Paper Citation Record · LEDGER

Finding all cospectral mates over a number field

As of 23 August 2026, this Paper Citation Record lists 52 of 52 outbound references and 0 inbound Pith citation observations for arXiv:2608.12410.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2608.12410 v1

Coverage vector

measured 52 of 52 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T14:27:32.801558Z

measured 52 of 52 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

52 of 52 outbound references displayed

verified exact11
verified fuzzy7
unresolved22
parse uncertain0
malformed identifier10
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 994bec24-bed8-47c3-ac90-9ea1b2f5247d · outbound

This paper cites Abiad, N.

Finding all cospectral mates over a number field Abiad, N

Reference 1

Resolution: metadata mismatch; raw_fallback, observed 2026-08-15T14:27:33.765626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation dee68e45-427a-4826-a500-123c8fc93132 · outbound

This paper cites Open problems in the spectral theory of signed graphs.

Finding all cospectral mates over a number field Open problems in the spectral theory of signed graphs

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.610453Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation acf0c092-237d-434c-9b43-d90aa02158b4 · outbound

This paper cites Bhargava, B.

Finding all cospectral mates over a number field Bhargava, B

Reference 3

Resolution: verified exact; doi, observed 2026-08-15T14:27:33.227009Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 32942864-c95a-4624-a1e5-ae11c30c98f8 · outbound

This paper cites Brouwer and E.

Finding all cospectral mates over a number field Brouwer and E

Reference 4

Resolution: malformed identifier; no resolver link, observed 2026-08-15T14:27:32.618924Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 784f7b1c-1e56-45d2-8d6a-d472b47757ee · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.623339Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 05c8598b-807b-4056-852e-66e0b2599968 · outbound

This paper cites Brown.Matrices over Commutative Rings.

Finding all cospectral mates over a number field Brown.Matrices over Commutative Rings

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:27:33.966802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1a04283b-3bd2-4437-83bd-c17978eacf51 · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-15T14:27:33.955312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation dbd145fb-4f4c-4fb8-a32e-e04576d6caa1 · outbound

This paper cites Dummit and R.

Finding all cospectral mates over a number field Dummit and R

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:27:33.943806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3d4ac75f-c69f-4ed2-a236-8d12e6fd1dbd · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 9

Resolution: verified exact; doi, observed 2026-08-15T14:27:33.189624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f0e00b0b-f726-4910-bde5-fc4a0fe72e74 · outbound

This paper cites Godsil and B.

Finding all cospectral mates over a number field Godsil and B

Reference 10

Resolution: malformed identifier; no resolver link, observed 2026-08-15T14:27:32.646254Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 459403d6-40ea-4bdf-b31e-75c9d5f1c635 · outbound

This paper cites Godsil and B.

Finding all cospectral mates over a number field Godsil and B

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.650279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 37649aa2-7233-4613-a13e-c4aa407834f6 · outbound

This paper cites Godsil and G.

Finding all cospectral mates over a number field Godsil and G

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.654218Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23c7b59b-b515-4159-80e7-2e7d816d513e · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 13

Resolution: verified exact; raw_fallback, observed 2026-08-15T14:27:33.699935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5b8f338c-4de8-4f65-bf5d-8e62a18937fd · outbound

This paper cites Günthard and H.

Finding all cospectral mates over a number field Günthard and H

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.661689Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c64528c6-9770-4974-83e2-2032da1040f2 · outbound

This paper cites Guo and W.

Finding all cospectral mates over a number field Guo and W

Reference 15

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T14:27:33.628732Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation accd2a97-5570-45ad-96da-0ad6f905c2f2 · outbound

This paper cites Haemers and E.

Finding all cospectral mates over a number field Haemers and E

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.669342Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ff746d6e-0b65-47cd-85de-ffd918d37572 · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-15T14:27:33.931653Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2a56cb7f-0d00-48cb-82a0-0d6e40291a83 · outbound

This paper cites Hartshorne.Algebraic geometry.

Finding all cospectral mates over a number field Hartshorne.Algebraic geometry

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.676441Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3923a4b5-6757-417f-9330-61884b7d8b8a · outbound

This paper cites Hoffmann and R.

Finding all cospectral mates over a number field Hoffmann and R

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:27:33.920248Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 111dfdf5-d7ed-44ac-b79e-bdbd6e4e53a3 · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 20

Resolution: malformed identifier; doi_truncated, observed 2026-08-15T14:27:33.135304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 67537af0-936b-425b-963d-eecb3074b31b · outbound

This paper cites Johnson and M.

Finding all cospectral mates over a number field Johnson and M

Reference 21

Resolution: verified exact; doi, observed 2026-08-15T14:27:33.124377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2e56d7b5-a444-4288-88b1-472930eb2bd1 · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-15T14:27:33.908104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 14b2e94e-6c02-4212-9df6-9ae3efc0e503 · outbound

This paper cites Lang.Algebra.

Finding all cospectral mates over a number field Lang.Algebra

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.698080Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dc1638eb-94eb-41df-9f31-999e69a12458 · outbound

This paper cites Lvov and A.

Finding all cospectral mates over a number field Lvov and A

Reference 24

Resolution: verified exact; doi, observed 2026-08-15T14:27:33.106029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 02737b44-74e8-47e9-9fd2-591bf3178642 · outbound

This paper cites Marcus and E.

Finding all cospectral mates over a number field Marcus and E

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.705925Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec02ec01-4bf7-4f1c-9695-5426caea32c0 · outbound

This paper cites Mohar and S.

Finding all cospectral mates over a number field Mohar and S

Reference 26

Resolution: verified exact; doi, observed 2026-08-15T14:27:33.037594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d470defb-3989-47d1-bf94-8277c7f1bec4 · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-15T14:27:33.895153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2408dd94-d75e-48fa-ac75-312be5fa2149 · outbound

This paper cites Neukirch.Algebraic number theory.

Finding all cospectral mates over a number field Neukirch.Algebraic number theory

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.716916Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 39113f4a-a370-41f3-8fe7-c3ed2bf6f92b · outbound

This paper cites O’Rourke and B.

Finding all cospectral mates over a number field O’Rourke and B

Reference 29

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T14:27:33.882414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation aed6b427-ea16-43d5-894a-844c5dd0cd79 · outbound

This paper cites Bordeaux.PARI/GP version 2.15.4, 2023.

Finding all cospectral mates over a number field Bordeaux.PARI/GP version 2.15.4, 2023

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:27:33.870238Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3565abd4-0759-4278-8d1a-f669d672ca83 · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 31

Resolution: verified exact; doi, observed 2026-08-15T14:27:33.019146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f70ce8af-facd-458d-bce8-d94aa7a00508 · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-15T14:27:33.857169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e1a07e25-ddd3-4c24-bcaf-e94774254caf · outbound

This paper cites Simoens and S.

Finding all cospectral mates over a number field Simoens and S

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:27:33.843490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e2a07f43-4eb5-4453-a67f-9879b9ef3b2e · outbound

This paper cites Tao and V.

Finding all cospectral mates over a number field Tao and V

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.738939Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce2c7bd9-bc37-476b-a201-0133e4451d28 · outbound

This paper cites https://www.sagemath.org.

Finding all cospectral mates over a number field https://www.sagemath.org

Reference 35

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T14:27:33.831506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 55d4abc0-5f9a-4ae7-84ac-5b343c0a08df · outbound

This paper cites Van Dam and W.

Finding all cospectral mates over a number field Van Dam and W

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.746248Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c976d785-1f2b-4235-b8dc-1d3b7f4ec4c3 · outbound

This paper cites Van Werde.

Finding all cospectral mates over a number field Van Werde

Reference 37

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T14:27:33.818545Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 43e9d6fc-81a2-4d63-b9e6-660837d853c1 · outbound

This paper cites Van Werde.

Finding all cospectral mates over a number field Van Werde

Reference 38

Resolution: verified exact; doi, observed 2026-08-15T14:27:32.993430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b269f4a1-5294-435b-8be0-35284707aeaf · outbound

This paper cites Van Werde.

Finding all cospectral mates over a number field Van Werde

Reference 40

Resolution: verified exact; doi, observed 2026-08-15T14:27:32.932734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 70ccc25d-d2b6-4974-a29f-971eb518e80a · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 41

Resolution: malformed identifier; no resolver link, observed 2026-08-15T14:27:32.763887Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 64438287-577c-487d-bbe8-6511e4f1eafb · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 42

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T14:27:33.806217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 84edb5d5-cea8-4075-8f2b-cc31f6bf7474 · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 43

Resolution: malformed identifier; doi_truncated, observed 2026-08-15T14:27:32.861100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ba5c6704-09d1-4559-9e7e-91a4ead9e577 · outbound

This paper cites Wang and W.

Finding all cospectral mates over a number field Wang and W

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.775244Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e9d3041-9409-4e0c-b7bc-8a59610383f0 · outbound

This paper cites Wang and C.-X.

Finding all cospectral mates over a number field Wang and C.-X

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:27:33.793183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1bef39a3-9cbb-4b01-8aee-e3bf02aa1d49 · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.786562Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f1eb11e3-b8d1-459f-bb1b-4f8aa83e41e7 · outbound

This paper cites Square-free Discriminants of Matrices and the Generalized Spectral Characterizations of Graphs.

Finding all cospectral mates over a number field Square-free Discriminants of Matrices and the Generalized Spectral Characterizations of Graphs

Reference 47

Resolution: verified exact; local_arxiv, observed 2026-08-15T14:27:32.840475Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 67170101-46bd-4d8e-b1e2-f0554c980665 · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.782833Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6eb022ae-27e7-4629-83f5-87945aa56713 · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 49

Resolution: metadata mismatch; raw_fallback, observed 2026-08-15T14:27:33.309440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation fcc94cd7-dfc8-4b2c-abf7-7c0f139f8312 · outbound

This paper cites Inconclusive.

Finding all cospectral mates over a number field Inconclusive

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:27:33.778940Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2f950b80-a945-4e18-b169-6e1f233cc6e5 · outbound

This paper cites Wang and D.

Finding all cospectral mates over a number field Wang and D

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.794365Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a20980c-3b6d-40b0-afe8-74bd22b5d8aa · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 1966

Resolution: unresolved; no resolver link, observed 2026-08-15T14:27:32.694325Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc4a046c-f04c-4978-89ff-759c79a0ed41 · outbound

This paper cites an unresolved cited work.

Finding all cospectral mates over a number field Unresolved cited work

Reference 2006

Resolution: verified exact; doi, observed 2026-08-15T14:27:33.201680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

No inbound Pith citation observations are available.