Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T23:18:14.391632Z
Paper Citation Record · LEDGER
As of 16 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 0 inbound Pith citation observations for arXiv:2412.21128.
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 2026-08-10T23:18:14.391632Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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
57 of 57 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 78181186-c9a1-4935-9efd-ec3c5127c68a · outbound
Lattice random walks and quantum A-period conjecture Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields,
Reference 1
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.
Observation 8fc1ac03-1919-4595-8c3c-000284c8bd03 · outbound
Lattice random walks and quantum A-period conjecture A tale of two fractals: The Hofstadter butterfly and the integral Apol- lonian gaskets,
Reference 2
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.
Observation b057130c-c39d-4f3b-bac8-92266c08196a · outbound
Lattice random walks and quantum A-period conjecture Nests and chains of Hofstadter butterflies,
Reference 3
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.
Observation 650e1066-50a5-4dca-b65e-d1f2826ac26f · outbound
Lattice random walks and quantum A-period conjecture New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance,
Reference 4
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.
Observation 1d760205-3c94-4188-bf6e-384adc5a2470 · outbound
Lattice random walks and quantum A-period conjecture Quantized Hall Conductance in a Two-Dimensional Periodic Potential,
Reference 5
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.
Observation a3e0fe77-8d37-4fe5-bc4c-0e5003f3cb35 · outbound
Lattice random walks and quantum A-period conjecture Topological invariant and the quantization of the Hall conductance,
Reference 6
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.
Observation c391130c-c741-421e-a5ad-458246b8efa9 · outbound
Lattice random walks and quantum A-period conjecture Spectroscopic signatures of localiza- tion with interacting photons in superconducting qubits,
Reference 7
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.
Observation 5677f526-dc2f-4490-a649-ad8ba35874e6 · outbound
Lattice random walks and quantum A-period conjecture Magnetic subband structure of electrons in hexag- onal lattices,
Reference 8
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.
Observation 37797a4b-edeb-4cfe-9891-0e88830d8c2e · outbound
Lattice random walks and quantum A-period conjecture Energy spectrum and the quantum Hall effect on the square lattice with next-nearest-neighbor hopping,
Reference 9
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.
Observation 05b55d7a-02da-4f28-ba7a-d242895bf096 · outbound
Lattice random walks and quantum A-period conjecture Analysis of the spectrum of a particle on a triangular lattice with two magnetic fluxes by algebraic and numerical methods,
Reference 10
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.
Observation ecc152be-2947-4ce4-9c28-df6d461622b5 · outbound
Lattice random walks and quantum A-period conjecture A study of the ambiguity in the solutions to the Diophantine equation for Chern numbers,
Reference 11
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.
Observation 6f5d6b34-0df5-44e9-8e7c-994787f6b55c · outbound
Lattice random walks and quantum A-period conjecture Landau level spectrum of Bloch electrons in a honeycomb lattice,
Reference 12
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.
Observation b8938e47-93bf-4219-9c86-220d1098a9ff · outbound
Lattice random walks and quantum A-period conjecture Models of the Hofstadter-type,
Reference 13
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.
Observation 9bc179af-4a6e-4aac-923a-45cc1feb3760 · outbound
Lattice random walks and quantum A-period conjecture The colored Hofstadter butterfly for the honeycomb lattice,
Reference 14
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.
Observation db2899cd-6253-411b-a7b3-a10be596ea57 · outbound
Lattice random walks and quantum A-period conjecture Landau levels in the case of two degenerate coupled bands: Kagom´ e lattice tight-binding spectrum,
Reference 15
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.
Observation a5b65b1b-4659-45bb-90ac-74fe1922a8c2 · outbound
Lattice random walks and quantum A-period conjecture Light-induced Hofstadter’s butterfly spectrum of ultracold atoms on the two-dimensional kagom´ e lattice,
Reference 16
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.
Observation 9dcc4292-0e12-4ea2-aa3f-2ccd30c6ba4f · outbound
Lattice random walks and quantum A-period conjecture Quantized Hall effect in three dimensions,
Reference 17
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.
Observation cd051080-d0cf-4453-aa3e-eb00e58d9464 · outbound
Lattice random walks and quantum A-period conjecture Generalized flux states on 3-dimensional lattice,
Reference 18
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.
Observation 1f2b8c2e-899c-48bb-98f4-8937bdaa3020 · outbound
Lattice random walks and quantum A-period conjecture Hofstadter butterfly and integer quantum Hall effect in three dimensions,
Reference 19
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.
Observation 4a147018-c65f-4ad6-9b59-d45b01ebcccc · outbound
Lattice random walks and quantum A-period conjecture Integer quantum Hall effect in isotropic three-dimensional crystals,
Reference 20
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.
Observation 1821366b-8746-47d3-bcf3-03cb8518c3af · outbound
Lattice random walks and quantum A-period conjecture Hofstadter-type spectral diagrams for the Bloch electron in three dimensions,
Reference 21
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.
Observation 98ce8fdd-57a1-4240-9043-cdbd87653572 · outbound
Lattice random walks and quantum A-period conjecture Linking topological features of the Hofstadter model to optical diffraction figures,
Reference 22
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.
Observation a00a3cf5-42ae-45d0-891b-e7a1ee5f738f · outbound
Lattice random walks and quantum A-period conjecture Universality of Hofstadter Butterflies on Hyperbolic Lattices,
Reference 23
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.
Observation c8bb2053-4d35-43f5-b015-2bb7bf40f9a6 · outbound
Lattice random walks and quantum A-period conjecture Signed area enumeration for lattice paths,
Reference 24
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.
Observation 70c9e927-0421-4891-8b2a-8da605f098d0 · outbound
Lattice random walks and quantum A-period conjecture Exact random walk distri- butions using noncommutative geometry,
Reference 25
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.
Observation 2c653cd1-d182-44c7-99e5-a644e4a84d75 · outbound
Lattice random walks and quantum A-period conjecture The algebraic area of closed lattice random walks,
Reference 26
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.
Observation eef7bd44-b5a0-4396-9aef-3fcc65f309a2 · outbound
Lattice random walks and quantum A-period conjecture Exclusion statistics and lattice random walks,
Reference 27
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.
Observation e0e93e12-4a64-413b-869c-83a46adfe4fd · outbound
Lattice random walks and quantum A-period conjecture Algebraic area of Lattice Random Walks and Exclusion Statistics,
Reference 28
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.
Observation c724e8cf-5121-4a4f-b265-444e76d086e4 · outbound
Lattice random walks and quantum A-period conjecture Lattice walk area combinatorics, some remark- able trigonometric sums and Ap´ ery-like numbers,
Reference 29
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.
Observation 1c098478-4b55-4f5b-b22d-06205fe92e5d · outbound
Lattice random walks and quantum A-period conjecture Algebraic area enumeration of random walks on the honeycomb lattice,
Reference 30
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.
Observation 1189e4bf-d86e-4966-b60e-ed7faa79a8c9 · outbound
Lattice random walks and quantum A-period conjecture ‘Fractional statistics’ in arbitrary dimensions: A generalization of the Pauli principle,
Reference 31
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.
Observation 4f813b71-f0c6-4ece-a056-33dabe4275a7 · outbound
Lattice random walks and quantum A-period conjecture Statistical Distribution for Generalized Ideal Gas of Fractional-Statistics Particles,
Reference 32
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.
Observation a150ed56-6b45-482d-aa2b-e78d2bba987a · outbound
Lattice random walks and quantum A-period conjecture Hofstadter’s butterfly in quantum ge- ometry,
Reference 33
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.
Observation df07d340-9895-411e-9200-778001ed1ef1 · outbound
Lattice random walks and quantum A-period conjecture Calabi–Yau geometry and electrons on 2d lattices,
Reference 34
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.
Observation 5357686e-dc1b-4d6e-88b7-1173f6eb9afe · outbound
Lattice random walks and quantum A-period conjecture Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves,
Reference 35
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.
Observation e247a849-e514-430b-bf6e-634619b31874 · outbound
Lattice random walks and quantum A-period conjecture Recent developments in topological string theory,
Reference 36
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.
Observation d5705b22-2fd0-40e3-89d8-2e9ad19d9459 · outbound
Lattice random walks and quantum A-period conjecture Bloch electrons on honeycomb lattice and toric Calabi- Yau geometry,
Reference 37
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.
Observation 20cb0154-7e0d-4321-b878-c6e5a06790ce · outbound
Lattice random walks and quantum A-period conjecture Chern-Simons theory and topological strings,
Reference 38
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.
Observation a8439eea-2bca-4a44-b3fa-ec539a320060 · outbound
Lattice random walks and quantum A-period conjecture Spectral theory and mirror symmetry,
Reference 39
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.
Observation 1537c986-00d1-420e-ba3a-38083fd4b499 · outbound
Lattice random walks and quantum A-period conjecture Lectures on Mirror Symmetry and Topological String Theory
Reference 40
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1bd8a295-397b-406c-a465-9224924b815d · outbound
Lattice random walks and quantum A-period conjecture Instantons, topological strings, and enumerative geometry,
Reference 41
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.
Observation eddeecdb-310a-40d7-a525-29e5ef61a029 · outbound
Lattice random walks and quantum A-period conjecture Topological Strings and Integrable Hierarchies,
Reference 42
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.
Observation 9deefc73-03bd-4f28-b2ce-d84cbd733c50 · outbound
Lattice random walks and quantum A-period conjecture Les Houches lectures on matrix models and topological strings
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 380754a1-a3db-4313-a664-d9070a790a04 · outbound
Lattice random walks and quantum A-period conjecture Spectral equations for the modular oscillator,
Reference 44
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.
Observation 9a659af8-ca2e-43d3-b8f0-8f34935785d3 · outbound
Lattice random walks and quantum A-period conjecture Explicit computation of the discriminant for the Harper equation with rational flux,
Reference 45
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.
Observation f44b23b6-cec3-4b26-aa4b-03f7967208f8 · outbound
Lattice random walks and quantum A-period conjecture Combinatorics of generalized Dyck and Motzkin paths,
Reference 46
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.
Observation 8d3809b0-1fc3-4bfe-bb2a-9a6bb5741c7c · outbound
Lattice random walks and quantum A-period conjecture Hofstadter point spectrum trace and the almost Mathieu operator,
Reference 47
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.
Observation 37673d7e-99dc-4452-bdd5-28f2bdc1094a · outbound
Lattice random walks and quantum A-period conjecture Maximal and minimal polyiamonds,
Reference 48
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.
Observation c80ceca5-d837-400b-be80-16833800a7ef · outbound
Lattice random walks and quantum A-period conjecture WKB method and quantum periods beyond genus one,
Reference 49
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.
Observation 0c255577-c492-49a7-baf4-4236fc6fcfa2 · outbound
Lattice random walks and quantum A-period conjecture On the resurgent structure of quantum periods,
Reference 50
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.
Observation 0b2afc77-3719-4f1f-84b0-e748dfd80ed2 · outbound
Lattice random walks and quantum A-period conjecture Quantum geometry of refined topological strings,
Reference 51
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.
Observation de961a5d-bb14-4271-8450-67f2784f4d41 · outbound
Lattice random walks and quantum A-period conjecture Topological strings and quantum spectral problems,
Reference 52
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.
Observation a4f4895f-c7da-4d83-8dbd-87a6ac8a6e3b · outbound
Lattice random walks and quantum A-period conjecture Topological strings from quantum mechan- ics,
Reference 53
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.
Observation 92c3ac94-deb8-4a12-9c77-e6d5c2df3569 · outbound
Lattice random walks and quantum A-period conjecture On the algebraic area of lattice walks and the Hofstadter model,
Reference 54
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.
Observation 34c0f9d2-d141-46bd-b1f1-3addabb7ab0c · outbound
Lattice random walks and quantum A-period conjecture Hofstadter-Toda spectral duality and quantum groups,
Reference 55
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.
Observation 3d24eb81-5c2e-4a6b-a51e-9e4ac6b14fd6 · outbound
Lattice random walks and quantum A-period conjecture Exact quantization conditions for the relativistic Toda lattice,
Reference 56
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.
Observation ecffce79-b382-478a-89d2-7a15f94a3bba · outbound
Lattice random walks and quantum A-period conjecture Algebraic area of cubic lattice walks,
Reference 57
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.
No inbound Pith citation observations are available.