Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-19T05:48:31.788237Z
Paper Citation Record · LEDGER
As of 5 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 1 inbound Pith citation observation for arXiv:2507.08551.
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 2026-05-19T05:48:31.788237Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-04T07:58:51.188202Z
A source-named dated measurement, never combined with another source.
Source: cited_works
51 of 51 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation e8ef4c7b-8fde-4101-ac01-e1539b2b55af · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Microscopic Origin of the Bekenstein-Hawking Entropy
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 5cad695f-a5d2-4c70-885f-dfb087bb0e1e · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Black Hole Entropy in M-Theory
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 3d5bd052-a578-4571-93ed-359c35b82c87 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Multiple D3-instantons and mock modular forms I
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 591bf180-ce98-47a4-aa95-037528ded1bf · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Multiple D3-instantons and mock modular forms II
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation b7095dba-f859-4eb5-b1ba-a3845818e1a3 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Black holes and higher depth mock modular forms
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 13fd10d1-ed25-4d77-a0a0-09f38dd94081 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions S-duality and refined BPS indices
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 8661c8fd-a2de-4daf-923b-704fc0d5b30f · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Mock modularity at work, or black holes in a forest
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 734d9c94-8600-421d-a1a3-feb0d200d8df · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Quantum Black Holes, Wall Crossing, and Mock Modular Forms
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 2401c497-c177-46c0-851e-9b462f475b98 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Mock theta functions
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation b8f9f373-861d-4327-8037-339b306efef7 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Zagier,Ramanujan’s mock theta functions and their applications (after Zwegers and Ono-Bringmann),Astérisque(2009) Exp
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation e696cb01-30e6-4f78-bcf7-f2848b0daf7d · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Vignéras,Séries thêta des formes quadratiques indéfinies,Springer Lecture Notes627(1977) 227
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 1bfd4d0f-8673-4fd0-b196-f9038c78a013 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Wall-crossing made smooth
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation f58ee812-d2e8-4638-b1df-24584eeb6fe4 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Mock modularity from black hole scattering states
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 3040aed7-2b7a-4808-b896-7ddce719f2a1 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions The non-compact elliptic genus: mock or modular
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation e8db8942-a2d2-4d85-a2d5-126e7a0b773b · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Non-holomorphic Modular Forms and SL(2,R)/U(1) Superconformal Field Theory
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 1f8e9f7b-0469-4754-bc3f-dda136f63394 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions A Twisted Non-compact Elliptic Genus
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation d9e259f3-d19b-478c-addf-47b4a12c62f4 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions A holomorphic anomaly in the elliptic genus
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 4476249a-0e9d-4661-9957-7997007cc0d7 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Localization and real Jacobi forms
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 0800b95f-369b-470e-bfb7-6f604f4cf339 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Elliptic genera of ALE and ALF manifolds from gauged linear sigma models
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 73b83aa1-fa8e-4687-80fa-ddb97166e08d · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Squashed toric sigma models and mock modular forms
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation a748636d-4414-4f6d-ba3b-07e1c10e187a · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Squashed Toric Manifolds and Higher Depth Mock Modular Forms
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation ae87890d-f83e-43d8-95ff-25952432ecd5 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Mock modularity and a secondary elliptic genus
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation bf5c1e7a-90c7-46cb-a663-9e8dfbc83073 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Indefinite theta series and generalized error functions
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 10ad9d82-3ba8-4b75-88d4-a1e5b566c012 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions $r$-Tuple Error Functions and Indefinite Theta Series of Higher-Depth
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation a5e28ea3-d9f1-4f94-95d2-1dc46e6ba7dd · outbound
Black Hole Quantum Mechanics and Generalized Error Functions A Strong Coupling Test of S-Duality
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 50f7b640-1698-4479-99ec-0565383bab51 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Refined $\mathrm{SU}(3)$ Vafa-Witten invariants and modularity
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation c88759a9-a25b-4df0-8a1b-4e74dfb7998c · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Equivariant K-theory and refined Vafa-Witten invariants
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 680c5b3b-0df5-4871-8692-5f406b5b4a34 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions From sheaves on P2 to a generalization of the Rademacher expansion
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 3df202d5-2d4a-49eb-a49a-f9390179070a · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Vafa-Witten theory and iterated integrals of modular forms
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 7a35334f-884c-464e-9c29-f8fe856b19b8 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Vafa-Witten invariants from modular anomaly
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 2223e0f4-fcac-4c92-a8e6-a22f70484e66 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Rank $N$ Vafa-Witten invariants, modularity and blow-up
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 2bab6a2a-908a-45fb-95f2-6f65a010137c · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Modular anomaly of BPS black holes
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 53f172c0-43da-4086-b6a1-895ec2ee66d0 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions $R^3$ index for four-dimensional $N=2$ field theories
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 649e9c05-71df-4455-aab1-2b957c447431 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Stability and duality in N=2 supergravity
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation df534973-527b-494b-9de5-d4fec8cbaf0f · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Quantum Quivers and Hall/Hole Halos
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 8e4c7b8b-38d0-4af6-8df5-67ca52209a65 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Framed BPS States, Moduli Dynamics, and Wall-Crossing
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 90ca4883-3b17-4a89-906e-b94dc367da07 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Ab Initio Wall-Crossing
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 4930393d-d16e-4879-be28-b4464ff44b28 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Quantizing N=2 Multicenter Solutions
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 84bce426-e888-4840-8902-a99b9a250542 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Scaling BPS Solutions and pure-Higgs States
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 6384a282-46f9-4e1d-a90a-7449465c4cb8 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions On the existence of scaling multi-centered black holes
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 8029452e-c60d-4962-82e0-82c234293278 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Wall-Crossing from Boltzmann Black Hole Halos
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 2db219f0-9173-47f6-93ef-19b66537b20b · outbound
Black Hole Quantum Mechanics and Generalized Error Functions A fixed point formula for the index of multi-centered N=2 black holes
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation c2eb64e7-15f7-4997-b7bb-e00f0f92d6d1 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Attractor flow trees, BPS indices and quivers
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 2c089c1c-262f-4891-8e8a-a76609e4573c · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Girardello, C
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 9c44efab-4cec-4799-96b9-36a0824ce318 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Imbimbo and S
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 87bbc663-c7f7-46d3-a27d-27b845287f0e · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Vafa-Witten invariants from exceptional collections
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation ac965d39-a64e-4500-890d-db6b59d56bdc · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Duality and Mock Modularity
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 1eb28a7d-608e-43cb-9764-348aca371886 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Göttsche,The Betti numbers of the Hilbert scheme of points on a smooth projective surface,Math
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation c6ca9b5d-16d7-4972-80ff-5981dd404ef0 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Scaling Black Holes and Modularity
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 6a1561d3-835d-4b13-997d-ecef9f74d1d7 · outbound
Black Hole Quantum Mechanics and Generalized Error Functions On the Coulomb and Higgs branch formulae for multi-centered black holes and quiver invariants
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 010530c0-2663-48fb-b966-3ad0475d5a2a · outbound
Black Hole Quantum Mechanics and Generalized Error Functions Witten Index and Wall Crossing
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation ec23adef-d7b8-47f8-842f-dc007561d312 · inbound
Revisiting the Quantum Geometry of Torus-fibered Calabi-Yau Threefolds Black Hole Quantum Mechanics and Generalized Error Functions
Reference 75
Source-reported events for the cited work
Unavailable: canonical work link unavailable.