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Paper Citation Record · LEDGER

Some lower bounds for optimal sampling recovery of functions with mixed smoothness

As of 19 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2412.02797.

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

pith.paper-citation-record.v1
2412.02797 v2

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T23:21:21.130055Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

23 of 23 outbound references displayed

  • verified exact15
  • verified fuzzy7
  • unresolved1
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6533d907-85b3-4b72-8aac-9031aa4ad0b8 · outbound

This paper cites A sharp upper bound for sampling numbers in $L_{2}$.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness A sharp upper bound for sampling numbers in $L_{2}$

Reference 1

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verified exact
local_arxiv, observed 2026-08-11T23:21:21.489323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

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Observation ac506309-94be-4890-8fad-62fecf47feac · outbound

This paper cites Universal discretization and sparse sampling recovery.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Universal discretization and sparse sampling recovery

Reference 2

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local_arxiv, observed 2026-08-11T23:21:21.476361Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

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Observation c341255e-6ae2-44de-aa02-307957218acc · outbound

This paper cites Random points are good for universal discretization.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Random points are good for universal discretization

Reference 3

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verified exact
local_arxiv, observed 2026-08-11T23:21:21.464388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

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Observation 4de41b3f-b88a-46cd-a196-da3a5535e7ce · outbound

This paper cites Lebesgue-type inequalities in sparse sampling recovery.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Lebesgue-type inequalities in sparse sampling recovery

Reference 4

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local_arxiv, observed 2026-08-11T23:21:21.451501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.068333Z digest=sha256:3ec1b678781d6f79486d4cc57b99ac04e91e3f61b6444042b7f72bebd6638c1f

Observation 856c72f4-9d66-4a46-82f9-c7be58d220b9 · outbound

This paper cites Hyperbolic Cross Approximation.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Hyperbolic Cross Approximation

Reference 5

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local_arxiv, observed 2026-08-11T23:21:21.439237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.071989Z digest=sha256:1f9ee6fb78f56dcefa23c95f12811e35c2afafbbe70128a063ed3f0430234a66

Observation c9f16b22-c0ee-4ff6-bc6c-a31ff722d315 · outbound

This paper cites Sampling numbers of smoothness classes via $\ell^1$-minimization.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Sampling numbers of smoothness classes via $\ell^1$-minimization

Reference 6

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local_arxiv, observed 2026-08-11T23:21:21.425856Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.075601Z digest=sha256:006858a995aec6585255446490759feefdc5e234d5f863999b81ff62602c24c5

Observation 36cf366c-e265-4a36-b5a4-a59a25ab0662 · outbound

This paper cites Bounds for the sampling discretization error and their applications to the universal sampling discretization.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Bounds for the sampling discretization error and their applications to the universal sampling discretization

Reference 7

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verified exact
local_arxiv, observed 2026-08-11T23:21:21.412395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.078974Z digest=sha256:25d4f2749af7756c3597d7fbcc5435aa44efd7c9db3b9ab02b3395e827b9cb83

Observation de4eae64-c1bd-4a50-9ef3-d9a1e474fe6d · outbound

This paper cites Function values are enough for $L_2$-approximation.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Function values are enough for $L_2$-approximation

Reference 8

Resolution
verified exact
local_arxiv, observed 2026-08-11T23:21:21.399750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.082634Z digest=sha256:f3949c6b08748e9f2d25d92a4deaa4e353711f592baa458e581139079d51df91

Observation 4fb366b2-95a9-4990-a377-495e22ca7c27 · outbound

This paper cites Krieg and M.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Krieg and M

Reference 9

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no resolver link, observed 2026-08-11T23:21:21.085853Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T23:21:21.085853Z digest=sha256:2213ae545d7efa5bd541c93ddefe3c04602ab66ff7355d34180e53366a76519b

Observation 390d79b9-2899-4ba1-b046-12d289e7f84f · outbound

This paper cites A new upper bound for sampling numbers.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness A new upper bound for sampling numbers

Reference 10

Resolution
verified exact
local_arxiv, observed 2026-08-11T23:21:21.232095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.088611Z digest=sha256:7bfdc6cad04527460fc736e190e370994d794ed75288448ca53d814c6181e3d0

Observation 18fe33da-c194-4487-ae34-9479c7caebcd · outbound

This paper cites Smolyak, Quadrature and interpolation formulas for tenso r prod- ucts of certain classes of functions.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Smolyak, Quadrature and interpolation formulas for tenso r prod- ucts of certain classes of functions

Reference 11

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raw_fallback, observed 2026-08-11T23:21:21.555408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.091635Z digest=sha256:268aea43ac6f9abc3161db869ac3f84b0741b2e69e69b64d91fbb7e17a627b78

Observation e39feefa-78a2-4602-92af-45cbdadbd659 · outbound

This paper cites Sampling recovery on function classes with a structural condition.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Sampling recovery on function classes with a structural condition

Reference 12

Resolution
verified exact
local_arxiv, observed 2026-08-11T23:21:21.219257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.094887Z digest=sha256:c30f0d3ef0a054a84b554d3680428774d7d4b52b35ec228edc41cfc9f0d4944b

Observation 04f52539-9ea3-41a0-abda-34373cc512d1 · outbound

This paper cites Temlyakov, Approximation of Periodic Functions of Several Vari- ables by Bilinear Forms, Izvestiya AN SSSR, Ser.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Temlyakov, Approximation of Periodic Functions of Several Vari- ables by Bilinear Forms, Izvestiya AN SSSR, Ser

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T23:21:21.545942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.098106Z digest=sha256:02bd4fae4a84f4092904b32e358fe4671e3bd1192e3c68e4983c5e61751f945f

Observation 511fa3d9-f175-448a-9ff9-b08022328180 · outbound

This paper cites Temlyakov, Approximation of functions with bounded mixed derivative, Trudy MIAN, 178 (1986), 1–112.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Temlyakov, Approximation of functions with bounded mixed derivative, Trudy MIAN, 178 (1986), 1–112

Reference 14

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verified fuzzy
raw_fallback, observed 2026-08-11T23:21:21.536930Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.100941Z digest=sha256:097b5de12912725d303567ee3f798884ced5e3df97e36839e013e7b59d158441

Observation 94c4add9-a8c0-4fd7-a153-13f437b570be · outbound

This paper cites Temlyakov, On a way of obtaining lower estimates for the er- rors of quadrature formulas, Matem.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Temlyakov, On a way of obtaining lower estimates for the er- rors of quadrature formulas, Matem

Reference 15

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verified fuzzy
raw_fallback, observed 2026-08-11T23:21:21.527242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.104783Z digest=sha256:84968f22b1c563cbb0bef749ba6f3e51d714b38f738553d9fabbbb6cf1efd122

Observation b6f1927a-273b-4a61-b9c5-d6deefb5b7fa · outbound

This paper cites Temlyakov, On Approximate Recovery of Functions with Bounded Mixed Derivative, J.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Temlyakov, On Approximate Recovery of Functions with Bounded Mixed Derivative, J

Reference 16

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raw_fallback, observed 2026-08-11T23:21:21.518254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.107594Z digest=sha256:5e6d3c47bbc7d581be2037ebee3668c57fd8f499a96fcf1070c08663b4580f72

Observation 571e21f3-573c-47bd-bd97-23b581f57643 · outbound

This paper cites Constructive sparse trigonometric approximation and other problems for functions with mixed smoothness.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Constructive sparse trigonometric approximation and other problems for functions with mixed smoothness

Reference 17

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local_arxiv, observed 2026-08-11T23:21:21.205842Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.110689Z digest=sha256:d57e50c87c0c45a029f3f7e665f814eccb563641962d4922c67effa7c05cfd41

Observation cf1f3fcc-68ea-43b1-92ad-9e7420d2038e · outbound

This paper cites Temlyakov, Multivariate Approximation , Cambridge University Press, 2018.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Temlyakov, Multivariate Approximation , Cambridge University Press, 2018

Reference 18

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raw_fallback, observed 2026-08-11T23:21:21.508555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.113979Z digest=sha256:2b350dc5dd5e39dda7b2c1e44a6ef2b96053e21ca7f05a8886610cb28ee378a9

Observation f1f815bb-b535-48c3-9ac3-4b34e7a036be · outbound

This paper cites On optimal recovery in $L_2$.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness On optimal recovery in $L_2$

Reference 19

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local_arxiv, observed 2026-08-11T23:21:21.193918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.116968Z digest=sha256:5c3ed7fbf047003ea58f6f3f649be26f85e8f9235c6c66f5e1fdc51d7b5fbc4b

Observation 836161e5-e372-49eb-ae9c-4778760bf90b · outbound

This paper cites Sparse sampling recovery by greedy algorithms.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Sparse sampling recovery by greedy algorithms

Reference 20

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verified exact
local_arxiv, observed 2026-08-11T23:21:21.182029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.120367Z digest=sha256:31f31f47b5e2151607004519f2ba7bbaf24eb08f7e5f61b01250fe9b41fc902c

Observation 4b5121b1-79ad-47b0-8197-571cee21972a · outbound

This paper cites Sparse sampling recovery in integral norms on some function classes.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Sparse sampling recovery in integral norms on some function classes

Reference 21

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local_arxiv, observed 2026-08-11T23:21:21.169588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.123410Z digest=sha256:966ea6105fc640c2579f959bbed2aa438490ac7e2fe6c4f94529af1806d10955

Observation d3c340a2-ba2d-47df-ab9a-58081920a109 · outbound

This paper cites Bounds on Kolmogorov widths and sampling recovery for classes with small mixed smoothness.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Bounds on Kolmogorov widths and sampling recovery for classes with small mixed smoothness

Reference 22

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local_arxiv, observed 2026-08-11T23:21:21.156586Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.127015Z digest=sha256:58271d6ebf999591661b2dd8147ad35c38812b2b2fd99983680784f2412bd93c

Observation 11125212-e671-4f86-9029-b680ed73bec7 · outbound

This paper cites Traub, G.W.

Some lower bounds for optimal sampling recovery of functions with mixed smoothness Traub, G.W

Reference 23

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raw_fallback, observed 2026-08-11T23:21:21.499030Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-11T23:21:21.130055Z digest=sha256:4d187e4f2acbceb94ab1214d9566fb8cda3fa649682a356a218f99a03a030263

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