Ambient Gaussian Landmarks and a Unit-Circle Obstruction to Nyström Approximation
Manuscript 24 October 2026 · Online 24 October 2026
Abstract
Ambient Gaussian Landmarks and a Unit-Circle Obstruction to Nyström Approximation Alper Ferudun, Mercury Software GmbH. English unrefereed preprint, version 1.0, 24 October 2026. For k(x,y)=1+x^T y and m ambient standard Gaussian landmarks in R^n, the manuscript derives an exact chi-square intercept law and a finite-sample lower bound on diagonal Nyström error. When m=o(n), the unit-query error tends to 2, even for data on a compact algebraic unit circle. More generally, if m/n tends to alpha, the approximant converges uniformly on that circle to alpha k. Three suitable on-circle landmarks instead reconstruct the rank-three restricted kernel exactly. This gives a full counterexample to the displayed global-constant tail bound on page 2501 of Oberwolfach Report 44/2014. It is a complete scoped obstruction result, not a claim to have resolved every suitably modified polynomial-kernel guarantee or the report's separate Gaussian-kernel problem. Classical feature-span and rotational-projection ingredients are credited. No absolute novelty or priority certification, formal verification or independent peer review is claimed. Source dataset record: OWR-13346-004 (ulamai/UnsolvedMath v1.6.0). The manuscript discloses OpenAI Codex assistance.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Complete scoped obstruction
- Categories
- math.NA · stat.ML
- Manuscript
- 24 October 2026
- Online release
- 24 October 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “Ambient Gaussian Landmarks and a Unit-Circle Obstruction to Nyström Approximation,” EulerSolve Research Papers, OWR-13346-004, 2026. https://doi.org/10.5281/zenodo.23621500.
BibTeX
@misc{ferudun2026ambientlandmarks,
author = {Ferudun, Alper},
title = {Ambient Gaussian Landmarks and a Unit-Circle Obstruction to Nyström Approximation},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/owr-13346-004/},
doi = {10.5281/zenodo.23621500},
note = {OWR-13346-004; unrefereed preprint}
}