Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T10:23:59.821685Z
Paper Citation Record · LEDGER
PODNO: Proper Orthogonal Decomposition Neural Operators
As of 20 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 0 inbound Pith citation observations for arXiv:2504.18513.
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 2026-08-20T06:33:59.587034+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
51 of 51 outbound references displayed
- verified exact1
- verified fuzzy31
- unresolved19
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 23e58da3-d1f4-417a-a3b1-8541c6e1be3d · outbound
This paper cites Berkooz, P.
PODNO: Proper Orthogonal Decomposition Neural Operators Berkooz, P
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.588544Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 9bac3d0c-8579-4388-8edb-12d0cd715b04 · outbound
This paper cites Bhattacharya, B.
PODNO: Proper Orthogonal Decomposition Neural Operators Bhattacharya, B
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.577013Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation fc836d97-975a-4cdd-b471-00c9f915ac69 · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.565344Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f2be1caa-e49e-48f2-99fb-35e27d95d46a · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.553005Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 488f2359-46ed-4d6f-872c-0283cd4ebefc · outbound
This paper cites Cheng, C.-L.
PODNO: Proper Orthogonal Decomposition Neural Operators Cheng, C.-L
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.540682Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 428e8d87-ca93-49ca-8268-ecf26f1352a1 · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.526708Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 207d0c5c-f07a-4f72-a3c3-b7af9378b356 · outbound
This paper cites Cottet, P.
PODNO: Proper Orthogonal Decomposition Neural Operators Cottet, P
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.512710Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 35f620d2-0df6-427a-8b8b-a641a3244072 · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.491523Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 294a64b9-8ade-4015-a7d0-7fc67e0c58d2 · outbound
This paper cites A variational neural network approach for glacier modelling with nonlinear rheology.
PODNO: Proper Orthogonal Decomposition Neural Operators A variational neural network approach for glacier modelling with nonlinear rheology
Reference 9
- Resolution
- verified exact
- local_arxiv, observed 2026-08-16T10:23:59.887796Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 801f280a-fc0d-43cd-9cde-640aa37a3f42 · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.475709Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ddd73b2d-8c7b-4e11-9e30-639ebe949def · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.461369Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ab9bc55f-84db-47a9-9f0d-0dfadd76b0db · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.448641Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 6b37d35b-4a59-4a85-a221-573f16287777 · outbound
This paper cites Fibich , The nonlinear Schr¨ odinger equation, vol.
PODNO: Proper Orthogonal Decomposition Neural Operators Fibich , The nonlinear Schr¨ odinger equation, vol
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.432994Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b7bef9be-5cab-4d71-ba5d-b1117f7c9417 · outbound
This paper cites Galati and S.
PODNO: Proper Orthogonal Decomposition Neural Operators Galati and S
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.418858Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 8ac55dce-0a5d-4ad8-97d1-dc77754c32eb · outbound
This paper cites Gottlieb and S.
PODNO: Proper Orthogonal Decomposition Neural Operators Gottlieb and S
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.405813Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 527d97a4-1ec1-428b-a972-19c3cf171aed · outbound
This paper cites Grava, C.
PODNO: Proper Orthogonal Decomposition Neural Operators Grava, C
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.388167Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 466191bb-3260-488d-88ef-b4170e55e77b · outbound
This paper cites Greiner, I.
PODNO: Proper Orthogonal Decomposition Neural Operators Greiner, I
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.375342Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 59f65689-ce28-455e-bc72-9ddcd2a9b43c · outbound
This paper cites Griffin, D.
PODNO: Proper Orthogonal Decomposition Neural Operators Griffin, D
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.362634Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 072fb738-c6ff-4579-a704-73d4f855489c · outbound
This paper cites Hornik , Approximation capabilities of multilayer feedforward networks , Neural Networks, 4 (1991), pp.
PODNO: Proper Orthogonal Decomposition Neural Operators Hornik , Approximation capabilities of multilayer feedforward networks , Neural Networks, 4 (1991), pp
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.350824Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 79bef81a-90f3-4699-a959-f08d3e34a939 · outbound
This paper cites Huang, V.
PODNO: Proper Orthogonal Decomposition Neural Operators Huang, V
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.338187Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 21b82db1-8da1-4fe8-88c7-307f3f78e16a · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.325350Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 11a6b4d6-3873-460c-8948-742aea80b3ab · outbound
This paper cites Jones and P.
PODNO: Proper Orthogonal Decomposition Neural Operators Jones and P
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.308971Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 8af40468-bd28-4804-9867-e023d07c25a5 · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.294499Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 718110bb-fe74-4da3-820c-e03b2b1b36c7 · outbound
This paper cites Kato , On nonlinear Schr¨ odinger equations, in Annales de l’IHP Physique th´ eorique, vol.
PODNO: Proper Orthogonal Decomposition Neural Operators Kato , On nonlinear Schr¨ odinger equations, in Annales de l’IHP Physique th´ eorique, vol
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.278447Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d61eea2b-17e0-47b7-94ee-2579fa6e4dfb · outbound
This paper cites Kato and G.
PODNO: Proper Orthogonal Decomposition Neural Operators Kato and G
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.262087Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 1582c050-a546-4cd9-ad71-94267069e5b3 · outbound
This paper cites Klein, C.
PODNO: Proper Orthogonal Decomposition Neural Operators Klein, C
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.247486Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d15b47cd-c6d8-47ab-b762-2868b9f6e808 · outbound
This paper cites Kovachki, S.
PODNO: Proper Orthogonal Decomposition Neural Operators Kovachki, S
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.234005Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 44223b0f-dc84-4e70-adbd-914c94238064 · outbound
This paper cites Kovachki, Z.
PODNO: Proper Orthogonal Decomposition Neural Operators Kovachki, Z
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.219779Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e48ceefa-1b2b-4544-8e8c-a33557099a6b · outbound
This paper cites Kunisch and S.
PODNO: Proper Orthogonal Decomposition Neural Operators Kunisch and S
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.206746Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 3e6b9bf1-c1e9-45aa-9639-86cd813de7bb · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.191602Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 9bb3f212-cd14-487f-8074-b9e2a228e088 · outbound
This paper cites Neural Operator: Graph Kernel Network for Partial Differential Equations.
PODNO: Proper Orthogonal Decomposition Neural Operators Neural Operator: Graph Kernel Network for Partial Differential Equations
Reference 31
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T10:23:59.742645Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0e2cac87-6c58-4872-b070-984b00cff4a7 · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.178685Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 96189442-6a9c-4a24-9824-97d94d80ee00 · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 33
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.162756Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation c68fa11c-4311-45fc-9035-5f9e8224dd93 · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 34
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.145255Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b0daab81-b2a2-436a-ae37-a85a2666ab9e · outbound
This paper cites SPFNO: Spectral operator learning for PDEs with Dirichlet and Neumann boundary conditions.
PODNO: Proper Orthogonal Decomposition Neural Operators SPFNO: Spectral operator learning for PDEs with Dirichlet and Neumann boundary conditions
Reference 35
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T10:23:59.758766Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9b0fbdb7-0d98-4938-a8ad-681bbf96db02 · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.126795Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 7d22bdd6-e34b-49c7-b2f7-b2aff0c491e2 · outbound
This paper cites Luttinger , The effect of a magnetic field on electrons in a periodic potential , Physical Review, 84 (1951), p.
PODNO: Proper Orthogonal Decomposition Neural Operators Luttinger , The effect of a magnetic field on electrons in a periodic potential , Physical Review, 84 (1951), p
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.109530Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation c4f4374a-317d-4391-a40f-489635f9d495 · outbound
This paper cites Marsiglio, The harmonic oscillator in quantum mechanics: A third way , American Journal of Physics, 77 (2009), pp.
PODNO: Proper Orthogonal Decomposition Neural Operators Marsiglio, The harmonic oscillator in quantum mechanics: A third way , American Journal of Physics, 77 (2009), pp
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.096070Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation dc9fc6a1-0e30-427c-8c22-0e2ad020b631 · outbound
This paper cites Morsch and M.
PODNO: Proper Orthogonal Decomposition Neural Operators Morsch and M
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.080495Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 4748b57f-2d39-4f46-bc50-3f9f5c07902f · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 40
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:24:00.066660Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ee552d98-ec5b-4fcc-a148-c650c145a084 · outbound
This paper cites Quarteroni and A.
PODNO: Proper Orthogonal Decomposition Neural Operators Quarteroni and A
Reference 41
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.049698Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a45d025b-40e6-4a7e-8060-373a69d1b546 · outbound
This paper cites Raissi, P.
PODNO: Proper Orthogonal Decomposition Neural Operators Raissi, P
Reference 42
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.024793Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d92b4066-9a0f-48b5-80d4-bcef713d3e61 · outbound
This paper cites Seaman, L.
PODNO: Proper Orthogonal Decomposition Neural Operators Seaman, L
Reference 43
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:24:00.004624Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b4a5eb7a-a9ab-424e-ae5a-dcfbaed5ad7a · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 44
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:23:59.990615Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 6a2ded81-456b-459b-bc01-438e4476edab · outbound
This paper cites an unresolved cited work.
PODNO: Proper Orthogonal Decomposition Neural Operators Unresolved cited work
Reference 45
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T10:23:59.978601Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 6af3bf6e-ec3b-4267-8b4c-7b75aab4db1f · outbound
This paper cites Smithies , Integral equations, no.
PODNO: Proper Orthogonal Decomposition Neural Operators Smithies , Integral equations, no
Reference 46
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:23:59.967454Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 56694fa5-348a-4dee-aca8-f6fd320082f2 · outbound
This paper cites Veselov and S.
PODNO: Proper Orthogonal Decomposition Neural Operators Veselov and S
Reference 47
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:23:59.954542Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 1f164be1-fdde-4d96-ab44-9e5c0c635dc1 · outbound
This paper cites W ang, H.
PODNO: Proper Orthogonal Decomposition Neural Operators W ang, H
Reference 48
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:23:59.941245Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation bb50af70-6ee4-4779-b380-3ff0a7f126ab · outbound
This paper cites W ang and Z.
PODNO: Proper Orthogonal Decomposition Neural Operators W ang and Z
Reference 49
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:23:59.928129Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation dbbab3e5-6311-444f-ad38-1581b053ccd4 · outbound
This paper cites Yu et al.
PODNO: Proper Orthogonal Decomposition Neural Operators Yu et al
Reference 50
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:23:59.914587Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 067ed2cb-4956-46fd-8d55-6c9659d38e13 · outbound
This paper cites Zhang and L.-L.
PODNO: Proper Orthogonal Decomposition Neural Operators Zhang and L.-L
Reference 51
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T10:23:59.901557Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Pith citing papers
No inbound Pith citation observations are available.