Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T01:03:41.420335Z
Paper Citation Record · LEDGER
As of 9 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 6 inbound Pith citation observations for arXiv:2508.04209.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T01:03:41.420335Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-05T22:15:34.621390Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-10T07:16:52.875015Z
57 of 57 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 6a51a3bd-c2c7-4f39-a893-638630177d07 · outbound
Sums of Laplacian eigenvalues and sums of degrees A Conjectural Brouwer Inequality for Higher-Dimensional Laplacian Spectra
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4360e865-87fd-489e-895d-23c2f0eca00c · outbound
Sums of Laplacian eigenvalues and sums of degrees Abebe and J
Reference 2
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 5ee8e6df-cae7-4e41-8234-1e8156345619 · outbound
Sums of Laplacian eigenvalues and sums of degrees Aharoni, E
Reference 3
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 3dd00c52-0422-455e-bf71-f64edd887c35 · outbound
Sums of Laplacian eigenvalues and sums of degrees Alon and V
Reference 4
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Observation 5f1f6228-8c08-4028-bee3-2e79e80a4460 · outbound
Reference 5
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 36833e22-a108-4a2f-97d1-593030bc4204 · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 6
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 5a57a991-4abb-4f04-8405-f0b22a288ef9 · outbound
Reference 7
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Observation b2485646-93fc-46d1-91d3-dd7ed76d24d1 · outbound
Sums of Laplacian eigenvalues and sums of degrees Bai, The Grone-Merris conjecture , Trans
Reference 8
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation be4f92bb-6e36-42c0-a233-1bcfee86c5d2 · outbound
Sums of Laplacian eigenvalues and sums of degrees Ballmann and J
Reference 9
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 74c7f1a8-119f-454f-87b7-9556f95b2bf7 · outbound
Sums of Laplacian eigenvalues and sums of degrees Berndsen, Three problems in algebraic combinatorics , Master’s Thesis, Eindhoven University of Technology, 2010
Reference 10
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 2c9c5e4a-cd50-41a2-806f-fa0112fb179a · outbound
Sums of Laplacian eigenvalues and sums of degrees Bollob´ as,Modern graph theory, Graduate Texts in Mathematics, vol
Reference 11
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 8537604a-8225-43f6-8038-1cb9726b0822 · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 12
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 3f16767c-d915-46bf-8f8b-b99b61274865 · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 13
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Observation 47ea37de-2374-4ec3-b554-a7c725ad51a2 · outbound
Reference 14
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Observation 0f4f3063-89fe-4ebb-a1d0-bf7d7cfaa735 · outbound
Sums of Laplacian eigenvalues and sums of degrees Chen, On Brouwer’s conjecture for the sum of k largest Laplacian eigenvalues of graphs, Linear Algebra Appl
Reference 15
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation ac6013c7-1ece-4932-96df-133ab4ef55d7 · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 16
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Observation 5e0790f1-8188-453b-88f3-e04993041654 · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 17
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Observation 5d99a898-280b-4536-a47c-b35841170d17 · outbound
Sums of Laplacian eigenvalues and sums of degrees More on the full Brouwer Laplacian spectrum conjecture
Reference 18
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Unavailable: canonical work link unavailable.
Observation 8fada80b-0b1d-4145-9f6a-55190a1c4d12 · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 19
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Observation c733c11c-86f1-4ea9-b0f1-2dd13d7f61cf · outbound
Reference 20
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Observation b235be92-e2c2-4f1a-b773-2e0102d1f78f · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 21
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Observation 9de38541-018b-4c8a-b64f-1d448d8ad739 · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 22
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Observation 2ade8df5-8a12-4473-9402-2d08caa4dbe8 · outbound
Sums of Laplacian eigenvalues and sums of degrees Eckmann, Harmonische Funktionen und Randwertaufgaben in einem Komplex , Comment
Reference 23
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 624a50bf-e275-44e1-92f8-be687fc5c92d · outbound
Reference 24
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 5a8a9390-4055-47e6-8bcc-e5b681cf9a4c · outbound
Sums of Laplacian eigenvalues and sums of degrees Fiedler, Algebraic connectivity of graphs , Czechoslovak Math
Reference 25
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 40415a65-894f-48b9-b15f-dd82b766c51c · outbound
Sums of Laplacian eigenvalues and sums of degrees Fritscher, C
Reference 26
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Observation 72ac6525-567d-40f7-b034-39226ba603e3 · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 27
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 76943110-3bfc-4493-9b77-0bc8d4d67a67 · outbound
Sums of Laplacian eigenvalues and sums of degrees Garland, p-adic curvature and the cohomology of discrete subgroups of p-adic groups, Ann
Reference 28
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 05c199cd-1e28-4301-a133-25266f124e58 · outbound
Sums of Laplacian eigenvalues and sums of degrees Grone and R
Reference 29
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Observation b791a583-6fc9-4902-be18-7f315c963ffb · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 30
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 34653aba-d960-4d5c-8c77-fe4396ba1718 · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 31
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation a740c018-44d5-4b8a-8453-62f74988a493 · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 32
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Observation 4e724292-8f45-45f9-9cd1-19673fe18a8d · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 33
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 9b1c78d9-3249-4459-827a-2a271c6808ae · outbound
Sums of Laplacian eigenvalues and sums of degrees Helmberg and V
Reference 34
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Observation 7a60631c-a773-4318-842f-f53002ee5dab · outbound
Sums of Laplacian eigenvalues and sums of degrees Horak and J
Reference 35
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 47c04f50-54d5-4f38-8230-f5c46e39c093 · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 36
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 04f7f273-0477-43ca-930f-e14e55bc02f5 · outbound
Sums of Laplacian eigenvalues and sums of degrees Kahle, Sharp vanishing thresholds for cohomology of random flag complexes , Ann
Reference 37
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation df985b07-7c18-42a7-9ab0-690cf9721d26 · outbound
Sums of Laplacian eigenvalues and sums of degrees Kalai, Enumeration of Q-acyclic simplicial complexes , Israel J
Reference 38
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation ce152840-063d-47b3-9ef6-9ef3dc76be98 · outbound
Sums of Laplacian eigenvalues and sums of degrees The Grone Merris Conjecture and a quadratic eigenvalue problem
Reference 39
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 44755fc8-ec11-4882-9a74-ed585cbfeaaf · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 40
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 8034c516-7c04-49af-b563-44f5a3cb8faa · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 41
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation af3f8a04-f36d-472c-97e3-88413041297c · outbound
Sums of Laplacian eigenvalues and sums of degrees Partition density, star arboricity, and sums of Laplacian eigenvalues of graphs
Reference 42
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Unavailable: canonical work link unavailable.
Observation b09cc373-116f-4b5f-9a6c-52bceb1d7181 · outbound
Sums of Laplacian eigenvalues and sums of degrees Li and Y.-L
Reference 43
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 8544b182-6c39-4452-9a36-249fc3e5bfe6 · outbound
Sums of Laplacian eigenvalues and sums of degrees Li and X.-D
Reference 44
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 613096a5-e9cf-4427-83c3-1a05e2d31da0 · outbound
Sums of Laplacian eigenvalues and sums of degrees Li and J.-M
Reference 45
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Observation 5cf1e28f-a534-4bb0-90d4-45402876c856 · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 46
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 0e06424a-cf8c-4a1c-8383-18a1c0498be2 · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 47
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation fa3a6dd0-84b0-4701-9d1c-cd6a6b6b42c2 · outbound
Sums of Laplacian eigenvalues and sums of degrees Merris, Laplacian matrices of graphs: a survey , Linear Algebra Appl
Reference 48
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation bcc25961-5f86-42dd-84e9-d9985db231c6 · outbound
Sums of Laplacian eigenvalues and sums of degrees Mohar, Isoperimetric numbers of graphs, J
Reference 49
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 60d3abdd-3eca-4158-939d-501cca550009 · outbound
Sums of Laplacian eigenvalues and sums of degrees Oppenheim, Local spectral expansion approach to high dimensional expanders Part I: Descent of spectral gaps, Discrete Comput
Reference 50
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 36de5a16-997c-4e97-ad80-5794ae490ca4 · outbound
Sums of Laplacian eigenvalues and sums of degrees Pirzada, R
Reference 51
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Observation ae2fdba6-bf14-4c56-9ac8-c305a3e886bf · outbound
Sums of Laplacian eigenvalues and sums of degrees Rocha, Brouwer’s conjecture holds asymptotically almost surely , Linear Algebra Appl
Reference 52
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation d2286019-20c5-4952-b32a-4f2f305b103b · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 53
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 2bf92cf1-1373-439a-801b-48ac81670277 · outbound
Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work
Reference 54
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation f35129c3-d596-48c8-b808-9850a9172bd2 · outbound
Sums of Laplacian eigenvalues and sums of degrees Yang and L
Reference 55
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Observation 11a681c7-aac9-415e-8ab1-e6fab45b57a4 · outbound
Sums of Laplacian eigenvalues and sums of degrees Zhou, C.-X
Reference 56
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Observation 105dcd09-d3c0-4a9d-9e81-b335b503b36f · outbound
Sums of Laplacian eigenvalues and sums of degrees ˙Zuk, La propri´ et´ e (T) de Kazhdan pour les groupes agissant sur les poly` edres, C
Reference 57
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation ea18151f-804b-4fb4-9509-6008cfa542e3 · inbound
Remarks on the Brouwer Conjecture Sums of Laplacian eigenvalues and sums of degrees
Reference 22
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Unavailable: canonical work link unavailable.
Observation b5b7439f-220a-43d7-b2d8-3eab6160f97a · inbound
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Sums of Laplacian eigenvalues and sums of degrees
Reference 16
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Observation 589d475f-bddd-4331-934f-7ab8c14ac6ff · inbound
Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Sums of Laplacian eigenvalues and sums of degrees
Reference 14
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 04d70e58-f487-48f2-aa39-c299867a98a1 · inbound
Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Sums of Laplacian eigenvalues and sums of degrees
Reference 17
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Unavailable: canonical work link unavailable.
Observation e61bf069-fc4a-436a-a297-dbdeefd4a6af · inbound
Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Sums of Laplacian eigenvalues and sums of degrees
Reference 18
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Unavailable: canonical work link unavailable.
Observation 63701420-f70d-4224-be08-f5f3a052f4cc · inbound
The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Sums of Laplacian eigenvalues and sums of degrees
Reference 17
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Unavailable: canonical work link unavailable.