Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T11:52:39.034082Z
Paper Citation Record · LEDGER
On the calculation of exact sum rules of rational order for quantum billiards
As of 16 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:1908.08561.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
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
Reference resolution
14 of 14 outbound references displayed
- verified exact0
- verified fuzzy11
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation f4b32798-efce-436e-9784-54f78c1c32e3 · outbound
This paper cites ”A perturbative approach to the spectral zeta functions of strings, drums, and quantum billiards.” Journal of Mathematical Physics 53.12 (2012): 123519.
On the calculation of exact sum rules of rational order for quantum billiards ”A perturbative approach to the spectral zeta functions of strings, drums, and quantum billiards.” Journal of Mathematical Physics 53.12 (2012): 123519
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:39.324806Z
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 51365af9-01e0-4e5a-9924-61ffbe06276b · outbound
This paper cites Moussa, and J.
On the calculation of exact sum rules of rational order for quantum billiards Moussa, and J
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:39.305381Z
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 26f630e5-55d9-4385-971c-de45c1b8fffd · outbound
This paper cites Berry, ”Spectral zeta functions for Aharonov-Bohm qua n- tum billiards”, Journal of Physics A 19 (1986): 2281-2296.
On the calculation of exact sum rules of rational order for quantum billiards Berry, ”Spectral zeta functions for Aharonov-Bohm qua n- tum billiards”, Journal of Physics A 19 (1986): 2281-2296
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:39.285193Z
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 d6500933-3568-4805-9d70-94500f58a968 · outbound
This paper cites ”Magic sum rules for confinement potentials.” Physics Letters B 159.4-6 (1985): 397-402.
On the calculation of exact sum rules of rational order for quantum billiards ”Magic sum rules for confinement potentials.” Physics Letters B 159.4-6 (1985): 397-402
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:39.265761Z
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 a3357fe0-fcfc-4500-ab68-90b0883598f5 · outbound
This paper cites ”Spectral Sum Rules for the Circu- lar AharonovBohm Quantum Billiard.” Fortschritte der Physik/Progress of Physics 35.1 (1987): 87-114.
On the calculation of exact sum rules of rational order for quantum billiards ”Spectral Sum Rules for the Circu- lar AharonovBohm Quantum Billiard.” Fortschritte der Physik/Progress of Physics 35.1 (1987): 87-114
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:39.249076Z
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 208a7bcf-f4df-4312-a38e-8e48fedde078 · outbound
This paper cites ”Zeta functions of nearly circular do- mains.” Journal of Physics A: Mathematical and General 29.19 (1996): 6379.
On the calculation of exact sum rules of rational order for quantum billiards ”Zeta functions of nearly circular do- mains.” Journal of Physics A: Mathematical and General 29.19 (1996): 6379
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:39.230793Z
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 ec1db7ab-d823-4212-9a8d-3233a7df1ff6 · outbound
This paper cites ”Sums of reciprocal eigenvalues of the Lapla- cian.” Mathematische Nachrichten 237.1 (2002): 45-61.
On the calculation of exact sum rules of rational order for quantum billiards ”Sums of reciprocal eigenvalues of the Lapla- cian.” Mathematische Nachrichten 237.1 (2002): 45-61
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:39.211696Z
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 3f2a7a07-d802-474e-b45b-e3b199a836c1 · outbound
This paper cites Dittmar and M.
On the calculation of exact sum rules of rational order for quantum billiards Dittmar and M
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T11:52:38.996432Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4077ec2e-0cc3-435d-8849-62319cb92e33 · outbound
This paper cites Dostani´ c, ”Regularized trace of the inverse of the Dirichle t Laplacian.” Communications on Pure and Applied Mathematics 64, 1148-1164 (2011).
On the calculation of exact sum rules of rational order for quantum billiards Dostani´ c, ”Regularized trace of the inverse of the Dirichle t Laplacian.” Communications on Pure and Applied Mathematics 64, 1148-1164 (2011)
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:39.179726Z
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 57c62842-787b-42ec-8867-0c3cf5154921 · outbound
This paper cites ”Exact sum rules for inhomogeneous strings.” An - nals of Physics 338 (2013): 341-360.
On the calculation of exact sum rules of rational order for quantum billiards ”Exact sum rules for inhomogeneous strings.” An - nals of Physics 338 (2013): 341-360
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:39.162179Z
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 c6213c3c-0187-4b3c-896a-f17609537d7c · outbound
This paper cites ”Exact sum rules for inhomogeneous drums.” An- nals of Physics 336 (2013): 223-244.
On the calculation of exact sum rules of rational order for quantum billiards ”Exact sum rules for inhomogeneous drums.” An- nals of Physics 336 (2013): 223-244
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:39.143782Z
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 700bac8d-38f6-44fb-817c-3e10a702b6bc · outbound
This paper cites ”Exact sum rules for inhomogeneous systems co n- taining a zero mode.” Annals of Physics 349 (2014): 253-267.
On the calculation of exact sum rules of rational order for quantum billiards ”Exact sum rules for inhomogeneous systems co n- taining a zero mode.” Annals of Physics 349 (2014): 253-267
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:39.124222Z
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 0b498fd1-342a-4246-bdf7-7bbb7c1aa8db · outbound
This paper cites an unresolved cited work.
On the calculation of exact sum rules of rational order for quantum billiards Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:52:39.099620Z
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 e8ea8041-e5dc-4618-b0a2-ab8212b23c97 · outbound
This paper cites Exact sum rules for heterogeneous spherical drums.
On the calculation of exact sum rules of rational order for quantum billiards Exact sum rules for heterogeneous spherical drums
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T11:52:39.034082Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
No inbound Pith citation observations are available.