Paper Citation Record · LEDGER

On the calculation of exact sum rules of rational order for quantum billiards

As of 23 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.

pith.paper-citation-record.v1
1908.08561 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:52:39.034082Z

measured 14 of 14 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+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

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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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.