Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-05T15:44:54.833793Z
Paper Citation Record · LEDGER
$\mathcal{C}^1$-approximation with rational functions and rational neural networks
As of 17 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 1 inbound Pith citation observation for arXiv:2508.19672.
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 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-05-15T21:44:44.879618Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z
Reference resolution
27 of 27 outbound references displayed
- verified exact1
- verified fuzzy19
- unresolved7
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z
Outbound references
Observation d6243d12-839a-4b58-b076-854b1d584dfa · outbound
This paper cites an unresolved cited work.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T15:44:55.500399Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation fd8a44a5-9bcc-45e0-9ca7-874d61f73af0 · outbound
This paper cites Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activations.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activations
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.472811Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 883a0373-7280-4341-90cd-cdb0bcfe9f04 · outbound
This paper cites Bengio, P.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Bengio, P
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.447745Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 59a28f72-3848-402c-a412-f4f231dbad02 · outbound
This paper cites Rational neural net- works.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Rational neural net- works
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.415369Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 77be9366-01de-4d0b-9120-e7c59dd57516 · outbound
This paper cites From ESPRIT to ESPIRA: estimation of signal parameters by iterative rational approximation.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks From ESPRIT to ESPIRA: estimation of signal parameters by iterative rational approximation
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.393400Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c9bbea63-8c92-4ef1-8bed-5ec31b338eb2 · outbound
This paper cites Neural network approx- imation.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Neural network approx- imation
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.374214Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 90f1fcb1-c077-46dd-894c-3d35b1e36d51 · outbound
This paper cites A descent algorithm for the optimal control of ReLU neural network informed PDEs based on approximate directional derivatives.SIAM Journal on Optimization, 34(3):2314–2349, 2024.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks A descent algorithm for the optimal control of ReLU neural network informed PDEs based on approximate directional derivatives.SIAM Journal on Optimization, 34(3):2314–2349, 2024
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.353126Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ba22d07a-f10e-4f53-9c8e-f408091d8817 · outbound
This paper cites First-order conditions for the optimal control of learning- informed nonsmooth PDEs.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks First-order conditions for the optimal control of learning- informed nonsmooth PDEs
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.335516Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c299e587-8bbb-4e62-9905-6a330070257b · outbound
This paper cites Driscoll, Yuji Nakatsukasa, and Lloyd N.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Driscoll, Yuji Nakatsukasa, and Lloyd N
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.317965Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5049a2dd-3ace-4455-881a-063595afeab4 · outbound
This paper cites Deep neural network approximation theory.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Deep neural network approximation theory
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.302861Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b9aae20a-c380-49a4-ab62-d7c0b604c757 · outbound
This paper cites Approximation spaces of deep neural networks.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Approximation spaces of deep neural networks
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.285796Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 236eb867-5ef0-4441-901e-c788c9dd4962 · outbound
This paper cites Error bounds for ap- proximations with deep ReLU neural networks in W s,p norms.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Error bounds for ap- proximations with deep ReLU neural networks in W s,p norms
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.271330Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f9ac95f8-4dbc-4531-b2f4-d31ab9b22a0f · outbound
This paper cites On uniqueness in structured model learning.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks On uniqueness in structured model learning
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T15:44:54.768315Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 16381b8d-a659-4765-9228-b0388cbfe753 · outbound
This paper cites Semiglobal optimal feedback stabilization of autonomous systems via deep neural network approximation.ESAIM: COCV, 27:16, 2021.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Semiglobal optimal feedback stabilization of autonomous systems via deep neural network approximation.ESAIM: COCV, 27:16, 2021
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.256646Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ece1656e-94f0-4482-b594-6208651777b7 · outbound
This paper cites Extrapolation and learning equa- tions.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Extrapolation and learning equa- tions
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.242371Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 33eb10c5-c2e8-4885-864a-3ac54c6941c8 · outbound
This paper cites an unresolved cited work.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T15:44:55.225203Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 566f0d6a-59a2-49e3-84e5-378f453279fb · outbound
This paper cites an unresolved cited work.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T15:44:55.210587Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2ec41bc2-e369-414a-8eea-7b8692ae1d4e · outbound
This paper cites Trefethen.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Trefethen
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.196818Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c7eb068a-8076-4c77-ad3e-5f7d2fbacb26 · outbound
This paper cites an unresolved cited work.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T15:44:55.181915Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e7864c73-b0e5-4402-8d51-8a10bb1ed7dd · outbound
This paper cites an unresolved cited work.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T15:44:55.166693Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ba6a3deb-663f-4d36-95b1-c27d7f5ec10f · outbound
This paper cites Learning equa- tions for extrapolation and control.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Learning equa- tions for extrapolation and control
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.150224Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 80069f96-3d59-41aa-ba33-fadc98f032e8 · outbound
This paper cites ParFam -- (Neural Guided) Symbolic Regression Based on Continuous Global Optimization.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks ParFam -- (Neural Guided) Symbolic Regression Based on Continuous Global Optimization
Reference 22
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T15:44:54.897444Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c77a376e-819d-472a-ba2a-76831ee30bb7 · outbound
This paper cites Neural networks and rational functions.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Neural networks and rational functions
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.134778Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e2cdfed6-25b2-4293-abd7-dd571b3d0250 · outbound
This paper cites Trefethen and Yuji Nakatsukasa.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Trefethen and Yuji Nakatsukasa
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.116802Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 618dc30f-ee71-4db4-ac17-6a141eb4b051 · outbound
This paper cites Trefethen and Heather D.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Trefethen and Heather D
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.100913Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9e22b93b-9d3e-45b0-be57-e09a8fd95ed8 · outbound
This paper cites Splines, rational functions and neu- ral networks.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Splines, rational functions and neu- ral networks
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:44:55.085610Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b3fdfc3b-f258-4524-b92d-3ba165bf2a9d · outbound
This paper cites Nearly Optimal Approximation Rates for Deep Super ReLU Networks on Sobolev Spaces.
$\mathcal{C}^1$-approximation with rational functions and rational neural networks Nearly Optimal Approximation Rates for Deep Super ReLU Networks on Sobolev Spaces
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T15:44:54.833793Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
Observation f317b882-9c60-4100-9d4e-faa2825b8286 · inbound
Symbolic recovery of PDEs from measurement data cites this paper.
Symbolic recovery of PDEs from measurement data $\mathcal{C}^1$-approximation with rational functions and rational neural networks
Reference 46
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T21:46:41.007718Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.