Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T21:34:02.002542Z
Paper Citation Record · LEDGER
On the heat content of compact quantum graphs
As of 14 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2502.09461.
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 2026-08-14T06:32:32.682623+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
50 of 50 outbound references displayed
- verified exact3
- verified fuzzy33
- unresolved14
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 4dad0235-44a2-4594-a4ae-e61bd75ca812 · outbound
This paper cites Abramowitz and I.A.
On the heat content of compact quantum graphs Abramowitz and I.A
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.951924Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 21a816b5-9ac7-44e8-a052-35f800cbd65a · outbound
This paper cites an unresolved cited work.
On the heat content of compact quantum graphs Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:34:02.934993Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 07274f42-3e9e-4620-86c3-92df0ee80703 · outbound
This paper cites an unresolved cited work.
On the heat content of compact quantum graphs Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:34:02.917704Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 8a7a301c-08e9-4b99-9f70-eb6bebfe2c72 · outbound
This paper cites Becker, F.
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.900440Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 59e11f9f-84b4-4b46-b751-5401fa642c0b · outbound
This paper cites van den Berg.
On the heat content of compact quantum graphs van den Berg
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.883570Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 1ad0567b-e878-4176-b24d-62b2efdbb169 · outbound
This paper cites van den Berg and E.B.
On the heat content of compact quantum graphs van den Berg and E.B
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.866424Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 21378302-5eca-4ef3-ad7c-b7d10c3ca8d1 · outbound
This paper cites van den Berg, E.B.
On the heat content of compact quantum graphs van den Berg, E.B
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.848866Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 6b79d3e1-85cb-4875-9226-9ee445c174a3 · outbound
This paper cites van den Berg and P.B.
On the heat content of compact quantum graphs van den Berg and P.B
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.830739Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation a96fcac4-c89c-467b-a5ae-105a4bac681f · outbound
This paper cites van den Berg and S.
On the heat content of compact quantum graphs van den Berg and S
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.812866Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation ebe07eff-3f1b-4008-8dd5-e007229b4ae2 · outbound
This paper cites Berkolaiko, J.B.
On the heat content of compact quantum graphs Berkolaiko, J.B
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.794595Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation b553db24-2539-4f67-bc37-6e769c33b61f · outbound
This paper cites Berkolaiko, J.B.
On the heat content of compact quantum graphs Berkolaiko, J.B
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.777640Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation f6bd8872-adbb-4d87-bd95-da6b400c5c38 · outbound
This paper cites Berkolaiko and P.
On the heat content of compact quantum graphs Berkolaiko and P
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.759783Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 332b759b-12ef-4998-a7bd-625fdd838da4 · outbound
This paper cites On the Lipschitz continuity of the heat kernel.
On the heat content of compact quantum graphs On the Lipschitz continuity of the heat kernel
Reference 13
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T21:34:02.145261Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 704b7b76-d7f6-478f-9070-a07106935058 · outbound
This paper cites Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion.
On the heat content of compact quantum graphs Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion
Reference 14
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T21:34:02.117460Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 9a5ab01a-3c34-48e7-9250-88fb112a4250 · outbound
This paper cites Bolte, S.
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.742612Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation f8c062bc-07ab-4235-9915-0e36d6ce99cb · outbound
This paper cites Bolte and S.
On the heat content of compact quantum graphs Bolte and S
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.725432Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3066f1de-6c24-4496-8d7b-c8ad75b7967f · outbound
This paper cites Borthwick, E.
On the heat content of compact quantum graphs Borthwick, E
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.708988Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation df63b427-5492-4cd8-b623-64cb096a72bf · outbound
This paper cites Camilli and L.
On the heat content of compact quantum graphs Camilli and L
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.693535Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 2232aa8c-1b52-49b5-a01f-fd5c7aeabc84 · outbound
This paper cites Caputo and T.
On the heat content of compact quantum graphs Caputo and T
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.677310Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation a3de7a3d-35bc-45fd-8246-32982e3e6dc8 · outbound
This paper cites Cardanobile and D.
On the heat content of compact quantum graphs Cardanobile and D
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.659581Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 88a5a54c-d419-4c7d-ae60-50491f5b977d · outbound
This paper cites Colladay, L.
On the heat content of compact quantum graphs Colladay, L
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.641032Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 1f4824e8-e185-4ba8-8960-97a1b27fd813 · outbound
This paper cites Engel and R.
On the heat content of compact quantum graphs Engel and R
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.619485Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation e3ae5b8b-9e89-4af8-988e-e0a57010d673 · outbound
This paper cites Heat kernel estimates and related inequalities on metric graphs.
On the heat content of compact quantum graphs Heat kernel estimates and related inequalities on metric graphs
Reference 23
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T21:34:02.089150Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation b42cd893-462d-480d-87fe-44cea61f3278 · outbound
This paper cites Haeseler.
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.601852Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation f7f18749-3384-4993-a194-0fc642fd8604 · outbound
This paper cites Keller, D.
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.584365Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 02a4d9b2-f92b-44c5-87b6-f0e6669a9637 · outbound
This paper cites Kennedy, P.
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.567488Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 9275425e-1b29-46a3-9f01-3d2f4e4eebb3 · outbound
This paper cites Kostenko, D.
On the heat content of compact quantum graphs Kostenko, D
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.548402Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 5fbb2e0f-0f3a-42d0-a70f-3684aaf183c0 · outbound
This paper cites Kostrykin, J.
On the heat content of compact quantum graphs Kostrykin, J
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.530212Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation bed2a4bd-e98a-415d-a8e6-fd2dd956685c · outbound
This paper cites Kottos and U.
On the heat content of compact quantum graphs Kottos and U
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.512481Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 045cc93d-9276-4631-8ddb-6a06611174af · outbound
This paper cites Kottos and U.
On the heat content of compact quantum graphs Kottos and U
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.495277Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation bdee17c3-d138-4a23-bd6f-c6b599b10dca · outbound
This paper cites Kramar Fijavˇ z, D.
On the heat content of compact quantum graphs Kramar Fijavˇ z, D
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.477965Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 87ade44d-ccc0-4b2e-aa31-8a7e8ebe8e31 · outbound
This paper cites an unresolved cited work.
On the heat content of compact quantum graphs Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:34:02.462386Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 668190a7-596d-40cc-87c5-d668f164269f · outbound
This paper cites an unresolved cited work.
On the heat content of compact quantum graphs Unresolved cited work
Reference 33
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:34:02.446412Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 8e825910-38a9-41e7-aaf4-cd3135e7c1a5 · outbound
This paper cites Kurasov and M.
On the heat content of compact quantum graphs Kurasov and M
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.431130Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 10df0e2e-5f1a-432b-92bf-6670061a1a0e · outbound
This paper cites Maz´ on, M.
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.414695Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 57da2403-d6d4-4bd1-bd1e-fb87c3343583 · outbound
This paper cites Miranda Jr, D.
On the heat content of compact quantum graphs Miranda Jr, D
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.397348Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation ba501c3c-aff9-47c8-a580-afd0885c3a5f · outbound
This paper cites What is actually a metric graph?.
On the heat content of compact quantum graphs What is actually a metric graph?
Reference 37
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T21:34:01.918993Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 42474d16-ce7b-41d1-859a-d18963e5e7d0 · outbound
This paper cites an unresolved cited work.
On the heat content of compact quantum graphs Unresolved cited work
Reference 38
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:34:02.379956Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3254d47b-16b9-4a3a-8fb5-d15e8d0817c8 · outbound
This paper cites an unresolved cited work.
On the heat content of compact quantum graphs Unresolved cited work
Reference 39
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:34:02.361586Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 79c21900-af68-4f8c-be27-ebc7f4730611 · outbound
This paper cites Mugnolo and M.
On the heat content of compact quantum graphs Mugnolo and M
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.344116Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 82733fb1-7a93-4af5-9e86-a4e696690978 · outbound
This paper cites an unresolved cited work.
On the heat content of compact quantum graphs Unresolved cited work
Reference 41
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:34:02.326068Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation b639a971-3245-4abd-aeb5-1dde032506b6 · outbound
This paper cites an unresolved cited work.
On the heat content of compact quantum graphs Unresolved cited work
Reference 42
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:34:02.307737Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3b1afa7a-ba0e-4dc2-8a1c-d5b486bfa231 · outbound
This paper cites an unresolved cited work.
On the heat content of compact quantum graphs Unresolved cited work
Reference 43
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:34:02.289807Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 7c62045b-2fb9-4b3d-958b-868582f38920 · outbound
This paper cites an unresolved cited work.
On the heat content of compact quantum graphs Unresolved cited work
Reference 44
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:34:02.271423Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation ee823f51-f46e-430a-91e4-385d13388b83 · outbound
This paper cites P´ olya and G.
On the heat content of compact quantum graphs P´ olya and G
Reference 45
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.252608Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 2e25849d-e35b-4bed-ac60-926d473fd663 · outbound
This paper cites Polya and A.
On the heat content of compact quantum graphs Polya and A
Reference 46
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.235986Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation c373d2cd-7004-4042-85ba-b4de5e6e4765 · outbound
This paper cites an unresolved cited work.
On the heat content of compact quantum graphs Unresolved cited work
Reference 47
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:34:02.219435Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation c1186834-a7ec-4b24-8886-4b9956c18a51 · outbound
This paper cites an unresolved cited work.
On the heat content of compact quantum graphs Unresolved cited work
Reference 48
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:34:02.201523Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 87bd4039-bda3-4312-91f3-94ef10ec5729 · outbound
This paper cites an unresolved cited work.
On the heat content of compact quantum graphs Unresolved cited work
Reference 49
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:34:02.183047Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 9da3ad6d-d96c-4089-8c4c-d11440cd5571 · outbound
This paper cites Stollmann and J.
On the heat content of compact quantum graphs Stollmann and J
Reference 50
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:34:02.164376Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Pith citing papers
No inbound Pith citation observations are available.