c54-ab5d-6e3361340dd8 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Developments in the quantum Hall effect
Reference 7
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.
Observation 9d480b34-469f-472f-88f7-024253595ed9 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Today January 33–8; I.I
Reference 8
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.
Observation 1cc5ad01-bc73-48cf-b76e-444295af0632 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 9
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.
Observation 73d2f233-f06a-4970-86d1-a300895b7e0e · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 10
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.
Observation 5f7cc51e-968a-48d7-a350-617eccd59650 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Satija and M
Reference 11
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.
Observation ff24bd83-1c58-4f8b-bca0-e4a8bb9ce362 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 12
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.
Observation 2aa02187-015c-4fff-9999-52b760b02774 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 13
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.
Observation 0799fcfd-7ca8-46e4-8562-81cd75c663d9 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Phys, JETP 19 634, 1964
Reference 14
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.
Observation e7851231-78a6-4e77-a9f7-752a57115aec · outbound
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
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.
Observation 2d464627-f435-4e3e-93c7-2c0a5760dc5b · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 16
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.
Observation 6c5ce342-7f56-4b03-897c-9fd949a0b62c · outbound
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
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.
Observation d58995bb-5897-4fa7-960c-4e15349ded3b · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 18
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.
Observation 9870636b-d494-4cbb-8c49-d7635b61367a · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 19
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.
Observation 317ec743-c9d4-4eb1-9189-bef612f6255a · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Harper, Proc
Reference 20
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.
Observation 0945cd8d-ccc0-4375-8bdf-fe98c45c4657 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory & André, G
Reference 21
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.
Observation 40aeaee8-b382-4733-937d-1564e1072669 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory , J. Ketoja and I. Satija, 75 , (1995)
Reference 22
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.
Observation c0f51cc6-f986-463f-9e5b-6511cf3f6899 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory RAY,Thesis, University of Oregon, 1978
Reference 23
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.
Observation 3449f5ce-f6ad-4f7b-8fa5-e2806b3af340 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Danna, Y Avron and J
Reference 24
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.
Observation 11cfa9ac-1a91-492f-abf6-9ee84756db3f · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 25
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.
Observation bac9c140-2499-4501-b7ae-33cfc5a60478 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 26
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.
Observation b83c9d66-5df4-48da-8131-9380bde2464a · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 27
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.
Observation 4610e5c6-917a-4322-8e27-1fbdbdbf830b · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 28
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.
Observation bf2d93b8-513c-4766-bbe2-90d39562cb75 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Wilkinson, J
Reference 29
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.
Observation e41094d5-a8f0-4b33-b1ba-f44eea3fa7f9 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Satija, J
Reference 30
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.
Observation 724898fa-005d-4152-8e25-6d60456337c4 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 31
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.
Observation 03e7f099-fa1e-446b-9c57-a6851b10062f · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Wilkinson, Proc
Reference 32
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.
Observation 8c93ca43-ed06-4d89-9c23-1f7b25c89463 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Wilkinson J
Reference 33
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.
Observation 5e0f184e-bc05-41f8-9283-4db5280019dd · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Simon, Adv
Reference 34
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.
Observation 7adf3898-03b9-4aa4-b229-62eeca7412f1 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory A theorem on circle configurations
Reference 35
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.
Observation 4f0e5637-0181-4edd-ba30-8e5a68f7a108 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Pythagorean Triplets, Integral Apollonians and The Hofstadter Butterfly
Reference 36
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.
Observation 9429ba11-1107-4b39-8f86-66ebf1559a8d · outbound
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
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.
Observation fd70647e-3916-4554-924f-0b5737d73d1a · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Kaleidoscopic Symmetries and Self-Similarity of Integral Apollonian Gaskets
Reference 38
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.
Observation 316c8946-c939-4a82-b542-335b608751c8 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 39
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.
Observation 8b694013-6a5f-486e-9aba-5389ba244d8b · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 40
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.
Observation 43389499-cd71-44a3-b100-67eb954a425c · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 41
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.
Observation e6e7026d-d2a7-4c05-b646-ceb80a1b4c7f · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 42
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.
Observation 0a504d0c-cfcf-4f3a-bc4c-8bce42eac4d4 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Nuckolls, Michael G
Reference 43
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.
Observation c13e1f85-d6b4-45b1-8235-1afa201c4f4d · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory MacDonald, Phys
Reference 44
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.
Observation a5a912da-32f9-4fa0-8168-72c36728139d · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Faddeev and R.M
Reference 45
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.
Observation 760d6746-277a-432a-a8f2-ae3ba115413d · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 46
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.
Observation 2e279c70-84a0-4a5f-8a62-c710e6467a5c · outbound
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
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.
Observation c8ff0e67-f19f-4d6d-8525-ec663e1c8eda · outbound
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
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.
Observation 3ed654c2-15ce-4801-bef9-4e5e51def449 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 49
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.
Observation 828a30f2-bb27-4b80-acb2-41ce985a7247 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory & Santos, L.H
Reference 50
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.
Observation e87ff17a-cd3d-40cf-8165-1be353fb6108 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Satija and Erhai Zhao, Phys Rev B, 94 , 245128 (2016)
Reference 51
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.
Observation 1319cb03-81f3-4f30-81e1-7a519e1f273f · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Anatomy of a periodically driven p-wave superconductor
Reference 52
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.
Observation cecf6309-72be-4adf-9752-753f537be160 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Galitski, G
Reference 53
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.
Observation 5ada19e3-4f74-4089-9f37-9ff3952a05de · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Linear-network model for magnetic breakdown in two dimensions
Reference 54
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.
Observation 63c2ae3e-0da6-4c50-ba3d-812bcfe3f660 · outbound
The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory Unresolved cited work
Reference 55
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.
No inbound Pith citation observations are available.