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Paper Citation Record · LEDGER

Tensor-product vertex patch smoothers for biharmonic problems

As of 23 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2412.05082.

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

pith.paper-citation-record.v1
2412.05082 v2

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T21:03:46.417446Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+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

28 of 28 outbound references displayed

  • verified exact2
  • verified fuzzy21
  • unresolved5
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 71a3b4ae-ae2a-4ad9-8a17-9d7364cfac6d · outbound

This paper cites The deal.II L ibrary, V ersion 9.5.

Tensor-product vertex patch smoothers for biharmonic problems The deal.II L ibrary, V ersion 9.5

Reference 1

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation a55fb7d9-b5e0-4123-baee-8f32041a0465 · outbound

This paper cites Arnold, Richard S.

Tensor-product vertex patch smoothers for biharmonic problems Arnold, Richard S

Reference 2

Resolution
verified fuzzy
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Source-reported events for the cited work

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Observation 5f8e6fdd-ebd7-4510-a00d-1e0016d7af72 · outbound

This paper cites an unresolved cited work.

Tensor-product vertex patch smoothers for biharmonic problems Unresolved cited work

Reference 3

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 0b0cda90-e8f8-43ad-84d8-169669a91f73 · outbound

This paper cites Brubeck and Patrick E.

Tensor-product vertex patch smoothers for biharmonic problems Brubeck and Patrick E

Reference 4

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 805f9d34-41cf-4230-b7cb-720aeee24640 · outbound

This paper cites an unresolved cited work.

Tensor-product vertex patch smoothers for biharmonic problems Unresolved cited work

Reference 5

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation df02228d-6605-44ad-9aac-7a5d11b27bf9 · outbound

This paper cites Brenner and Li-Yeng Sung.

Tensor-product vertex patch smoothers for biharmonic problems Brenner and Li-Yeng Sung

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:03:46.792673Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 673bcf57-a282-4cab-83c7-67b095ad7d60 · outbound

This paper cites Brenner and Kening Wang.

Tensor-product vertex patch smoothers for biharmonic problems Brenner and Kening Wang

Reference 7

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.343014Z digest=sha256:d683cfdeeb71e6d999ac64ea34b43d9892df65a0e8e715cf021b5f20d82c810f

Observation 23702500-8f60-4331-8aff-10927ca396da · outbound

This paper cites Brenner and Jie Zhao.

Tensor-product vertex patch smoothers for biharmonic problems Brenner and Jie Zhao

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:03:46.771381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.346491Z digest=sha256:6e0ed9675949f41bba558d476d8d9c7632731b2f41e1d3ff2605179e516fe5ea

Observation ded2eb78-6ee0-41cc-aaa8-4e35543dbc41 · outbound

This paper cites An implementation of tensor product patch smoothers on gpus.

Tensor-product vertex patch smoothers for biharmonic problems An implementation of tensor product patch smoothers on gpus

Reference 9

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.349891Z digest=sha256:aceccf5075418f4a18667803df4eaaf4978af0958d3bee587537f12760921fcf

Observation 9e50efa0-986f-43ba-ad02-684486395ab4 · outbound

This paper cites Multigrid methods for the Stokes problem on GPU systems.

Tensor-product vertex patch smoothers for biharmonic problems Multigrid methods for the Stokes problem on GPU systems

Reference 10

Resolution
verified exact
local_arxiv, observed 2026-08-11T21:03:46.570510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 24fb5066-6587-4703-b12e-eee777e81e95 · outbound

This paper cites Multilevel interior penalty methods on GPU s.

Tensor-product vertex patch smoothers for biharmonic problems Multilevel interior penalty methods on GPU s

Reference 11

Resolution
verified exact
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 7c65434a-d118-4479-b29c-375d75235121 · outbound

This paper cites an unresolved cited work.

Tensor-product vertex patch smoothers for biharmonic problems Unresolved cited work

Reference 12

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 6968a333-331e-4ac8-aaf5-5d8394cf221d · outbound

This paper cites Acceleration of T ensor- P roduct O perations with T ensor C ores.

Tensor-product vertex patch smoothers for biharmonic problems Acceleration of T ensor- P roduct O perations with T ensor C ores

Reference 13

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.365020Z digest=sha256:4b025e7b6ce2e3c88b562ddfd953445bb67acf7883942e20f0dd09cc228617e2

Observation 8e1dbd36-259e-4074-a610-c7206140c509 · outbound

This paper cites Karakashian.

Tensor-product vertex patch smoothers for biharmonic problems Karakashian

Reference 14

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.369245Z digest=sha256:dc70f51adf584f9d1486d5fd174bc3fdc19e0c7cac4d920144398f79f3e15c70

Observation 860cb3bb-03b1-45d1-aa78-25bdeccedf8e · outbound

This paper cites Performance and accuracy of hardware-oriented native-, emulated-and mixed-precision solvers in FEM simulations.

Tensor-product vertex patch smoothers for biharmonic problems Performance and accuracy of hardware-oriented native-, emulated-and mixed-precision solvers in FEM simulations

Reference 15

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.372648Z digest=sha256:5b90045e954864bec6c8c7eeefb2efff44b1e8d06b1d6c8589fe7c292e5fab50

Observation 2c2d4565-667e-4642-9674-85d7835bef13 · outbound

This paper cites Kronbichler and K.

Tensor-product vertex patch smoothers for biharmonic problems Kronbichler and K

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:03:46.709306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 744670ca-bbcf-4c01-865b-db5679c6867c · outbound

This paper cites Fast matrix-free evaluation of discontinuous G alerkin finite element operators.

Tensor-product vertex patch smoothers for biharmonic problems Fast matrix-free evaluation of discontinuous G alerkin finite element operators

Reference 17

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.379023Z digest=sha256:903907d84564babe147a723d9a50607ef3f607693137aeaa4d01bf58587ecc71

Observation 8ea08618-858c-4801-a0f1-bb6631365be3 · outbound

This paper cites Kanschat, R.

Tensor-product vertex patch smoothers for biharmonic problems Kanschat, R

Reference 18

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.382188Z digest=sha256:2160a95da14aa420527305cf56eae7a30fafd9474ca4480f3a46b8a1e16e6d2d

Observation 6728b78a-2488-4aef-b6b1-a8391cf8b89c · outbound

This paper cites Kanschat and Y.

Tensor-product vertex patch smoothers for biharmonic problems Kanschat and Y

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:03:46.679316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.385040Z digest=sha256:3d2f20c476556e16176b8a3965c13de6bda71da711eedaa9ccc41805f5b0f1ed

Observation 62096e0d-8ef4-4590-aeca-487a2b79b276 · outbound

This paper cites Divergence-conforming discontinuous G alerkin methods and C^0 interior penalty methods.

Tensor-product vertex patch smoothers for biharmonic problems Divergence-conforming discontinuous G alerkin methods and C^0 interior penalty methods

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:03:46.669814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.388359Z digest=sha256:5b6bb955ee0ea0c2853923e0af9e447b08c31425784dac86e6c17a2ea7162d81

Observation 75058fed-7309-4dae-be45-0960bfb12c58 · outbound

This paper cites Lynch, John R.

Tensor-product vertex patch smoothers for biharmonic problems Lynch, John R

Reference 21

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation 6f68dc1f-e8a9-4fa7-a79b-2192edbd6661 · outbound

This paper cites Melenk, K.

Tensor-product vertex patch smoothers for biharmonic problems Melenk, K

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:03:46.648788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.395476Z digest=sha256:98c7ab22f06ce26461eeea0ae68378120313a5e5f29735c3e2ace0fc21ae0976

Observation 0cefbdbf-eb29-476a-9c17-923156d735c6 · outbound

This paper cites \"U ber ein V ariationsprinzip zur L ösung von D irichlet- P roblemen bei V erwendung von T eilräumen, die keinen R andbedingungen unterworfen sind.

Tensor-product vertex patch smoothers for biharmonic problems \"U ber ein V ariationsprinzip zur L ösung von D irichlet- P roblemen bei V erwendung von T eilräumen, die keinen R andbedingungen unterworfen sind

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:03:46.637454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.398969Z digest=sha256:b01e72123ebe004b2dd03fee50a7f40eb0a68acd4214687ca06761a6acb69b8d

Observation 7c2b9d91-2ffe-4a6b-b827-52ca2a1b9916 · outbound

This paper cites N sight C ompute, 2023.

Tensor-product vertex patch smoothers for biharmonic problems N sight C ompute, 2023

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:03:46.626424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.402498Z digest=sha256:371c016e41b559ad652641546f4c7cd5af7fc1a76b7b5bf87646c22af7dfda0b

Observation f08df84c-3912-44ce-8612-d0b666a7ecd2 · outbound

This paper cites Fast tensor product schwarz smoothers for high-order discontinuous galerkin methods.

Tensor-product vertex patch smoothers for biharmonic problems Fast tensor product schwarz smoothers for high-order discontinuous galerkin methods

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:03:46.615252Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.406221Z digest=sha256:cf84e43ac2cf666acc2e517005c8485cc33f7046a008bfe515b620089bbbb499

Observation 2c109ae9-6b01-435e-94eb-129157811aa8 · outbound

This paper cites an unresolved cited work.

Tensor-product vertex patch smoothers for biharmonic problems Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-11T21:03:46.603007Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.409713Z digest=sha256:781ec4ea74b829f7c4624be41bc5265738166b5bd95df8826f76be0d4e59b2ad

Observation 2471711b-e1ac-4985-b3e9-a66e4401d596 · outbound

This paper cites An optimal order multigrid method for biharmonic, C^1 finite element equations.

Tensor-product vertex patch smoothers for biharmonic problems An optimal order multigrid method for biharmonic, C^1 finite element equations

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:03:46.591852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.413948Z digest=sha256:f9bfcb10d13d7c2a2529f40adc43c1c96e79cb01d81f18612a22622592d260a4

Observation 650adc07-04fb-4c87-aa74-672a924c7e4c · outbound

This paper cites an unresolved cited work.

Tensor-product vertex patch smoothers for biharmonic problems Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-11T21:03:46.581463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-11T21:03:46.417446Z digest=sha256:516231ea7f135e24f925085f2a30559891d9fd11f94785a9ca1968a7daef0719

Pith citing papers

No inbound Pith citation observations are available.