Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T11:51:29.189232Z
Paper Citation Record · LEDGER
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue)
As of 16 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 0 inbound Pith citation observations for arXiv:1908.08562.
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
16 of 16 outbound references displayed
- verified exact1
- verified fuzzy15
- unresolved0
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation be6a98c1-e99c-40f5-abd1-5b1d62869d98 · outbound
This paper cites On the calculation of exact sum rules of rational order for quantum billiards.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) On the calculation of exact sum rules of rational order for quantum billiards
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.371692Z
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 36a25f68-9dae-49d3-935f-a29398895c46 · outbound
This paper cites Exact sum rules for inhomogeneous systems containing a zero mode.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) Exact sum rules for inhomogeneous systems containing a zero mode
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.362185Z
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 836929f8-8e6f-47cf-ad6e-7ab6c39a635a · outbound
This paper cites Exact sum rules for heterogeneous spherical drums.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) Exact sum rules for heterogeneous spherical drums
Reference 3
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:51:29.222907Z
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 ed2f0a11-46de-4922-a280-9fda97d8ed84 · outbound
This paper cites A perturbative approach to the spectral zeta functions of strings, drums, and quantum billiards.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) A perturbative approach to the spectral zeta functions of strings, drums, and quantum billiards
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.353005Z
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 58c6a533-789b-46c8-9249-d47bb440b7a3 · outbound
This paper cites The string of variable density: Further results.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) The string of variable density: Further results
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.343322Z
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 512d75b7-e512-4d4c-84fe-d1d1ed09c60b · outbound
This paper cites Exact sum rules for inhomogeneous strings.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) Exact sum rules for inhomogeneous strings
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.333924Z
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 0e4eda25-46bc-45ee-b0e4-5c0634cfddb9 · outbound
This paper cites Exact sum rules for inhomogeneous drums.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) Exact sum rules for inhomogeneous drums
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.324206Z
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 6bf60ba1-6076-4a25-9db6-afc0544d02f3 · outbound
This paper cites Exact sum rules for quantum billiards of arbitrary shape.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) Exact sum rules for quantum billiards of arbitrary shape
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.314734Z
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 5cbeb507-30ad-447f-a9a8-0485178ad178 · outbound
This paper cites Sum rules for quantum billiards.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) Sum rules for quantum billiards
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.305278Z
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 9f3ea1c4-8b33-429e-8f6f-f683d5bd2951 · outbound
This paper cites Spectral zeta functions for Aharonov-Bohm quantum billiards.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) Spectral zeta functions for Aharonov-Bohm quantum billiards
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.295884Z
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 457b3546-8d16-4851-8d14-143f6e458412 · outbound
This paper cites Magic sum rules for confinement potentials.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) Magic sum rules for confinement potentials
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.286388Z
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 b531df6c-38bd-4598-8e4f-7c2ed1284817 · outbound
This paper cites Spectral Sum Rules for the Circular Aharonov‐Bohm Quantum Billiard.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) Spectral Sum Rules for the Circular Aharonov‐Bohm Quantum Billiard
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.275552Z
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 41f7eab9-bd32-46d2-b61b-ebf129581199 · outbound
This paper cites Zeta functions of nearly circular domains.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) Zeta functions of nearly circular domains
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.265284Z
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 65a5a6ae-c9ca-4510-b9f4-5690b06be3cc · outbound
This paper cites Sums of reciprocal eigenvalues of the Laplacian.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) Sums of reciprocal eigenvalues of the Laplacian
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.255040Z
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 561a8821-10b5-4712-af27-4d30ba20900e · outbound
This paper cites Dittmar and M.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) Dittmar and M
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.244095Z
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 61e87f57-9a60-40ab-8bbb-ec3333d64b6c · outbound
This paper cites Regularized trace of the inverse of the Dirichlet Laplacian.
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue) Regularized trace of the inverse of the Dirichlet Laplacian
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:51:29.234063Z
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.
Pith citing papers
No inbound Pith citation observations are available.