Paper Citation Record · LEDGER

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs

As of 14 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2509.13228.

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

pith.paper-citation-record.v1
2509.13228 v2

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T16:41:06.488506Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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

38 of 38 outbound references displayed

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verified fuzzy0
unresolved38
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malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b6ccc658-c0dd-47f5-a07d-4d8ab602049f · outbound

This paper cites ``Neumann Domains on Graphs and Manifolds".

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs ``Neumann Domains on Graphs and Manifolds"

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:04.632789Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e668c87-2f57-4d99-bc10-55d8f016a501 · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 2

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Observation b57b2be7-0ce9-41a5-8eab-17293ebe53c4 · outbound

This paper cites Alon and R.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Alon and R

Reference 3

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Observation fa05699f-52fd-40e8-8795-bbfcb0c08820 · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 4

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Observation 991cbf6d-57d2-4643-be82-8a5f97d96b69 · outbound

This paper cites Eigenvalue estimates on quantum graphs.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Eigenvalue estimates on quantum graphs

Reference 5

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Observation 6603ba14-fd67-4643-9932-39b563f99972 · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 6

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Observation 2057281e-3340-4f2d-b6d5-55121576ca58 · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:05.065174Z

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Observation ec242423-6285-4595-9ee4-fa90a72947a8 · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:05.109017Z

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Observation 1fc352c2-61b5-433f-99f2-dab42f121848 · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:05.158782Z

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Observation c69dcdc4-c22d-4d86-a046-04b46ac5f65c · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:05.216855Z

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Observation 88cb1f2c-1e54-4054-af07-c3c19c14a18f · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:05.271099Z

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Observation ad146daf-0197-4014-9e37-6c7e330cff82 · outbound

This paper cites B., Kurasov, P., Mugnolo, D., Edge connectivity and the spectral gap of combinatorial and quantum graphs, J.\ Phys.\ A: Math.\ Theor.\ 50 (2017), 365201, 29pp.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs B., Kurasov, P., Mugnolo, D., Edge connectivity and the spectral gap of combinatorial and quantum graphs, J.\ Phys.\ A: Math.\ Theor.\ 50 (2017), 365201, 29pp

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:05.354923Z

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Observation eb782403-f9ff-4e12-b3a6-20483cd84774 · outbound

This paper cites B., Kurasov, P., Mugnolo, D., Surgery principles for the spectral analysis of quantum graphs, Trans.\ Amer.\ Math.\ Soc.\ 372 (2019), 5153--5197.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs B., Kurasov, P., Mugnolo, D., Surgery principles for the spectral analysis of quantum graphs, Trans.\ Amer.\ Math.\ Soc.\ 372 (2019), 5153--5197

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:05.441253Z

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Observation b6c3aac0-e5ce-45c5-82ef-8b11204687aa · outbound

This paper cites (ed.), Shape optimization and spectral theory, De Gruyter Open, Warsaw-Berlin, 2017.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs (ed.), Shape optimization and spectral theory, De Gruyter Open, Warsaw-Berlin, 2017

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:05.519018Z

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Observation a94aabd9-639f-4c10-a4d4-59d16c062462 · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 15

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Observation 574f641f-4265-4a25-bb41-3b5fe03d37dc · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:05.603502Z

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Observation 5ae0cdb9-2045-4867-b449-9d384de42033 · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:05.688631Z

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Observation 4dcdbbe7-9888-43cd-8eff-748fe822444b · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:05.857848Z

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Observation 9397694d-3aea-4796-89fa-6885a80fa013 · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:05.980082Z

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Observation 1d883d7b-e214-47d4-97a1-b376b7a8e2fc · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.061135Z

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Observation 8304cad7-b718-4aa5-9694-6c56c0326e54 · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.261518Z

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Observation a7db5b63-f55e-4127-9242-7831ca6208e9 · outbound

This paper cites B., Mugnolo, D., Plümer, M., Asymptotics and Estimates for Spectral Minimal Partitions of Metric Graphs, Int.\ Equ.\ Oper.\ Theory 93 (2021), 26.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs B., Mugnolo, D., Plümer, M., Asymptotics and Estimates for Spectral Minimal Partitions of Metric Graphs, Int.\ Equ.\ Oper.\ Theory 93 (2021), 26

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.368255Z

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Observation 91016afd-bece-4eaa-9439-28339f16a692 · outbound

This paper cites B., Mugnolo, D., Plümer, M., On Pleijel’s Nodal Domain Theorem for Quantum Graphs.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs B., Mugnolo, D., Plümer, M., On Pleijel’s Nodal Domain Theorem for Quantum Graphs

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.372843Z

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Observation 3a2cb971-3a44-4295-94d1-3e545a475132 · outbound

This paper cites B., Interlacing and Friedlander-type inequalities for spectral minimal partitions of metric graphs, Lett.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs B., Interlacing and Friedlander-type inequalities for spectral minimal partitions of metric graphs, Lett

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.383275Z

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Observation 585cfcf9-c6f8-4a24-a6c8-438616a55428 · outbound

This paper cites B., Geometric spectral theory of quantum graphs, Commun.\ Math.\ 32 (2024), no.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs B., Geometric spectral theory of quantum graphs, Commun.\ Math.\ 32 (2024), no

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.389225Z

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Observation cbb16652-3ba7-4d19-9fac-a93d05e91cdc · outbound

This paper cites B., Kurasov, P., L\'ena, C., Mugnolo, D., A theory of spectral partitions of metric graphs, Calc.\ Var.\ Partial Differential Equations 60 (2021), 61.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs B., Kurasov, P., L\'ena, C., Mugnolo, D., A theory of spectral partitions of metric graphs, Calc.\ Var.\ Partial Differential Equations 60 (2021), 61

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.395623Z

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Observation 3c0493ea-7ee5-47ef-b139-51c7b30db4a7 · outbound

This paper cites B., Kurasov, P., Malenov\'a, G., Mugnolo, D., On the spectral gap of a quantum graph, Ann.\ Henri Poincar\'e 17 (2016), 2439--2473.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs B., Kurasov, P., Malenov\'a, G., Mugnolo, D., On the spectral gap of a quantum graph, Ann.\ Henri Poincar\'e 17 (2016), 2439--2473

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.401274Z

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Observation 58767ef8-fb31-48ab-a4d5-1bb5c5c10333 · outbound

This paper cites and Smilansky, U., Periodic orbit theory and spectral statistics for quantum graphs, Ann.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs and Smilansky, U., Periodic orbit theory and spectral statistics for quantum graphs, Ann

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.406634Z

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Observation ebc13694-445c-4063-900a-a76c80d16ecf · outbound

This paper cites Rep.\ Math.\ Phys.\ 82 (2018), 63--80.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Rep.\ Math.\ Phys.\ 82 (2018), 63--80

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.424345Z

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Observation 6693b1a8-8873-4e9b-a4f7-10325022e7ce · outbound

This paper cites Lett Math Phys 109, 2491–2512 (2019).

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Lett Math Phys 109, 2491–2512 (2019)

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.431744Z

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Observation d2749100-ea8d-420f-9911-a6b3881ed18f · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.441708Z

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Observation bce37f29-36d1-4376-83d2-bac7c694a826 · outbound

This paper cites What is actually a metric graph?.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs What is actually a metric graph?

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.451513Z

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Observation ed2988c5-fe10-4390-9a91-314de7ff72b7 · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.458698Z

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Observation e0b09254-fee5-4fab-997d-020b573c09b8 · outbound

This paper cites Comm.\ Pure Appl.\ Math., 9 (1956), 543–550.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Comm.\ Pure Appl.\ Math., 9 (1956), 543–550

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.463085Z

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Observation 08f61173-4a07-4619-a87f-1918a8b7ff02 · outbound

This paper cites an unresolved cited work.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Unresolved cited work

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.469821Z

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Observation 100d65be-2eba-42f6-8031-403fbdd5b075 · outbound

This paper cites 3, 167--178.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs 3, 167--178

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.476586Z

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Observation ab075762-75b6-4c20-b5cc-0952f0c9eabd · outbound

This paper cites J.\ Phys.\ A: Math.\ Theor.\ 54 (2021), 015202, 14 pp.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs J.\ Phys.\ A: Math.\ Theor.\ 54 (2021), 015202, 14 pp

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.483632Z

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Observation f8bdc092-54bd-4d28-8a52-1533c3051555 · outbound

This paper cites Journal de Mathématiques Pures et Appliquées (1836), 106–186.

On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs Journal de Mathématiques Pures et Appliquées (1836), 106–186

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-04T16:41:06.488506Z

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Pith citing papers

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