Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-12T11:39:12.494670Z
Paper Citation Record · LEDGER
One can hear a discrete rectangular torus
As of 16 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2411.18120.
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
28 of 28 outbound references displayed
- verified exact3
- verified fuzzy21
- unresolved4
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation e4823072-3915-400f-a2b4-057daa7b4ad3 · outbound
This paper cites Barden, H.
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:13.131213Z
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 1ac5073e-215a-4dd3-baad-91123ff9a77a · outbound
This paper cites Brooks, R.
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:13.116913Z
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 5e292826-1dca-45cf-96e5-529c899bc6eb · outbound
This paper cites Brooks, Constructing isospectral manifolds , Amer.
One can hear a discrete rectangular torus Brooks, Constructing isospectral manifolds , Amer
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:13.102951Z
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 5f4bbd49-b4cd-4cbc-af18-5d0b9755af9d · outbound
This paper cites Buser, Geometry and spectra of compact Riemann surfaces , Progress in Mathematics, 106, Birkh¨ auser, Boston, MA, 1992.
One can hear a discrete rectangular torus Buser, Geometry and spectra of compact Riemann surfaces , Progress in Mathematics, 106, Birkh¨ auser, Boston, MA, 1992
Reference 4
- Resolution
- verified exact
- raw_fallback, observed 2026-08-12T11:39:12.753698Z
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 01d5ade0-cd4c-4737-a5ad-20171658c907 · outbound
This paper cites Buser, Isospectral Riemann surfaces, Ann.
One can hear a discrete rectangular torus Buser, Isospectral Riemann surfaces, Ann
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:13.089357Z
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 58e32091-5661-4d7e-a64a-e23ac6b5e032 · outbound
This paper cites an unresolved cited work.
One can hear a discrete rectangular torus Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:39:13.075887Z
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 59865e6c-2295-494f-a237-79014c97bc0e · outbound
This paper cites an unresolved cited work.
One can hear a discrete rectangular torus Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:39:13.062073Z
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 a84ffde0-65fb-46ff-a39f-13f579f121b1 · outbound
This paper cites an unresolved cited work.
One can hear a discrete rectangular torus Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:39:13.047231Z
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 42e8522e-1e3e-43c8-a451-d1576fc1a446 · outbound
This paper cites Fiedler, Algebraic connectivity of graphs , Czech.
One can hear a discrete rectangular torus Fiedler, Algebraic connectivity of graphs , Czech
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:13.031948Z
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 3cc909c4-3e75-43bc-b459-0f727398a6f0 · outbound
This paper cites Friedli, The bundle Laplacian on discrete tori , Ann.
One can hear a discrete rectangular torus Friedli, The bundle Laplacian on discrete tori , Ann
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:13.016866Z
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 5197315b-1e34-44bd-bd54-07ff4477e98a · outbound
This paper cites Godsil, D.A.
One can hear a discrete rectangular torus Godsil, D.A
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:13.001152Z
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 bb48b9ed-427c-41f6-8c14-6d4c347d9fc9 · outbound
This paper cites Imrich, S.
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:12.985022Z
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 924235fb-d4a0-4e98-9d51-6601d2501408 · outbound
This paper cites Isangulov, Isospectral flat Klein bottles (Russian), Mat.
One can hear a discrete rectangular torus Isangulov, Isospectral flat Klein bottles (Russian), Mat
Reference 13
- Resolution
- verified exact
- raw_fallback, observed 2026-08-12T11:39:12.674593Z
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 21531a50-e209-42c2-b846-f5e37e2b0526 · outbound
This paper cites Kac, Can one hear the shape of a drum? , Amer.
One can hear a discrete rectangular torus Kac, Can one hear the shape of a drum? , Amer
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:12.969976Z
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 35d1c7c5-49fb-4c70-8c49-94f31e844139 · outbound
This paper cites Kitaoka, Positive definite quadratic forms with the same representat ion numbers, Arch.
One can hear a discrete rectangular torus Kitaoka, Positive definite quadratic forms with the same representat ion numbers, Arch
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:12.955745Z
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 57fa1069-4c5e-4b4b-a7a0-e172f3bc1536 · outbound
This paper cites Kneser, Lineare Relationen zwischen Darstellungsanzahlen quadra tischer Formen (German), Math.
One can hear a discrete rectangular torus Kneser, Lineare Relationen zwischen Darstellungsanzahlen quadra tischer Formen (German), Math
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:12.941244Z
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 e29dcc5d-725c-45b8-b347-4d34225182e2 · outbound
This paper cites Connection Laplacian on discrete tori with converging property.
One can hear a discrete rectangular torus Connection Laplacian on discrete tori with converging property
Reference 17
- Resolution
- verified exact
- local_arxiv, observed 2026-08-12T11:39:12.538600Z
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 b00ee7f7-f0b5-48fb-98b3-af348dc28fbf · outbound
This paper cites Algorithms Appl., 8:2 (2016) 1650028 (10 pages) MR3505475.
One can hear a discrete rectangular torus Algorithms Appl., 8:2 (2016) 1650028 (10 pages) MR3505475
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:12.926509Z
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 9d577d6f-dc10-4795-8577-93f1d0b2ed6c · outbound
This paper cites Louis, Asymptotics for the determinant of the combinatorial Lapla cian on hypercubic lattices European J.
One can hear a discrete rectangular torus Louis, Asymptotics for the determinant of the combinatorial Lapla cian on hypercubic lattices European J
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:12.910371Z
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 fbec0bbb-0c43-444b-a01c-928880241b5c · outbound
This paper cites Mednykh, I.
One can hear a discrete rectangular torus Mednykh, I
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:12.894506Z
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 2c00412d-1c5e-4a9a-8cfc-8eaed6192749 · outbound
This paper cites Milnor, Eigenvalues of the Laplace operator on certain manifolds , Proc.
One can hear a discrete rectangular torus Milnor, Eigenvalues of the Laplace operator on certain manifolds , Proc
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:12.878715Z
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 68791c81-e4e4-4821-ba15-dbb7f4125146 · outbound
This paper cites Mohar, The Laplacian spectrum of graphs , in Graph theory, combinatorics, and applications 2, Ed.
One can hear a discrete rectangular torus Mohar, The Laplacian spectrum of graphs , in Graph theory, combinatorics, and applications 2, Ed
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:12.863018Z
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 112e9588-6a43-4371-8fe5-b6bd2e0c5aab · outbound
This paper cites Nilsson, J.
One can hear a discrete rectangular torus Nilsson, J
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:12.847911Z
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 6d00e02b-64d4-49b5-9aca-5c20dd563753 · outbound
This paper cites Sabidussi, Graph multiplication, Math.
One can hear a discrete rectangular torus Sabidussi, Graph multiplication, Math
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:12.832531Z
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 15ee5651-f91a-4c32-a654-6637001020ad · outbound
This paper cites Schiemann, Ein Beispiel positiv definiter quadratischer Formen der Dim ension 4 mit gleichen (German), Arch.
One can hear a discrete rectangular torus Schiemann, Ein Beispiel positiv definiter quadratischer Formen der Dim ension 4 mit gleichen (German), Arch
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:12.816826Z
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 4dc844bb-a8f7-4db9-8df8-5bb85177d697 · outbound
This paper cites Shiota, On theta series and the splitting of S2(Γ 0(q)), J.
One can hear a discrete rectangular torus Shiota, On theta series and the splitting of S2(Γ 0(q)), J
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:12.799982Z
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 04ec04ec-3263-48d9-9dc9-19f28f1a0106 · outbound
This paper cites an unresolved cited work.
One can hear a discrete rectangular torus Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:39:12.783907Z
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 0e5755c4-1312-40d9-bafe-0e9064da0573 · outbound
This paper cites Wolpert, The length spectra as moduli for compact Riemann surfaces , Ann.
One can hear a discrete rectangular torus Wolpert, The length spectra as moduli for compact Riemann surfaces , Ann
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:39:12.768883Z
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.