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.

pith.paper-citation-record.v1
2411.18120 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T11:39:12.494670Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+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

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.

One can hear a discrete rectangular torus 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 2026-08-15T06:32:42.880941+00:00.

Observation 1ac5073e-215a-4dd3-baad-91123ff9a77a · outbound

This paper cites Brooks, R.

One can hear a discrete rectangular torus 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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

Observation bb48b9ed-427c-41f6-8c14-6d4c347d9fc9 · outbound

This paper cites Imrich, S.

One can hear a discrete rectangular torus 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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

No inbound Pith citation observations are available.